Cognitive approach to modeling. Summary: Cognitive modeling. identify possible scenarios for the development of the situation, taking into account the consequences of making the most important decisions and compare them

In order to understand and analyze the behavior of a complex system, a structural diagram of cause-and-effect relationships is built. Such schemes that interpret the opinion and views of the decision maker are called a cognitive map.

The term "cognitive map" was coined by the psychologist Tolman in 1948. A cognitive map is a type of mathematical model that allows you to formalize the description of a complex object, problem or system functioning and identify the structures of cause-and-effect relationships between the elements of the system, the complex object that make up the problem and assess the consequences as a result of impact on these elements or changes in the nature of relationships. The English scientist K.Idei suggested using cognitive maps for collective development and decision-making.

Cognitive map of the situation is a directed graph, the nodes of which are some objects (concepts), and the arcs are the connections between them, characterizing the cause-and-effect relationships.

The development of the model begins with the construction of a cognitive map that reflects the situation "as is". On the basis of the generated cognitive map, a situation self-development simulation is carried out in order to identify positive development trends. Self-development allows you to compare subjective expectations with model ones.

The main concept in this approach is the concept of "situation". The situation is characterized by a set of so-called basic factors, with the help of which the processes of changing states in a situation are described. Factors can influence each other, and such an influence can be positive, when an increase (decrease) in one factor leads to an increase (decrease) in another factor, and negative, when an increase (decrease) in one factor leads to a decrease (increase) in another factor.

The matrix of mutual influences presents the weights of only direct influences between factors. Rows and columns of the matrix are mapped to the factors of the cognitive map, and the signed value at the intersection of the i-th row and the j-ro column indicates the weight and direction of the influence of the i-ro factor on the j-th factor. To display the degree (weight) of influence, a set of linguistic variables such as "strong", "moderate", "weak", etc. is used; such a set of linguistic variables are compared with numerical values from the interval: 0.1 - "very weak"; 0.3 - "moderate"; 0.5 - "significant"; 0.7 - "strong"; 1.0 - "very strong". The direction of influence is given by a sign: positive, when an increase (decrease) in one factor leads to an increase (decrease) in another factor, and negative, when an increase (decrease) in one factor leads to a decrease (increase) in another factor.

Identification of Initial Trends

Initial tendencies are given by linguistic variables of the type

"strongly", "moderately", "weakly", etc.; such a set of linguistic variables are compared with numerical values from the interval . If a trend is not set for some factor, this means that either there are no noticeable changes in the factor under consideration, or there is not enough information to evaluate the existing trend on it. When modeling, it is considered that the value of this factor is 0 (i.e., it does not change).

Selection of target factors

Among all the selected factors, it is necessary to determine the target and control factors. Target factors are factors whose dynamics must be brought closer to the required values. Ensuring the required dynamics of target factors is the solution that is pursued when building a cognitive model.

Cognitive maps can be used to qualitatively assess the influence of individual concepts on each other and on the stability of the system as a whole, to model and evaluate the use of various strategies in decision-making and forecast decisions.

It should be noted that the cognitive map reflects only the fact that the factors influence each other. It does not reflect either the detailed nature of these influences, nor the dynamics of changes in influences depending on changes in the situation, nor temporary changes in the factors themselves. Taking into account all these circumstances requires a transition to the next level of structuring information displayed in a cognitive map, that is, a cognitive model. At this level, each relationship between the factors of the cognitive map is revealed to the corresponding equation, which can contain both quantitative (measured) variables and qualitative (not measured) variables. At the same time, quantitative variables enter in a natural way in the form of their numerical values, since each qualitative variable is associated with a set of linguistic variables, and each linguistic variable corresponds to a certain numerical equivalent in the scale [-1,1]. With the accumulation of knowledge about the processes occurring in the situation under study, it becomes possible to reveal in more detail the nature of the relationships between factors.

There are mathematical interpretations of cognitive maps, such as soft mathematical models (the famous Lotka-Volterra model of the struggle for existence). Mathematical methods can predict the development of the situation and analyze the stability of the solution obtained. There are two approaches to the construction of cognitive maps - procedural and process. A procedure is an action that is discrete in time and has a measurable result. Mathematics made significant use of discreteness, even if we measured by linguistic variables. The process approach speaks more about maintaining processes, it is characterized by the concepts of “improve”, “activate”, without reference to measurable results. The cognitive map of this approach has an almost trivial structure - there is a target process and surrounding processes that have a positive or negative impact on it.

There are two types of cognitive maps: traditional and fuzzy. Traditional maps are set in the form of a directed graph and represent the modeled system as a set of concepts that display its objects or attributes, interconnected by cause-and-effect relationships. They are used to qualitatively assess the impact of individual concepts on the stability of the system.

In order to expand the possibilities of cognitive modeling, fuzzy cognitive maps are used in a number of works. In a fuzzy cognitive map, each arc determines not only the direction and nature, but also the degree of influence of the associated concepts.

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Ministry of Education and Science of the Russian Federation

Federal State Budgetary Educational Institution

higher professional education

"Kuban State University" (FGBOU VPO "Kubu")

Department of Function Theory

Bachelor's final qualifying work

Mathematical model of the cognitive structure of the learning space

I've done the work

V.A. Bakuridze

supervisor

cand. Phys.-Math. Sciences, Associate Professor

B.E. Levitsky

normocontroller,

Art. laboratory assistant N.S. katchina

Krasnodar 2015

Content

Introduction

2. Skills
4. Minimum skill card
7. Markings and filters
7.1 Marking examples
Conclusion
Introduction
The work is abstract in nature and is devoted to the study of one of the sections of the monograph Zh-Kl. Falmazh and Zh-P. Duanon (see), whose name is translated into Russian as "Learning Spaces". The monograph is devoted to the construction of an abstract mathematical theory that develops formal methods for studying the interrelations and relations of the states of knowledge of subjects in a certain subject area.
The paper provides an adapted translation into Russian of a part of one of the chapters of the monograph, which is called "Skill Maps, Labels and Filters". This chapter develops a formal apparatus for investigating the relationship between states of knowledge and what are commonly called "skills." It is assumed that a certain amount of skill is needed to achieve a certain state of knowledge.
The idea of the authors is to associate with each question (problem) q from domain Q a subset of skills from S that can be used to answer question q (solution of problem q). Along with explanatory examples given by the authors in the paper, similar examples from the course "Complex Analysis" are given.
The first section of the diploma work contains the necessary information from the first chapters of the monograph, the adapted translation of which was made in the theses of T.V. Aleinikova and N.A. Ralco.
In the second section, an adapted translation of the corresponding section of the monograph with an example (see paragraph 2.1) is made, on the basis of which a formalized concept of "skill maps" is introduced in the third section. By analogy with this example, an example from the course "Complex Analysis" was independently constructed (see section 2.2.).
The fourth section deals with the concept of a minimum skill map. The conjunctive skill map model is discussed in Section 5.
Section 6 provides a formalized definition of the competency model. The last section of the thesis is devoted to the problem of describing (labeling) elements and integrating (filters) the corresponding reference information contained in the knowledge states.
1. Basic notation and preliminary information
Definition 1 (see). A knowledge structure is a pair (Q, K), in which Q is a non-empty set, and a K-family of subsets of Q, containing at least Q and an empty set. The set Q is called the knowledge structure domain. Its elements are called questions or positions, and subsets of the family. K are called states of knowledge.
Definition 2 (see). A knowledge structure (Q, K) is called a learning space if the following two conditions are met:
(L1) Smoothness of learning. For any two states K, L such that
, there is a finite chain of states
(2.2)
for which |Ki\ Ki-1| = 1 for 1 ? i? p and |L \ K| = r.
(L2) Learning consistency. If K, L are two states of knowledge such that and q is a question (position) such that K + (q)K, then
Definition 3 (see). A family of sets K is called closed with respect to union if FK for any FK. In particular, K, because the union of empty subfamilies is the empty set. If the family K of the knowledge structure (Q, K) is closed under union, then the pair (Q, K) is called the knowledge space. Sometimes in this case they say that K is the space of knowledge. We say that K is closed with respect to a finite union if for any K and L from K the set KLK.
Note that in this case the empty set does not necessarily belong to the family K.
The dual knowledge structure on Q with respect to the knowledge structure K is the knowledge structure containing all the additions of the states of K, that is,
Thus, Ki have the same domain. It is obvious that if K is a knowledge space, then is a knowledge structure closed with respect to intersection, that is, F for any F, moreover, Q.
Definition 4 (see ). By a collection on a set Q we mean a family of K subsets of the domain Q. To denote a collection, one often writes (Q, K). Note that the collection may be empty. A collection (Q, L) is a closed space when the family L contains Q and is closed under an intersection. This closed space is called simple if it belongs to L. Thus, the collection K of subsets of the domain Q is a knowledge space on Q if and only if the dual structure is a simple closed space.
Definition 5 (see ). A chain in a partially ordered set (X, P) is any subset C of the set X such that cPc? or c?Pc for all c, c"C (in other words, the order induced by the relation P on C is a linear order).
Definition 6 (see ). The learning trajectory in the knowledge structure (Q,K) (finite or infinite) is the maximum chain C in the partially ordered set (K,). According to the definition of a chain, we have cc "or c" c for all c, c "C. A chain C is maximal if it follows from the condition CC` for some chain of states C` that C \u003d C`. Thus, the maximum chain necessarily contains and Q.
Definition 7 (see ). The scope of a family of sets G is a family G? that contains any set that is the union of some subfamily of G. In this case, we write (G)=G? and say that G is covered by G?. By definition, (G) is closed under union. The base of a union-closed family F is the minimal subfamily B of F enclosing F (here "minimal" is defined with respect to the inclusion of sets: if (H)=F for some HB, then H=B). It is customary to assume that the empty set is the union of empty subfamilies from B. Thus, since the base is the minimum subfamily, the empty set cannot belong to the base. Obviously, a state K belonging to some base B from K cannot be a union of other elements from B. In addition, a knowledge structure has a base only if it is a knowledge space.
Theorem 1 (). Let B be the base for the knowledge space (Q, K). Then BF for some subfamily of states F covering K. Therefore, the knowledge space admits at most one base.
Definition 8 (see). The symmetric-difference distance or canonical distance on the set of all subsets of the set of a finite set E is the value:
defined for any A, B 2E. Here, denotes the symmetric difference of sets A and B.
2. Skills

Cognitive interpretations of the above mathematical concepts are limited to the use of words associated with the learning process, such as "knowledge structure", "knowledge state", or "learning path". This is due to the fact that many of the results obtained in are potentially applicable to a wide variety of scientific fields. It can be seen that the introduced fundamental concepts are consistent with such a traditional concept of psychometric theory as "skills". This chapter explores some of the possible relationships between knowledge states, skills, and other item features.

For any knowledge structure (Q, K), the existence of some basic set of "skills" S is assumed. These skills may consist of methods, algorithms or techniques that are in principle identifiable. The idea is to associate with each question (problem) q from domain Q skills from S that are useful or helpful in answering that question (solving the problem) and inferring what the state of knowledge is. The following example is provided.

Example 2.1 of compiling a program in the UNIX language.

Question a): How many lines of the file "lilac" (lilac) contains the word "purple" (purple)? (Only one command line is allowed.)

The object being checked corresponds to the UNIX command line being entered. This question can be answered in a variety of ways, three of which are listed below. For each method, we provide a printable command line following the ">" sign:

>greppurplelilac | wc

The system responds with three numbers; the first is the answer to the question. (The "grep" command followed by the two options `purple" and `lilac" extracts all lines containing the word `purple" from the file `lilac"; the "|" (separator) command directs this output to the word count command "wc ", which outputs the number of lines, words, and characters in this output).

>catlilac | greppurple | wc

This is a less efficient solution that achieves the same result. (The "cat" command requires the file "lilac" to be listed, which is not necessary.)

>morelilac | greppurple | wc;

Similar to the previous solution.

The study of these three methods suggests several possible types of relationships between skills and questions and the corresponding ways to determine the knowledge states corresponding to these skills. The simple idea is to treat each of these three methods as a skill. A complete skill set S would contain these three skills and some others. The connection between questions and skills, thus, could be formalized by the function

f (a) = ((1); (2); (3)).

Consider an object that includes a certain subset T of skills, containing some skills from f(a) plus some other skills related to other questions; For example,

T = ((1); (2); s; s").

This set of skills provides a solution to problem a), since T?f(a) = (1; 2) ? . In fact, the state of knowledge K corresponding to this set includes all those tasks that can be solved using at least one of the skills contained in T; i.e

This relationship between skills and states is explored in the next section, entitled "disjunctive model". We will see that the knowledge structure induced by the disjunctive model is necessarily a knowledge space. This fact is proved in Theorem 3.3. We also briefly, for the sake of completeness, consider a model that we will call "conjunctive" and which is the dual of the disjunctive model. In the disjunctive model, only one of the skills associated with task q is sufficient to solve this task. In the case of the conjunctive model, all skills corresponding to this element are required. Thus, K is a state of knowledge if there is a set T of skills such that for each element q, we have q K only if φ(q) (in contrast to the requirement φ(q)T? for the disjunctive model). The conjunctive model formalizes the situation in which, for any question q, there is a unique solution method represented by a set f(q) that includes all the required skills. The resulting knowledge structure is closed with respect to the intersection. Various types of relationships between skills and states will also be considered. The disjunctive and conjunctive models were derived from the elemental analysis of Example 2.1, which treated the three methods themselves as skills, even though multiple commands were required in each case.

A more thorough analysis could be obtained by considering each command as a skill, including the command "|" ("delimiter"). The complete skill set S would look like

S = (grep; wc; cat, |, more, s1, …,sk),

where, as before, s1, ..., sk correspond to skills related to other issues in the considered domain. To answer question a), a suitable subset of S can be used. For example, an object corresponding to a subset of skills

R = (grep; wc; |; more; s1; s2)

could be a solution to question a) using either Method 1 or Method 3. In fact, two relevant sets of commands are included in the R skill set; namely, (grep; wc; |) ?R and (more, grep, wc,|) ?R.

This example suggests a more complex relationship between questions and skills.

We postulate the existence of a function relating each question q to the set of all subsets of the skill set corresponding to possible solutions. In the case of question a), we have

m(a) = ((grep; |; wc); (cat; grep; |; wc); (more; grep; |; wcg)).

In general, an object that includes some set of skills R is capable of solving some question q if there is at least one element C in m(q) such that C R. Each of the subsets of C in m(q) will be referred to as "competence for" q. This particular relationship between skills and states will be referred to under the name "competency model".

Example 2.1 might lead one to think that the skills associated with a certain domain (a certain fragment of a knowledge area) can be easily identified. In fact, it is far from obvious how such an identification is possible at all. For most of this chapter, we will leave the skill set unspecified and treat S as an abstract set. Our focus will be on a formal analysis of some of the possible links between issues, skills, and knowledge states. Cognitive or educational interpretations of these skills will be deferred to the last section of this chapter, where we discuss a possible systematic labeling of the elements that could lead to the identification of skills, and more broadly to the description of the content of the knowledge states themselves.

Example 2.2 from the theory of functions of a complex variable.

Consider the problem of calculating the integral:

There are three ways to solve the problem.

First way (solution using Cauchy residue theorem):

Algorithm for calculating contour integrals using residues:

1. Find singular points of a function

2. Determine which of these points are located in the area bounded by the contour. To do this, it is enough to make a drawing: draw a contour and mark special points.

3. Calculate the residues at those special points that are located in the area

All singular points of the integrand are located in the circle

We find the roots of the equation:

Multiplicity pole 2.

The roots of the equation are found by the formula:

Therefore, by the Cauchy residue theorem:

Used skills:

1) Finding singular points (A)

2) Ability to extract the root of a complex number (B)

3) Calculation of deductions (C)

4) Ability to apply the Cauchy residue theorem (D)

The second way (solution using the Cauchy integral formula for derivatives):

Algorithm for calculating contour integrals using the Cauchy integral formula for derivatives:

N = 0,1,2,….

1. Find singular points of the function.

2. Determine which of these points are located in the area bounded by the contour: . To do this, it is enough to make a drawing: draw a contour and mark special points (see Fig. 1).

3. Calculate the following integrals using the Cauchy integral formula for derivatives:

where, r > 0 is small enough, zk (k = 1,2,3,4) are singular points of the integrand located inside the circle:

, (see figure 1).

Figure 1 - Calculation of the integral using the Cauchy integral formula

1) Assuming, we find:

2) Assuming, we find:

3) Assuming, we find:

4) Assuming, we find:

Used skills:

1) finding singular points (A)

2) the ability to extract the root of a complex number (B)

3) the ability to apply the Cauchy integral formula (E)

4) the ability to apply the Cauchy integral formula for prod. (F)

Third way:

By the total residue theorem:

Used skills:

1) Ability to find special points (G)

2) Investigation of a function at infinity (H)

3) Finding the residue at an infinitely distant point (I)

4) Ability to apply the total residue theorem (J)

Analyzing the three solutions of the integral above, we note that the most efficient solution is the last one, since we do not need to calculate residues at the end points.

3. Skill maps: disjunctive model

Definition 3.1 A skills map is a triple (Q;S;), where Q is a non-empty set of elements, S is a non-empty set of skills, and φ is a mapping from Q to 2S \ (). If the sets Q and S are clear from the context, a skill map is called a function f. For any q from Q, a subset of φ(q) from S will be considered as a set of skills mapped to q (skill map). Let (Q; S; φ) be a skill map and T be a subset of S. K Q is said to represent the state of knowledge formed by the set T within the disjunctive model if

K = (q Q | f (q) T ?).

Note that the empty subset of skills forms an empty knowledge state (since φ(q)? for each element q), and the set S forms the knowledge state Q. The family of all knowledge states formed under the sets S is the knowledge structure formed by the skills map (Q ;S;φ) (disjunctive model). When the term "formed" by a skill map is used without reference to a specific model, it is understood that a disjunctive model is being considered. In the case when all ambiguities are eliminated by the content of the context, the family of all states formed by subsets of S is called the formed knowledge structure.

Example 3.2 Let Q = (a, b, c, d, e) and S = (s, t, u, v). Let's define

Assuming

Thus (Q;S;f) is a skill card. The state of knowledge formed by the set of skills T = (s, t) is (а, b, c, d). On the other hand, (a, b, c) is not a state of knowledge, since it cannot be formed by any subset R of S. Indeed, such a subset R would necessarily contain t (because it must contain the answer to the question); thus the knowledge state formed by R would also contain d. The formed knowledge structure is the set

Note that K is the space of knowledge. This is not a coincidence, since the following result takes place:

Theorem 3.3. Any knowledge structure formed by a skills map (within the disjunctive model) is a knowledge space. Conversely, any knowledge space is formed by at least one skill map.

Proof

Suppose (Q; S; T) is a skill map, and let (Ki) i? I is some arbitrary subset of the formed states. If, for someone i?I, the state Ki is formed by a subset Ti of S, then it is easy to check what is formed; that is, it is also a state of knowledge. Thus, the knowledge structure formed by the skills map is always a knowledge space. Conversely, let(Q; K) be a knowledge space. We will construct a skill map by choosing S = K and setting φ(q) = Kq for any q ? Q. (The states of knowledge containing q are thus determined by the skills corresponding to q; note that φ(q) ? ? follows from the fact that q ? Q ?K). For TS = K, check that the state K formed by T belongs to K. Indeed, we have

whence it follows that K? K, since K is the space of knowledge. Finally, we will show that any state K of K is formed by some subset of S, namely, the subset (K). Denoting by L the state formed by the subset (K), we obtain

Whence it follows that the space K is formed by (Q; K; φ).

4. Minimum skill card

In the last proof, we built a special skills map for an arbitrary knowledge space that forms this space. It is tempting to regard such a representation as a possible explanation for the organization of a set of states, in terms of the skills used to master the elements of those states. In science, explanations of phenomena are usually not unique, and there is a tendency to favor the "economical". The material in this section is inspired by the same considerations.

We will start by examining a situation in which two distinct skills differ only by a simple relabeling of the skills. In such a case, we will speak of "isomorphic skill maps, and will sometimes speak of such skill maps that they are essentially the same" with respect to any q element. This notion of isomorphism is given in the following definition.

Definition 4.1. Two skill maps (Q; S;) and (Q; ;) (with the same set of Q elements) are isomorphic if there exists a one-to-one mapping f of the set S onto which, for an arbitrary, satisfies the condition:

The function f is called an isomorphism between (Q; S;) and (Q; ;).

Definition 4.1. Determines the isomorphism of skill cards with the same set of elements. A more general situation is considered in Problem 2.

Example 4.2 Let Q = (a; b; c; d) and = (1; 2; 3; 4). Let's define a skill map.

The skill map (Q; ;) is isomorphic to the map shown in Example 3.2: the isomorphism is given by:

The next result is obvious.

Theorem 4.3. Two isomorphic skill maps (Q; S;) and (Q; ;) form the same knowledge spaces on Q.

Remark 4.4. Two skill cards can form the same knowledge spaces without being isomorphic. As an illustration, note that by removing skill v from the set S in Example 2.2 and redefining φ by setting φ(b) = (c; u), we arrive at the same formed space K. The skill v is thus of paramount importance for the formation Figure K. As mentioned in the introduction to this section, it is common in science to seek parsimonious explanations for phenomena in the course of research. In our context, this is represented by a preference for small, perhaps minimal, skill sets. More precisely, we will call a skill map "minimum" if the removal of any skill changes the formed knowledge state. If this knowledge space is finite, the minimum skill map always exists and contains the smallest possible number of skills. (This statement follows from Theorem 4.3.) In the case where the knowledge space is not finite, the situation is somewhat more complicated, because a minimal skill map does not necessarily exist. However, a skill map that forms the knowledge space and has a minimum cardinal number always exists, since the class of all cardinal numbers is well ordered. It should be noted that such a skill map with a minimum number of skills is not necessarily uniquely defined, even up to isomorphism.

Example 4.5. Consider a family O of all open subsets of the set R of real numbers and let J be an arbitrary family of open intervals from enclosing O. For, we set. Then the skill map (R; J;), forms the space (R; O). Indeed, a subset T of J forms a state of knowledge, and, in addition, an open subset O is formed by a family of those intervals from J that are contained in O (It is known that there are countable families J that satisfy the above conditions. Note that such countable families generate charts skills with a minimum number of skills, that is, with a set of skills of minimum power (minimum cardinal number. However, there is no minimum skill map. This can be proven directly or derived from Theorem 4.8. As for uniqueness, the minimum skill maps that form given knowledge space are isomorphic.This will be shown in Theorem 4.8.This theorem also characterizes knowledge spaces that have a base (in the sense of Definition 5).Such knowledge spaces are exactly the same as the knowledge spaces that can be formed by any minimal map skills.

Definition 4.6 The skill map (Q"; S"; f") continues (strictly continues) the skill map (Q; S; f) if the following conditions are met:

A skill map (Q; S"; f") is minimal if there is no skill map forming the same space that strictly continues (Q; S"; f").

Example 4.7. Removing skill v from the skill map in Example 3.2 gives:

It can be verified that (Q; S; f) is the minimum skill card.

Theorem 4.8. A knowledge space is formed by some minimal skill map if and only if this space has a base. In this case, the power (cardinal number) of the base is equal to the power of the set of skills. In addition, any two minimal skill maps that form the same knowledge space are isomorphic. And also any skill map (Q; S; f), forming a space (Q; K), which has a base, is a continuation of the minimum skill map that forms the same space.

Proof

Consider an arbitrary (not necessarily minimal) skill map (Q; S; f), and denote (Q; K) the skill space formed by this map. For any sS, denote by K(s) the state of knowledge from K formed by(s). We thus obtain

qK (s)s φ (q).(1)

Let's take any state K K and consider the subset of skills T that forms this state. By virtue of (1) for any element q, we have:

Whence it follows that. Therefore, covers K. Assuming that the skill map (Q, S, φ) is minimal, then the enclosing family A must be the base. Indeed, if A is not a base, then some K(s)A can be represented as the union of other elements of A. Removing s from S would result in a skill map strictly continuing with the skill map (Q, S, φ) and still forming ( Q, K), which contradicts the minimality conjecture (Q, S, φ). We conclude that any knowledge space formed by a minimal skill map has a base. In addition, the power (cardinal number) of the base is equal to the power of the set of skills. (When (Q, S, φ) is minimal, we have |A| = |S|).

Suppose now that the space (Q,K) has a base B. It follows from Theorem 3.3 that (Q,K) has at least one skill map, for example, (Q,S,φ). According to Theorem 1 () the base B. for (Q,K) must be contained in any enclosing subset of K. We thus have BA= where again K(s) is formed by (s). Assuming B:K(s) = B) and, we conclude that (Q,) is the minimum skill map.

Note that the minimal skills map (Q, S, φ) for the knowledge space with base B is isomorphic to the minimal skills map (Q, B,), where (q)=Bq. Isomorphism is defined by the correspondence sK (s)B, where K (s) is the state of knowledge formed by s. The two minimum skill cards are thus always isomorphic to each other.

Finally, let (Q, S, φ) be an arbitrary skill map forming a knowledge space K with base B. Defining K(s), S" and φ" as before, we obtain a minimal skill map extendable by (Q, S, f).

5. Skill Maps: Conjunctive Model

In the conjunctive model, knowledge structures that are formed by skill maps are simple enclosed spaces in the sense of Definition 3 (see Theorem 5.3 below). Since these knowledge structures are dual to the knowledge spaces formed within the framework of the disjunctive model, there is no need for deeper detail.

Definition 5.1. Let (Q,S,) be a skills map and let T be a subset of S. The state of knowledge K, formed by T within the framework of the conjunctive model, is determined by the rule:

The resulting family of all such knowledge states forms a knowledge structure formed within the framework of the conjunctive model by the skill map (Q,S,).

Example 5.2. Let, as in Example 3.2, Q = (a, b, c, d, e) and S = (s, t, u, v), where is defined by the relations:

Then T =(t, u, v) forms the state of knowledge (a, c, d, e), within the framework of the conjunctive model. On the other hand, (a, b, c) is not a state of knowledge. Indeed, if (a, b, c) were a state of knowledge formed by some subset T of S, then T would also include; thus d and e would also belong to the formed state of knowledge. The knowledge structure formed by this skill map is

Note that L is a simple closed space (see Definition 4). The dual knowledge structure coincides with the knowledge space K formed by the same skill map within the framework of the disjunctive model; this space K was obtained in Example 3.2.

Theorem 5.3. The knowledge structures formed within the framework of the disjunctive and conjunctive models by the same skill map are dual to each other. As a consequence, the knowledge structures formed within the framework of the conjunctive model are simple closed spaces.

Remark 5.4. In the final case, Theorems 3.3 and 5.3 are a simple paraphrase of a well-known result about "Galois lattices" of relations. We can reformulate skill maps (Q, S, T), with finite Q and S, as a relation R between sets Q and S: for q Q and sS, we define

Then the state of knowledge formed by a subset T of S within the conjunctive model is a set:

Such sets K can be considered as elements of the "Galois lattice" with respect to R.

It is well known that any finite family of finite sets, closed with respect to intersection, can be obtained as elements of the "Galois lattice" in some relation. Theorems 3.3 and 5.3 generalize this result to the case of infinite sets. Of course, there is a direct analog of Theorem 4.8 for families of sets that are closed under intersection.

6. Multi-skill maps: competency model

The last two sections dealt with the formation of knowledge structures that are closed with respect to union or intersection. However, the general case was not discussed.

The formation of an arbitrary structure of knowledge is possible with the help of a generalization of the concept of a skill map. Intuitively, this generalization is quite natural. With each q question, we associate a collection (q) of skill subsets. Any subset of skills C in (q) can be considered as a method, called "competence" in the following definition, to solve question q. Thus, the presence of only one of these competencies is sufficient to solve question q.

Definition 6.1. A skill multimap is a triple (Q, S,), where Q is a non-empty set of elements (questions), S is a non-empty set of skills, and is a mapping that connects with each element q a non-empty family (q) of non-empty subsets of S. Thus, - mapping of the set Q into a set. Any set belonging to (q) is called a competence for the element q. A subset K of Q is called a generated subset of skills T if K contains all elements that have at least one competency from T; formally:

Assuming T = and T = S, we see what is formed by an empty set of skills, and Q is formed by S. The set K of all subsets of Q formed in this way forms a knowledge structure. In this case, the knowledge structure (Q, K) is said to be formed by a multimap of skills (Q, S,). This model is called the competency model.

Example 6.2. Let Q = (a, b, c, d) and S = (c, t, u). Let's define the mapping by listing competencies for each element from Q:

Applying definition 6.1, we see that this multi-skill map forms a knowledge structure:

Note that the knowledge structure K is not closed either with respect to the union or with respect to the intersection.

Theorem 6.3. Each knowledge structure is formed by at least one multi-skill map.

Proof

Let (Q,K) be the knowledge structure. We define the skills multimap by setting S = K and KKq) for.

Thus, each state of knowledge M, containing the question q, corresponds to competence K for q. Note that K is not empty because it contains, as an element, an empty subset of Q. To show that (Q, S,), forms a knowledge structure K, we apply Definition 6.1.

For any K, consider a subset K of K and calculate the state L that forms it:

Thus, each state in K is formed by some subset of S. On the other hand, if S = K, the state L formed is determined by the rule:

mathematical knowledge skill map

which implies that L belongs to K. Thus, K is indeed formed by the skill multimap(Q, S,).

We will not continue the study of the multi-skill map. As in the case of a simple skill map, one can investigate the existence and uniqueness of a minimum multi-skill map for a given knowledge structure. Other options for the formation of knowledge structures are possible. For example, one can define a state of knowledge as a subset K of Q, consisting of all elements q for which competencies belong to a certain subset of S (depending on K).

7. Markings and filters

For any subject in a natural area of knowledge, such as arithmetic or grammar, there are usually rich opportunities to describe the relevant skills and the associated knowledge structure. These possibilities could be used to describe the student's state of knowledge to a parent or teacher.

Indeed, the complete list of elements contained in a student's state of knowledge may have hundreds of elements and may be difficult to digest even for an expert. A list of significant information reflected in questions that form the student's state of knowledge can be compiled. This list can be about much more than the skills a student has or lacks, and can include features such as predicting success on an upcoming test, suggesting directions for research, or troubleshooting.

This section outlines a program for describing (tagging) elements (questions) and integrating (filtering) the relevant reference information contained in knowledge states.

The examples given are taken from the ALEKS distance learning system (see http://www.ales.com).

7.1 Marking examples

Assume that a large pool of questions is selected that covers all the basic concepts of a high school mathematics curriculum in a certain country.

Detailed information regarding each of these questions can be collected using the following labels:

1. A descriptive question name.

2. The class in which the question is being studied.

3. Topic (section of a standard book) to which the question relates.

4. The chapter (of a standard book) where the question is presented.

5. Subsection of the program to which the question belongs.

6. Concepts and skills needed to answer the question.

7. Type of question (text problem, calculation, justification, etc.).

8. Type of answer required (word, sentence, formula).

Needless to say, the above list is for illustrative purposes only. The actual list could be much longer, and expanded as a result of collaboration with experts in the field (in this case, experienced teachers). Two examples of questions with their associated labels are shown in Table 1.

Each of the questions in the pool would be labeled in the same way. The task is to develop a set of computer routines that allow analyzing the state of knowledge in terms of markings. In other words, suppose that a certain state of knowledge K has been diagnosed by some knowledge assessment program. Question labels indicate that the state of knowledge will be determined by a set of "filters" that translate a set of statements into plain language in terms of educational concepts.

7.2 Reflecting the level of knowledge through evaluation

Suppose that at the beginning of the school year, a teacher wants to know which class (Math, for example) is best for a student who has just arrived from a foreign country. The knowledge assessment program used determined that the student's knowledge state is K. A suitable set of filters can be designed as follows. As before, we denote by Q the area of knowledge (domain). For each class n (1n12 in the US), the filter computes a subset Gn of Q containing all questions studied at or before that level (marked 2. in the list above). If the educational system is reasonable, there must be

Table 1 - Two sample questions and their associated list of markings.

List of markings
(1) Measure of the missing angle in a triangle (3) Sum of angles of a flat triangle (4) Triangle geometry (5) Elementary Euclidean geometry (6) Angle measure, triangle sum of angles, addition, division, subtraction (7) Calculation (8) Numeric notation	In triangle ABC, angle A is X degrees and angle B is Y degrees. How many degrees is angle C?
(1) Addition and subtraction of double numbers with carry (3) Addition and subtraction (4) Decimals (5) Arithmetic (6) Addition, subtraction, decimals, carry, currency (7) Text problem and calculation (8) Numeric notation	Mary bought two books worth X dollars and Y dollars. She gave the Clerk Z dollars. How much change will she get?

We can find

for some n, which implies that the student can be assigned to class n-1.

However, this is not the best solution if very few. More information needed. In addition, we must provide for situations in which there is no such n. Next, the filter calculates the standard distance for each class n and fixes the set

Thus, S(K) contains all classes that minimize the distance to K. Suppose that S(K) contains a single element nj, and GnjK. It is reasonable then to recommend that the student accept no + 1 into the class, but S(K) may contain more than one element. We still need more information. In particular, the content of K, with its advantages and disadvantages relative to its proximity to Gnj, should ultimately be useful. Without going into the technical details of such a conclusion, we outline, in general terms, an example of a report that the system could make in such a situation:

Student X is closest to 5th grade. However, X would be an unusual student in this class. Knowledge of elementary geometry significantly exceeds the knowledge of a 5th grade student. For example, X knows about the Pythagorean Theorem and is capable of using it. On the other hand, X has surprisingly poor knowledge of arithmetic.

Descriptions of this type require the development of different sets of new filters, in addition to those used to calculate S(K). In addition, the system must be able to convert through a natural language generator and output filters into grammatically correct statements in ordinary language. We will not discuss this here. The purpose of this section was to illustrate how labeling elements, by greatly expanding the concept of skills, can lead to improved descriptions of knowledge states that can be useful in a variety of situations.

Conclusion

The paper gives an adapted translation into Russian of a part of one of the chapters of the monograph Zh-Kl. Falmazh and Zh-P. Duanon, which is called "Skill Cards, Tags and Filters".

The necessary information is given from the first chapters of the monograph, the translation of which was carried out in theses and . Along with explanatory examples given by the authors in the monograph, similar examples from the course "Complex Analysis" are given.

List of sources used

1. J.-Cl. Falmagneand, J.P. Doignon. Learning Space Berlin Heidelberg. 2011, 417 p.

2. N.A. Ralco. Mathematical models of knowledge spaces. Degree work, KubSU, 2013, 47 p.

3. T.V. Aleinikov. Ontological engineering in knowledge management systems. Thesis, Kubu, 2013, 66 p.

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The theory of organizational knowledge creation by I. Nonaki and H. Takeuchi.

Individual and organizational learning.

Cognitive analysis and modeling in strategic management

The essence of the concept of cognition. organization cognition.

TOPIC 5. COGNITIVITY AS A PREREQUISITE FOR THE STRATEGIC DEVELOPMENT OF THE ENTERPRISE.

5.1. The essence of the concept of "cognitiveness". organization cognition.

cognitive science- interdisciplinary (philosophy, neuropsychology, psychology, linguistics, computer science, mathematics, physics, etc.) scientific direction that studies the methods and models of the formation of knowledge, cognition, universal structural schemes of thinking.

Cognitiveness (from Latin cognitio - knowledge, study, awareness) within the framework of management science means the ability of managers to mentally perceive and process external information. The study of this concept is based on the mental processes of the individual and the so-called "mental states" (confidence, desire, belief, intentions) in terms of information processing. This term is also used in the context of the study of the so-called "contextual knowledge" (abstractization and concretization), as well as in areas where concepts such as knowledge, skills or learning are considered.

The term "cognitivity" is also used in a broader sense, meaning the "act" of cognition or self-knowledge itself. In this context, it can be interpreted as the emergence and "becoming" of knowledge and the concepts associated with this knowledge, reflected both in thoughts and in actions.

Organization Cognitiveness characterizes the totality of the cognitive abilities of individuals in the company and the effects that arise from the combination of individual cognitive abilities. The application of this concept in relation to a company (organization, firm, enterprise) means the intention to consider it in a plane that is characterized by a specific apparatus of analysis and a special angle of view on the interaction of the enterprise or its components with the external environment.

Term organization cognition allows you to assess the company's ability to assimilate information and turn it into knowledge.

One of the most productive solutions to problems that arise in the field of management and organization is the application of cognitive analysis.

The methodology of cognitive modeling, designed for analysis and decision making in ill-defined situations, was proposed by the American researcher R. Axelrod.

Cognitive analysis is sometimes referred to by researchers as "cognitive structuring". Cognitive analysis is considered as one of the most powerful tools for studying an unstable and semi-structured environment. It contributes to a better understanding of the problems existing in the environment, the identification of contradictions and a qualitative analysis of ongoing processes.

The essence of cognitive (cognitive) modeling - the key moment of cognitive analysis - is to reflect the most complex problems and trends in the development of the system in a simplified form in the model, to explore possible scenarios for the emergence of crisis situations, to find ways and conditions for their resolution in a model situation. The use of cognitive models qualitatively increases the validity of managerial decision-making in a complex and rapidly changing environment, saves the expert from "intuitive wandering", saves time for understanding and interpreting events occurring in the system. The use of cognitive technologies in the economic sphere makes it possible to develop and justify the strategy for the economic development of an enterprise in a short time, taking into account the impact of changes in the external environment.

Cognitive modeling- this is a method of analysis that determines the strength and direction of the influence of factors on the transfer of the control object to the target state, taking into account the similarities and differences in the influence of various factors on the control object.

Cognitive analysis consists of several stages, each of which implements a specific task. Consistent solution of these problems leads to the achievement of the main goal of cognitive analysis.

We can single out the following stages, which are typical for the cognitive analysis of any situation:

1. Formulation of the purpose and objectives of the study.

2. The study of a complex situation from the standpoint of the goal: collection, systematization, analysis of existing statistical and qualitative information regarding the control object and its external environment, determination of the requirements, conditions and restrictions inherent in the situation under study.

3. Identification of the main factors influencing the development of the situation.

4. Determining the relationship between factors by considering cause-and-effect chains (building a cognitive map in the form of a directed graph).

5. Studying the strength of mutual influence of different factors. To do this, both mathematical models are used that describe some precisely identified quantitative relationships between factors, as well as the subjective views of an expert regarding non-formalizable qualitative relationships between factors.

As a result of passing stages 3-5, a cognitive model of the situation (system) is built, which is displayed in the form of a functional graph. Therefore, we can say that stages 3 - 5 are cognitive modeling.

6. Verification of the adequacy of the cognitive model of the real situation (verification of the cognitive model).

7. Using a cognitive model to determine possible options for the development of a situation (system), to find ways, mechanisms to influence the situation in order to achieve the desired results, prevent undesirable consequences, that is, develop a management strategy. Setting the target, desired directions and the strength of the change in the trends of the processes in the situation. Selection of a set of measures (a set of control factors), determination of their possible and desired strength and direction of impact on the situation (concrete-practical application of the cognitive model).

Classic cognitive map is a directed graph in which the privileged vertex is some future (usually target) state of the control object, the remaining vertices correspond to factors, the arcs connecting the factors with the state vertex have a thickness and sign corresponding to the strength and direction of influence of this factor on the transition of the control object into a given state, and the arcs connecting the factors show the similarity and difference in the influence of these factors on the control object.

A cognitive map consists of factors (elements of the system) and links between them.

In order to understand and analyze the behavior of a complex system, a block diagram of cause-and-effect relationships of system elements (situation factors) is built. Two elements of the system A and B are depicted on the diagram as separate points (vertices) connected by an oriented arc, if element A is connected to element B by a causal relationship: A à B, where: A is the cause, B is the effect.

Factors can influence each other, and such an influence, as already mentioned, can be positive, when an increase (decrease) in one factor leads to an increase (decrease) in another factor, and negative, when an increase (decrease) in one factor leads to a decrease (increase) ) of another factor. Moreover, the influence can also have a variable sign, depending on possible additional conditions.

Such schemes for representing cause-and-effect relationships are widely used to analyze complex systems in economics and sociology.

Example. A cognitive block diagram for analyzing the problem of energy consumption can look like this (Fig. 5.1):

Rice. 5.1. Cognitive block diagram for the analysis of the problem of energy consumption

The cognitive map reflects only the fact of the presence of influences of factors on each other. It does not reflect either the detailed nature of these influences, nor the dynamics of changes in influences depending on changes in the situation, nor temporary changes in the factors themselves. Taking into account all these circumstances requires a transition to the next level of information structuring, that is, to a cognitive model.

At this level, each relationship between the factors of the cognitive map is revealed by the corresponding dependencies, each of which can contain both quantitative (measured) variables and qualitative (not measured) variables. In this case, quantitative variables are presented in a natural way in the form of their numerical values. Each qualitative variable is associated with a set of linguistic variables that reflect the various states of this qualitative variable (for example, consumer demand can be “weak”, “moderate”, “rush”, etc.), and each linguistic variable corresponds to a certain numerical equivalent in the scale. With the accumulation of knowledge about the processes occurring in the situation under study, it becomes possible to reveal in more detail the nature of the relationships between factors.

Formally, a cognitive model of a situation can, like a cognitive map, be represented by a graph, but each arc in this graph already represents a certain functional relationship between the corresponding factors; those. the cognitive model of the situation is represented by a functional graph.

An example of a functional graph reflecting the situation in a conditional region is shown in fig. 5.2.

Fig.5. 2. Functional graph.

Note that this model is a demonstration model, so many environmental factors are not taken into account in it.

Such technologies are gaining more and more confidence from structures that are engaged in strategic and operational planning at all levels and in all areas of management. The use of cognitive technologies in the economic sphere makes it possible to develop and justify the strategy for the economic development of an enterprise in a short time, taking into account the impact of changes in the external environment.

The use of cognitive modeling technology makes it possible to act proactively and not to bring potentially dangerous situations to the level of threatening and conflict, and in case of their occurrence, to make rational decisions in the interests of the enterprise.

Cognitive modeling (or modeling with cognitive maps) is of particular importance for political analysis. It is designed to model complex, semi-structured objects, such as most political processes and situations.

This method is based on a cognitive approach that has been rapidly developing since the 1960s. The term itself appeared a little earlier - in 1948, after the publication of the well-known work of the American psychologist E. Tolman "Cognitive maps in rats and humans." Considering the behavior of a rat in a maze, Tolman came to the conclusion that over time, it forms a special "cognitive map" of the maze - a structured idea of the environment. It is this card that determines the reactions of the animal.

Yu.M. Plotinsky calls the COGNITIVE approach “the solution of problems traditional for a given science by methods that take into account cognitive aspects, which include the processes of perception, thinking, cognition, explanation and understanding. The cognitive approach in any subject area focuses on "knowledge", or rather, on the processes of their representation, storage, processing, interpretation and production of new knowledge.

With all the diversity of cognitive science, there are two fundamental accents for us. If we are interested in a system of knowledge and ideas, a “picture of the world” of a certain person (or group of people) in order to obtain information about this person or group, then such a cognitive analysis will be subject-oriented. For example, the analysis of a political leader's system of ideas about reality can be extremely useful in predicting his actions and decisions in a certain situation, and the construction of a cognitive map of a wide social group will be required to predict the perception of this or that group of certain actions of the power elite.

If we are interested not in the subject of the cognitive process, but in its product - a cognitive map of one or another fragment of political reality (for example, when compiling cognitive maps of experts regarding the factors influencing the situation in the Middle East region, we are not interested in the peculiarities of the perception of experts, but the situation in the Middle East). East), then the expert is not an object of study, as in the example with political leaders or social groups, but a “tool” for building an adequate model of the situation, and this approach will be object-oriented.

The cognitive map itself is a so-called signed directed graph, in which:

The vertices correspond to the basic factors that describe the processes in the situation;

Direct relationships between factors are determined by analyzing cause-and-effect chains that describe the distribution of the influences of one factor on others. It is believed that the factors included in the premise "if ..." of the chain "if ... then ..." affect the factors of the consequence "then ..." of this chain. Moreover, this influence can be either reinforcing (positive), or inhibitory (negative), or of variable sign, depending on possible additional conditions. In a “softer” version of the cognitive map, it is not a rigid implication “if ... then ...”, but a probabilistic influence: the realization of event A increases (decreases) the probability of the realization of event B.

Links are visualized as lines, called arcs, with the corresponding sign;

A closed directed path, all vertices of which are different, is called a loop (or feedback loop). The loop that amplifies the deflection is a positive feedback loop, and the loop that opposes the deflection is a negative feedback loop.

For example, we believe that the isolationist policy towards Russia by the United States and NATO will contribute to the growth of patriotic sentiments in the country. Under the pressure of these sentiments, the Russian leadership will be forced to increase spending on the army and the military-industrial complex, which in turn will push the US to further intensify its policy of isolation. We can visualize this set of representations using the simplest cognitive map with three vertices and three arcs. Three existing vertices are closed in a reinforcing contour.

A much more complex cognitive map below describes the system of factors of the Palestinian-Israeli conflict” (try to analyze it yourself by highlighting the feedback loops).

By itself, the cognitive map reflects only the system of factors and the most general idea of their relationship. It fixes neither the detailed nature of the influence of factors on each other, nor the dynamics of changes in these influences depending on the situation. In this regard, the cognitive map is a meaningful model of the object under study. At the same time, as in the general case with meaningful models, it can be transformed into a formal model - a system of equations. This, of course, requires reaching a certain level of structuring factors and their relationships.

We will return to modeling using cognitive maps in the course of studying the scenario method.

Control questions and tasks

1. Define the concept of "model". What are the unique possibilities of modeling in political research?

2. What is the difference between linear and non-linear models? Justify the significance of non-linear modeling in relation to the features of the political process.

3. Name the main features of structural models, as well as ways to build them.

4. What is a cognitive map? What elements does it consist of? What is the difference between subject-oriented and object-oriented approaches in cognitive mapping?

5. Describe the algorithm for constructing the "Parties in the Space of Political Orientations" model.

COGNITIVE MODELING

CONTENT
Introduction
1. Subject of cognitive analysis
1.1. External environment
1.2. Instability of the external environment
1.3. Weakly structured external environment
2. General concept of cognitive analysis
3. Stages of cognitive analysis
4. Goals, stages and basic concepts of cognitive modeling
4. 1. The purpose of building a cognitive model
4.2. Stages of cognitive modeling
4.3. Directed graph (cognitive map)
4.4. Functional graph (completion of the cognitive model building)
5. Types of factors

6.1. Identification of factors (elements of the system)
6.2. Two approaches to identifying relationships between factors
6.3.Examples of highlighting factors and relationships between them
6.4. The problem of determining the strength of the influence of factors
7. Checking the adequacy of the model
8. Using a cognitive model
8.1. Application of cognitive models in decision support systems
8.2. An example of working with a cognitive model
9. Computer systems for supporting management decisions
9.1. General characteristics of decision support systems
9.2. "Situation - 2"
9.3. "Compass-2"
9.4. "Canvas"
Conclusion
Bibliography
Appendix

Introduction
At present, obtaining reliable information and its rapid analysis have become the most important prerequisites for successful management. This is especially true if the control object and its external environment are a complex of complex processes and factors that significantly affect each other.
One of the most productive solutions to problems that arise in the field of management and organization is the use of cognitive analysis, which is the subject of study in the course work.
The methodology of cognitive modeling, designed for analysis and decision making in ill-defined situations, was proposed by the American researcher R. Axelrod 1 .
Initially, cognitive analysis was formed within the framework of social psychology, namely, cognitivism, which studies the processes of perception and cognition.
The application of the developments of social psychology in management theory led to the formation of a special branch of knowledge - cognitive science, concentrating on the study of management and decision-making problems.
Now the methodology of cognitive modeling is developing in the direction of improving the apparatus for analyzing and modeling situations.
Theoretical achievements of cognitive analysis have become the basis for the creation of computer systems focused on solving applied problems in the field of management.
Work on the development of the cognitive approach and its application to the analysis and control of so-called semi-structured systems is currently being carried out at the Institute of Control Problems of the Russian Academy of Sciences 2 .
By order of the Administration of the President of the Russian Federation, the Government of the Russian Federation, the Government of the city of Moscow, a number of socio-economic studies using cognitive technology were carried out at the IPU RAS. The developed recommendations are successfully applied by the relevant ministries and departments 3 .
Since 2001, under the auspices of the IPU RAS, international conferences “Cognitive Analysis and Situation Development Management (CASC)” have been regularly held.
When writing a term paper, the works of domestic researchers were involved - A.A. Kulinich, D.I. Makarenko, S.V. Kachaeva, V.I. Maksimova, E.K. Kornoushenko, E. Grebenyuk, G.S. Osipova, A. Raikov. Most of these researchers are specialists from the Institute of Computer Science, Russian Academy of Sciences.
Thus, cognitive analysis is being actively developed not only by foreign, but also by domestic specialists. Nevertheless, within the framework of cognitive science there are a number of problems, the solution of which could significantly improve the results of applying applied developments based on cognitive analysis.
The purpose of the course work is to analyze the theoretical basis of cognitive technologies, the problems of the methodology of cognitive analysis, as well as computer decision support systems based on cognitive modeling.
The set goals correspond to the structure of the work, which sequentially reveals the basic concepts and stages of cognitive analysis in general, cognitive modeling (as a key moment of cognitive analysis), general principles for applying the cognitive approach in practice in the field of management, as well as computer technologies that apply methods of cognitive analysis.

1. The subject of cognitive analysis
1.1. External environment
For effective management, forecasting and planning, it is necessary to analyze the external environment in which the objects of management operate.
The external environment is usually defined by researchers as a set of economic, social and political factors and subjects that have a direct or indirect impact on the possibility and ability of the subject (be it a bank, an enterprise, any other organization, an entire region, etc.) to achieve the set development goals.
For orientation in the external environment and for its analysis, it is necessary to clearly represent its properties. Specialists of the Institute of Control Problems of the Russian Academy of Sciences identify the following main characteristics of the external environment:
1. Complexity - this refers to the number and variety of factors to which the subject must respond.
2. The relationship of factors, that is, the force with which a change in one factor affects the change in other factors.
3. Mobility - the speed with which changes occur in the external environment 4 .
The selection of such characteristics to describe the environment indicates that researchers apply a systematic approach and consider the external environment as a system or a set of systems. It is within the framework of this approach that it is customary to represent any objects in the form of a structured system, to single out the elements of the system, the relationships between them and the dynamics of the development of elements, relationships and the entire system as a whole. Therefore, cognitive analysis used to study the external environment and develop ways and methods of functioning in it is sometimes considered as a component of system analysis 5 .
The specificity of the external environment of control objects lies in the fact that this environment is subject to the influence of the human factor. In other words, it includes subjects endowed with an autonomous will, interests and subjective ideas. This means that this environment does not always obey linear laws that unambiguously describe the relationship of causes and effects.
From this follow two basic parameters of the external environment in which the human factor operates - instability and weakly structured. Let's take a closer look at these parameters.

1.2. Instability of the external environment

The instability of the external environment is often identified by researchers with unpredictability. “The degree of instability of the external economic and political environment for ... [the object of control] is characterized by the familiarity of expected events, the expected pace of change, and the ability to predict the future” 6 . This unpredictability is generated by multifactorial nature, variability of factors, pace and direction of development of the environment.
“The cumulative effect of all factors of the external environment, summarize V. Maksimov, S. Kachaev and E. Kornoushenko, forms the level of its instability and determines the expediency and direction of surgical intervention in ongoing processes” 7 .
The higher the instability of the external environment, the more difficult it is to develop adequate strategic decisions. Therefore, there is an objective need to assess the degree of instability of the environment, as well as to develop approaches to its analysis.
According to I. Ansoff, the choice of strategy for managing and analyzing situations depends on the level of instability of the external environment. For moderate instability, conventional control is applied based on extrapolation of knowledge about the environment's past. With an average level of instability, management is carried out on the basis of a forecast of changes in the environment (for example, a "technical" analysis of financial markets). At a high level of instability, management is used based on flexible expert decisions (for example, "fundamental" 8 analysis of financial markets) 9 .

1.3. Weakly structured external environment

The environment in which the subjects of management are forced to work is characterized not only as unstable, but also as weakly structured. These two characteristics are closely related, but distinct. However, these terms are sometimes used interchangeably.
Thus, specialists from the IPU RAS, defining semi-structured systems, point to some of their properties inherent in unstable systems: “Difficulties in analyzing processes and making managerial decisions in such areas as economics, sociology, ecology, etc. due to a number of features inherent in these areas, namely: the multidimensional nature of the processes occurring in them (economic, social, etc.) and their interconnectedness; because of this, it is impossible to isolate and study individual phenomena in detail - all the phenomena occurring in them must be considered as a whole; the lack of sufficient quantitative information about the dynamics of processes, which forces us to proceed to a qualitative analysis of such processes; variability of the nature of processes over time, etc. Due to these features, economic, social, etc. systems are called semi-structured systems” 10 .
However, it should be noted that the term "instability" implies the impossibility or difficulty of predicting the development of the system, and weakly structured - the impossibility of formalizing it. Ultimately, the characteristics "instability" and "weakly structured", in my opinion, reflect different aspects of the same phenomenon, since we traditionally perceive a system that we cannot formalize and thus absolutely accurately predict its development (that is, a weakly structured system) as unstable, prone to chaos. Therefore, hereinafter, following the authors of the articles studied, I will use these terms as equivalent. Sometimes researchers, along with the above concepts, use the term "difficult situations".
So, unlike technical systems, economic, socio-political and other similar systems are characterized by the absence of a detailed quantitative description of the processes occurring in them - the information here is of a qualitative nature. Therefore, for semi-structured systems, it is impossible to create formal traditional quantitative models. Systems of this type are characterized by uncertainty, description at a qualitative level, and ambiguity in assessing the consequences of certain decisions 11 .
Thus, the analysis of an unstable external environment (weakly structured systems) is fraught with many difficulties. When solving them, an expert's intuition, his experience, associativity of thinking, guesses are needed.
Computer means of cognitive (cognitive) modeling of situations make it possible to cope with such an analysis. These funds have been used in economically developed countries for decades, helping enterprises to survive and develop their business, and the authorities to prepare effective regulatory documents 12 . Cognitive modeling is designed to help the expert reflect on a deeper level and streamline his knowledge, as well as formalize his ideas about the situation to the extent possible.

2. General concept of cognitive analysis

Cognitive analysis is sometimes referred to by researchers as "cognitive structuring" 13 .
Cognitive analysis is considered as one of the most powerful tools for studying an unstable and semi-structured environment. It contributes to a better understanding of the problems existing in the environment, the identification of contradictions and a qualitative analysis of ongoing processes. The essence of cognitive (cognitive) modeling - the key point of cognitive analysis - is to reflect the most complex problems and development trends of the system in a simplified form in the model, to explore possible scenarios for the emergence of crisis situations, to find ways and conditions for their resolution in a model situation. The use of cognitive models qualitatively increases the validity of managerial decision-making in a complex and rapidly changing environment, saves the expert from "intuitive wandering", saves time for comprehending and interpreting events occurring in the system 14 .
IN AND. Maksimov and S.V. Kachaev, to explain the principles of using information cognitive (cognitive) technologies to improve management, use the metaphor of a ship in a raging ocean - the so-called "frigate-ocean" model. Most commercial and non-commercial activities in a volatile and semi-structured environment “are inevitably associated with risk, both from the uncertainty of future operating conditions and from the potential for mismanagement decisions…. It is very important for management to be able to anticipate such difficulties and develop strategies in advance to overcome them, i.e. to have predetermined attitudes of possible behavior. These developments are proposed to be carried out on models in which the information model of the control object (“frigate”) interacts with the model of the external environment - economic, social, political, etc. ("ocean"). “The purpose of such a simulation is to give recommendations to the “frigate” on how to cross the “ocean” with the least “effort” ... Of interest ... are the ways to achieve the goal, taking into account the favorable “winds” and “currents” ... So, we set the goal: to determine the “wind rose” ... [ external environment], and then we will see which “winds” will be favorable, which will be opposite, how to use them and how to discover the properties of the external situation that are important for ... [an object]” 15 .
Thus, the essence of the cognitive approach lies, as already mentioned, in helping the expert to reflect on the situation and develop the most effective management strategy, based not so much on his intuition as on ordered and verified (as far as possible) knowledge about a complex system. Examples of the application of cognitive analysis to solve specific problems will be discussed below in paragraph “8. Using a cognitive model”.

3. Stages of cognitive analysis

Cognitive analysis consists of several stages, each of which implements a specific task. Consistent solution of these problems leads to the achievement of the main goal of cognitive analysis. Researchers give a different nomenclature of stages depending on the specifics of the studied object (objects) 16 . If we summarize and generalize all these approaches, we can distinguish the following stages, which are characteristic of the cognitive analysis of any situation.

(As a result of passing stages 3 - 5, a cognitive model of the situation (system) is built, which is displayed in the form of a functional graph. Therefore, we can say that stages 3 - 5 are cognitive modeling. In more detail, all these stages and basic concepts cognitive modeling will be discussed in paragraphs 4 - 7).

Let us consider in detail each of the above stages (with the exception of the first and second, which are essentially preparatory), the mechanisms for implementing the particular tasks of each of the stages, as well as the problems that arise at different stages of cognitive analysis.

4. Goals, stages and basic concepts of cognitive modeling

A key element of cognitive analysis is the construction of a cognitive model.

4. 1. The purpose of building a cognitive model

Cognitive modeling contributes to a better understanding of the problem situation, the identification of contradictions and a qualitative analysis of the system. The purpose of modeling is to form and refine a hypothesis about the functioning of the object under study, considered as a complex system, which consists of separate, but still interconnected elements and subsystems. In order to understand and analyze the behavior of a complex system, a block diagram of the cause-and-effect relationships of the elements of the system is built. An analysis of these relationships is necessary for the implementation of various process controls in the system 18 .

4.2. Stages of cognitive modeling

In general terms, the stages of cognitive modeling are discussed above. The works of IPU RAS specialists contain a concretized presentation of these stages. Let's highlight the main ones.

Thus, the cognitive model includes a cognitive map (directed graph) and graph arc weights (assessment of mutual influence or influence of factors). When determining the weights of the arcs, the directed graph turns into a functional one.
The problems of identifying factors, assessing the mutual influence of factors and the typology of factors will be discussed in paragraphs 5 and 6; here we will consider such basic concepts of cognitive modeling as a cognitive map and a functional graph.

4.3. Directed graph (cognitive map)

Within the framework of the cognitive approach, the terms "cognitive map" and "directed graph" are often used interchangeably; although, strictly speaking, the concept of a directed graph is broader, and the term "cognitive map" indicates only one of the applications of a directed graph.
A cognitive map consists of factors (elements of the system) and links between them.
In order to understand and analyze the behavior of a complex system, a block diagram of the cause-and-effect relationships of the elements of the system (situation factors) is built. Two elements of the system A and B are depicted on the diagram as separate points (vertices) connected by an oriented arc, if element A is connected to element B by a causal relationship: A a B, where: A is the cause, B is the effect.
Factors can influence each other, and such an influence, as already mentioned, can be positive, when an increase (decrease) in one factor leads to an increase (decrease) in another factor, and negative, when an increase (decrease) in one factor leads to a decrease (increase) ) another factor 20 . Moreover, the influence can also have a variable sign, depending on possible additional conditions.
Such schemes for representing cause-and-effect relationships are widely used to analyze complex systems in economics and sociology.
An example of a cognitive map of some economic situation is shown in Figure 1.

Figure 1. Directed graph 21 .

4.4. Functional graph (completion of the cognitive model building)
The cognitive map reflects only the fact of the presence of influences of factors on each other. It does not reflect either the detailed nature of these influences, nor the dynamics of changes in influences depending on changes in the situation, nor temporary changes in the factors themselves. Taking into account all these circumstances requires a transition to the next level of information structuring, that is, to a cognitive model.
At this level, each relationship between the factors of the cognitive map is revealed by the corresponding dependencies, each of which can contain both quantitative (measured) variables and qualitative (not measured) variables. In this case, quantitative variables are presented in a natural way in the form of their numerical values. Each qualitative variable is associated with a set of linguistic variables that reflect the various states of this qualitative variable (for example, consumer demand can be “weak”, “moderate”, “rush”, etc.), and each linguistic variable corresponds to a certain numerical equivalent in the scale. With the accumulation of knowledge about the processes occurring in the situation under study, it becomes possible to reveal in more detail the nature of the relationships between factors.
Formally, a cognitive model of a situation can, like a cognitive map, be represented by a graph, but each arc in this graph already represents a certain functional relationship between the corresponding factors; those. the cognitive model of the situation is represented by a functional graph 22 .
An example of a functional graph reflecting the situation in a conditional region is shown in fig. 2.

Figure 2. Functional graph 23 .
Note that this model is a demonstration model, so many environmental factors are not taken into account in it.

5. Types of factors
To structure the situation (system), researchers subdivide factors (elements) into different groups, each of which has a certain specificity, namely, a functional role in modeling. Moreover, depending on the specifics of the analyzed situation (system), the typology of factors (elements) can be different. Here I will highlight some types of factors used in cognitive modeling of most systems (situations, environments).
First, among all the discovered factors, there are basic (affecting the situation in a significant way, describing the essence of the problem) and "excessive" (insignificant) factors, "weakly connected" with the "core" of basic factors 24 .
When analyzing a particular situation, the expert usually knows or assumes what changes in the basic factors are desirable for him. The factors of greatest interest to the expert are called target factors. IN AND. Maksimov, E.K. Kornoushenko, S.V. Kachaev describes the target factors as follows: “These are the “output” factors of the cognitive model. The task of developing decisions on managing processes in a situation is to provide the desired changes in target factors, this is the goal of management. The goal is considered correctly set if the desired changes in some target factors do not lead to undesirable changes in other target factors” 25 .
In the initial set of basic factors, a set of so-called control factors is distinguished - “”input” factors of the cognitive model, through which control actions are fed into the model. The control action is considered consistent with the goal if it does not cause undesirable changes in any of the target factors” 26 . To identify control factors, factors influencing the target ones are determined. The controlling factors in the model will be potentially possible levers of influence on the situation 27 .
The influence of control factors is summed up in the concept of "control vector" - a set of factors, each of which is supplied with a control impulse of a given value 28 .
The factors of the situation (or elements of the system) can also be divided into internal (belonging to the object of management and under more or less complete control of the management) and external (reflecting the impact on the situation or system of external forces that may not be controlled or only indirectly controlled by the subject of management) .
External factors are usually divided into predictable ones, the occurrence and behavior of which can be predicted on the basis of an analysis of the available information, and unpredictable ones, the behavior of which the expert learns about only after their occurrence 29 .
Sometimes researchers identify so-called indicator factors that reflect and explain the development of processes in a problem situation (system, environment) 30 . For such purposes, the concept of integral indicators (factors) is also used, by changing which one can judge the general trends in this area 31 .
Factors are also characterized by a trend in their values. Distinguish the following trends: growth, decline. If there is no change in the factor, one speaks of the absence of a trend or a zero trend 32 .
Finally, it should be noted that it is possible to identify causal factors and factors-consequences, short-term and long-term factors.

6. Main problems of building a cognitive model
There are two main problems in constructing a cognitive model.
First, it is difficult to identify factors (elements of the system) and to rank factors (selection of basic and secondary ones) (at the stage of constructing a directed graph).
Secondly, identifying the degree of mutual influence of factors (determining the weights of graph arcs) (at the stage of constructing a functional graph).

6.1. Identification of factors (elements of the system)

It can be stated that the researchers have not developed a clear algorithm for identifying the elements of the systems under study. It is assumed that the studied factors of the situation are already known to the expert conducting the cognitive analysis.
Usually, when considering large (for example, macroeconomic) systems, the so-called PEST-analysis is used (Policy - policy, Economy - economy, Society - society, Technology - technology), which involves the allocation of 4 main groups of factors through which political, economic, socio - cultural and technological aspects of the environment 33 . This approach is well known in all socio-economic sciences.
PEST analysis is a tool for the historically established four-element strategic analysis of the external environment. At the same time, for each specific complex object, there is a special set of key factors that directly and most significantly affect the object. The analysis of each of the identified aspects is carried out systematically, since in life all these aspects are closely interconnected 34 .
In addition, it is assumed that the expert can judge the range of factors, in accordance with their subjective ideas. Thus, the "Fundamental" analysis of financial situations, close in some parameters to cognitive analysis, is based on a set of basic factors (financial and economic indicators) - both macroeconomic and lower order, both long-term and short-term. These factors, in accordance with the "fundamental" approach, are determined on the basis of common sense 35 .
Thus, the only conclusion that can be drawn regarding the process of identifying factors is that the analyst, in pursuing this goal, should be guided by ready-made knowledge of various socio-economic sciences dealing with the specific study of various systems, as well as his experience and intuition.

6.2. Two approaches to identifying relationships between factors

To display the nature of the interaction of factors, positive and normative approaches are used.
The positive approach is based on taking into account the objective nature of the interaction of factors and allows you to draw arcs, assign signs (+ / -) and exact weights to them, that is, reflect the nature of this interaction. This approach is applicable if the relationship of factors can be formalized and expressed by mathematical formulas that establish precise quantitative relationships.
However, not all real systems and their subsystems are described by certain mathematical formulas. We can say that only some special cases of interaction of factors are formalized. Moreover, the more complex the system, the less likely it is to be fully described by traditional mathematical models. This is primarily due to the fundamental properties of unstable, semi-structured systems, described in paragraph 1. Therefore, a positive approach is complemented by a normative one.
The normative approach is based on a subjective, evaluative perception of the interaction of factors, and its use also allows you to assign weights to arcs, i.e., reflect the strength (intensity) of the interaction of factors. The clarification of the influence of factors on each other and the assessment of these influences are based on the "estimations" of the expert and are expressed in quantitative form using the scale [-1,1] or linguistic variables such as "strongly", "weakly", "moderately" 36 . In other words, with the normative approach, the expert is faced with the task of intuitively determining the strength of the mutual influence of factors, based on their knowledge of the qualitative relationship.
In addition, as already mentioned, the expert needs to determine the negative or positive nature of the influence of factors, and not just the strength of influence. In carrying out this task, obviously, it is possible to use the two approaches indicated above.

6.3.Examples of highlighting factors and relationships between them
Here are some examples used by researchers to illustrate the selection of factors and the establishment of relationships between them.
Thus, V. Maksimov, S. Kachaev and E. Kornoushenko identify the following basic factors to build a cognitive model of processes occurring in a crisis economy: 1. Gross domestic product (GDP); 2. Aggregate demand; 3. inflation; 4. Savings; 5. Consumption; 6. Investments; 7. Public procurement; 8. Unemployment; 9. Offer of money; 10. State transfer payments; 11. Government spending; 12. Government revenues; 13. State budget deficit; 14. Taxes; 15. Non-payment of taxes; 16. interest rate; 17. Demand for money 37 .
V. Maksimov, E. Grebenyuk, E. Kornoushenko in the article “Fundamental and technical analysis: integration of two approaches” give another example of identifying factors and reveal the nature of the links between them: “The most important economic indicators that affect the stock market in the US and Europe, are: gross national product (GNP), manufacturing output index (PPI), consumer price index (CPI), producer price index (CPI), unemployment rate, oil price, dollar exchange rate ... If the market is growing and economic indicators confirm the stable development of the economy , then further price growth can be expected ... Stocks rise in price if the company's profits grow and there is a prospect of their further growth ... If the real growth rates of economic indicators diverge from the expected ones, this leads to a panic in the stock market and to its sharp changes. The change in the gross national product is normally 3-5% per year. If the annual GNP growth exceeds 5%, then this is called an economic boom, which can eventually lead to a market collapse. The change in GNP can be predicted by changes in the index of the manufacturing industry. A sharp increase in the IPI indicates a possible increase in inflation, which leads to a fall in the market. The growth of the CPI and CPI and oil prices also leads to a fall in the market. High unemployment in the US and Europe (over 6%) is forcing the federal agencies to lower the bank interest rate, which leads to a revival of the economy and a rise in stock prices. If unemployment decreases gradually, then the market does not react to these changes. If the level of unemployment drops sharply and becomes less than the expected value, then the market begins to fall, because a sharp decrease in unemployment can increase the rate of inflation beyond the expected one” 38 .

6.4. The problem of determining the strength of the influence of factors

So, the most important problem of cognitive modeling is to identify the weights of graph arcs, that is, a quantitative assessment of the mutual influence or influence of factors. The fact is that the cognitive approach is used in the study of an unstable, semi-structured environment. Recall that its characteristics: variability, difficult to formalize, multifactorial, etc. This is the specificity of all systems in which people are included. Therefore, the inoperability of traditional mathematical models in many cases is not a methodological defect of cognitive analysis, but a fundamental property of the subject of study 39 .

Thus, the most important feature of most situations studied in control theory is the presence of thinking participants in them, each of which represents the situation in its own way and makes certain decisions based on “their own” representation. As J. Soros noted in his book The Alchemy of Finance, “when thinking participants act in a situation, the sequence of events does not lead directly from one set of factors to another; instead, it crisscrosses ... connects factors with their perceptions, and perceptions with factors. This leads to the fact that "the processes in the situation do not lead to equilibrium, but to a never-ending process of change" 40 . Hence it follows that a reliable prediction of the behavior of processes in a situation is impossible without taking into account the assessment of this situation by its participants and their own assumptions about possible actions. J. Soros called this feature of some systems reflexivity.
Formalized quantitative dependencies of factors are described by different formulas (regularities) depending on the subject of research, that is, on the factors themselves. However, as already mentioned, the construction of a traditional mathematical model is not always possible.

The problem of universal formalization of mutual influence of factors has not yet been solved and is unlikely to ever be solved.

Therefore, it is necessary to come to terms with the fact that it is far from always possible to describe the relationships of factors by mathematical formulas, i.e. it is by no means always possible to accurately quantify the dependences 41 .
Therefore, in cognitive modeling, when estimating the weights of arcs, as mentioned, the subjective opinion of an expert is often taken into account 42 . The main task in this case is to compensate for the subjectivity and distortion of estimates through various verification procedures.

In this case, one check of the expert's assessments for consistency is usually not enough. The main goal of the expert's subjective opinion processing procedure is to help him reflect, more clearly understand and systematize his knowledge, evaluate their consistency and adequacy of reality.

In the process of extracting expert knowledge, the expert - the source of knowledge - interacts with a cognitologist (knowledge engineer) or with a computer program, which makes it possible to follow the course of reasoning of specialists when making decisions and reveal the structure of their ideas about the subject of research 43 .
In more detail, the procedures for checking and formalizing the expert's knowledge are disclosed in the article by A.A. Kulinich “The system of cognitive modeling “Canva”” 44 .

7. Checking the adequacy of the model
Researchers have proposed several formal procedures for checking the adequacy of the constructed model 45 . However, since the model is based not only on formalized relationships of factors, mathematical methods for checking its correctness do not always give an accurate picture. Therefore, the researchers proposed a kind of "historical method" for testing the adequacy of the model. In other words, the developed model of any situation is applied to similar situations that existed in the past and whose dynamics are well known 46 . In the event that the model turns out to be workable (that is, it produces forecasts that coincide with the real course of events), it is recognized as correct. Of course, not one of the methods for verifying the model separately is exhaustive, so it is advisable to use a set of validation procedures.

8. Using a cognitive model

8.1. Application of cognitive models in decision support systems
The main purpose of the cognitive model is to help the expert in the process of learning and, accordingly, making the right decision. Therefore, the cognitive approach is used in decision support systems.
The cognitive model visualizes and organizes information about the environment, intent, goals and actions. At the same time, visualization performs an important cognitive function, illustrating not only the results of the actions of the subject of control, but also prompting him to analyze and generate solutions 47 .
However, the cognitive model serves not only to systematize and "clarify" the expert's knowledge, but also to identify the most beneficial "points of application" of the control actions of the subject of management 48 . In other words, the cognitive model explains which factor or the relationship of factors must be acted upon, with what force and in what direction, in order to obtain the desired change in target factors, that is, in order to achieve the goal of control at the lowest cost.
Control actions can be short-term (impulse) or long-term (continuous), acting until the goal is achieved. It is also possible to use pulsed and continuous control actions 49 .
When a given goal is achieved, the task immediately arises of keeping the situation in the achieved favorable state until a new goal appears. In principle, the task of keeping the situation in the desired state does not differ from the task of achieving the goal 50 .
A complex of interrelated control actions and their logical time sequence constitute an integral control strategy (control model).
The use of different management models can lead to different results. Here it is important to be able to predict what consequences this or that management strategy will ultimately lead to.
To develop such forecasts, a scenario approach (scenario modeling) is used within the framework of cognitive analysis. Scenario modeling is sometimes referred to as "dynamic simulation".
The scenario approach is a kind of “acting out” different scenarios depending on the chosen management model and the behavior of unpredictable factors. For each scenario, a triad "initial prerequisites - our impact on the situation - the result obtained" is built 51 . The cognitive model in this case makes it possible to take into account the whole complex of effects of control actions for different factors, the dynamics of factors and their relationships under different conditions.
Thus, all possible options for the development of the system are identified and proposals are developed regarding the optimal control strategy for the implementation of the desired scenario out of possible 52 .
Researchers quite often include scenario modeling as part of their cognitive analysis or consider scenario modeling as an adjunct to cognitive analysis.
If we summarize and generalize the opinions of researchers regarding the stages of scenario modeling, then in the most general form the stages of scenario analysis can be represented as follows.
1. Development of the goal of management (the desired change in target factors).
2. Development of scenarios for the development of the situation when applying different management strategies.
3. Determination of the achievability of the set goal (feasibility of scenarios leading to it); checking the optimality of the already planned control strategy (if any); selection of the optimal strategy corresponding to the best, in terms of the goal, scenario.
4. Concretization of the optimal management model - development of specific practical recommendations for managers. This specification includes the identification of control factors (through which it is possible to influence the development of events), determining the strength and direction of control actions on control factors, predicting probable crisis situations due to the influence of unpredictable external factors, etc.
It should be noted that the stages of scenario modeling may vary depending on the object of study and management.
At the initial stage of modeling, there may be enough high-quality information that does not have an exact numerical value and reflects the essence of the situation. In the transition to modeling specific scenarios, the use of quantitative information, which is numerical estimates of the values of any indicators, becomes more and more significant. In what follows, quantitative information is mainly used to carry out the necessary calculations 53 .
The very first scenario that does not require any actions of the researcher to form it is the self-development of the situation (in this case, the vector of control actions is “empty”). The self-development of the situation is the starting point for the further formation of scenarios. If the researcher is satisfied with the results obtained during self-development (in other words, if the set goals are achieved in the course of self-development), then further scenario research is reduced to studying the impact of certain changes in the external environment on the situation 54 .
There are two main classes of scenarios: scenarios simulating external influences and scenarios simulating purposeful (controlled) development of the situation 55 .

8.2. An example of working with a cognitive model

Consider an example of working with a cognitive model given in the article by S.V. Kachaeva and D.I. Makarenko "Integrated information and analytical complex for situational analysis of the socio-economic development of the region."
“The use of an integrated information-analytical complex of situational analysis can be considered on the example of developing a strategy and program for the socio-economic development of the region.
At the first stage, a cognitive model of the socio-economic situation in the region is built... Next, scenarios of the potential and real possibility of changing the situation in the region and achieving the goals set are modeled.
The following were chosen as the goals of socio-economic policy:

To achieve the goals set, the following “levers” (control factors - Yu.M.) were selected, with the help of which the decision maker can or wants to influence the situation:

As a result of modeling, the potential and real possibility of achieving the set goals with the help of the selected levers and the resulting control actions is clarified (see Fig. 3).

Figure 3. Cognitive and dynamic simulation (scenario) modeling.

At the next stage, they move from developing a strategy for achieving goals to developing a program of specific actions. The tool for implementing the strategy is the regional budgetary and tax policy.
The levers chosen at the previous stage and certain impacts correspond to the following directions of budgetary and tax policy.

Levers of Achievement strategic goals	Directions of the budget and tax policy
Population income	Social policy spending
Investment climate	Public Administration Expenditure Law Enforcement Expenses Expenses for industry, power industry, construction and agriculture
production costs	Regulation of tariffs for electricity, fuel, heat, rent, etc.
Development of production infrastructure	Market Infrastructure Development
Tax collection	Regulation of the level of non-payment of taxes
tax incentives	Regulation of the level of tax incentives
Political and economic preferences for the region.	Free transfers from other levels of government

Thus, the integrated information and analytical complex of situational analysis is a powerful tool for developing a strategy for the development of the region and implementing this strategy into reality” 56 .
It should be noted that in studies examples of the use of cognitive and scenario modeling are usually given in a very general form, since, firstly, this kind of information is exclusive and has a certain commercial value, and, secondly, each specific situation (system, environment, control object) requires an individual approach.
The existing theoretical base of cognitive analysis, although it requires clarification and development, allows different management subjects to develop their own cognitive models, since, as mentioned, it is assumed that specific models are compiled for each area, for each problem.

9. Computer systems for supporting management decisions

Conducting a cognitive analysis of unstable, semi-structured situations and environments is an extremely difficult task, for which information systems are involved. In essence, these systems are designed to improve the efficiency of the decision-making mechanism, since the main applied task of cognitive analysis is the optimization of control.

9.1. General characteristics of decision support systems
Decision support systems, as a rule, are interactive. They are designed to process data and implement models that help solve individual, mostly weakly or unstructured tasks (for example, making investment decisions, making forecasts, etc.). These systems can provide workers with the information they need to make individual and group decisions. Such systems provide direct access to information reflecting current situations and all the factors and relationships necessary for decision-making 57
etc.................

Cognitive approach to modeling. Summary: Cognitive modeling. identify possible scenarios for the development of the situation, taking into account the consequences of making the most important decisions and compare them

1.2. Instability of the external environment

1.3. Weakly structured external environment

2. General concept of cognitive analysis

3. Stages of cognitive analysis

4. Goals, stages and basic concepts of cognitive modeling

A key element of cognitive analysis is the construction of a cognitive model.

4. 1. The purpose of building a cognitive model

4.2. Stages of cognitive modeling

4.3. Directed graph (cognitive map)

6.1. Identification of factors (elements of the system)

6.2. Two approaches to identifying relationships between factors

The problem of universal formalization of mutual influence of factors has not yet been solved and is unlikely to ever be solved.

In this case, one check of the expert's assessments for consistency is usually not enough. The main goal of the expert's subjective opinion processing procedure is to help him reflect, more clearly understand and systematize his knowledge, evaluate their consistency and adequacy of reality.

8. Using a cognitive model

8.2. An example of working with a cognitive model

9. Computer systems for supporting management decisions

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Cognitive approach to modeling. Summary: Cognitive modeling. identify possible scenarios for the development of the situation, taking into account the consequences of making the most important decisions and compare them

1.2. Instability of the external environment

1.3. Weakly structured external environment

2. General concept of cognitive analysis

3. Stages of cognitive analysis

4. Goals, stages and basic concepts of cognitive modeling

A key element of cognitive analysis is the construction of a cognitive model.

4. 1. The purpose of building a cognitive model

4.2. Stages of cognitive modeling

4.3. Directed graph (cognitive map)

6.1. Identification of factors (elements of the system)

6.2. Two approaches to identifying relationships between factors

The problem of universal formalization of mutual influence of factors has not yet been solved and is unlikely to ever be solved.

In this case, one check of the expert's assessments for consistency is usually not enough. The main goal of the expert's subjective opinion processing procedure is to help him reflect, more clearly understand and systematize his knowledge, evaluate their consistency and adequacy of reality.

8. Using a cognitive model

8.2. An example of working with a cognitive model

9. Computer systems for supporting management decisions

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