The main stages in the development of a cognitive model of a problem situation. Cognitive analysis and modeling in strategic management. Concepts and essence of "Cognitive modeling" and "Cognitive map"

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.

Cognitive modeling

Introduction

1. Concepts and essence of "Cognitive modeling" and "Cognitive map"

2. Problems of the cognitive approach

Conclusion

List of used literature

INTRODUCTION

In the middle of the 17th century, the famous philosopher and mathematician René Descartes uttered an aphorism that has become a classic: "Cogito Ergo Sum" (I think, therefore I am). The Latin root cognito has an interesting etymology. It consists of the parts “co-“ (“together”) + “gnoscere” (“I know”). AT English language there is a whole family of terms with this root: "cognition", "cognize", etc.

In the tradition that we have designated by the term "cognitive", only one "face" of thought is visible - its analytical essence (the ability to decompose the whole into parts), decompose and reduce reality. This side of thinking is associated with the identification of cause-and-effect relationships (causality), which is characteristic of reason. Apparently, Descartes absolutized reason in his algebraic system. Another "face" of thought is its synthesizing essence (the ability to construct a whole from an unprejudiced whole), perceive the reality of intuitive forms, synthesize solutions and anticipate events. This side of thinking, revealed in the philosophy of Plato and his school, is inherent in the human mind. It is no coincidence that we find two bases in Latin roots: ratio (rational relations) and reason (reasonable insight into the essence of things). The rational face of thought originates from the Latin reri ("to think"), going back to the Old Latin root ars (art), then turned into the modern concept of art. Thus, reason (reasonable) is a thought akin to the work of an artist. Cognitive as "reason" means "the ability to think, explain, justify actions, ideas and hypotheses."

For "strong" cognition, a special, constructive status of the category "hypothesis" is essential. It is the hypothesis that is the intuitive starting point for deducing the image of the solution. When considering the situation, the decision maker discovers in the situation some negative links and structures (“breaks” in the situation) that are to be replaced by new objects, processes and relationships that eliminate the negative impact and create a clearly expressed positive effect. This is the essence of innovation management. In parallel with the discovery of the "breaks" of the situation, often qualified as "challenges" or even "threats", the subject of management intuitively imagines some "positive answers" as integral images of the state of the future (harmonized) situation.

Cognitive analysis and modeling are fundamentally new elements in the structure of decision support systems.

The technology of cognitive modeling allows you to explore problems with fuzzy factors and relationships; - take into account changes in the external environment; - use objectively established trends in the development of the situation in your own interests.

Such technologies are gaining more and more confidence from structures involved in strategic and operational planning at all levels and in all areas of management. The use of cognitive technologies in the economic sphere allows in a short time to develop and justify the strategy for the economic development of an enterprise, bank, region or the whole state, taking into account the impact of changes in the external environment. In the field of finance and the stock market, cognitive technologies make it possible to take into account the expectations of market participants. In the military field and area information security the use of cognitive analysis and modeling makes it possible to resist strategic information weapons, to recognize conflict structures without bringing the conflict to the stage of an armed clash.

1. Concepts and essence of "Cognitive modeling" and "Cognitive map"

A cognitive modeling methodology designed for analysis and decision making in ill-defined situations was proposed by Axelrod. It is based on modeling the subjective ideas of experts about the situation and includes: a methodology for structuring the situation: a model for representing expert knowledge in the form of a signed digraph (cognitive map) (F, W), where F is a set of situation factors, W is a set of cause-and-effect relationships between factors situations; methods of situation analysis. At present, the methodology of cognitive modeling is developing in the direction of improving the apparatus for analyzing and modeling the situation. Here, models for forecasting the development of the situation are proposed; methods for solving inverse problems

Cognitive map (from Latin cognitio - knowledge, cognition) - an image of a familiar spatial environment.

Cognitive maps are created and modified as a result of the active interaction of the subject with the outside world. In this case, cognitive maps of varying degrees of generality, “scale” and organization can be formed (for example, an overview map or a path map, depending on the completeness of the representation of spatial relations and the presence of a pronounced reference point). This is a subjective picture, having, first of all, spatial coordinates, in which individual perceived objects are localized. A path map is singled out as a sequential representation of links between objects along a certain route, and an overview map as a simultaneous representation of the spatial arrangement of objects.

leading scientific organization The Institute of Management Problems of the Russian Academy of Sciences, subdivision: Sector-51, scientists Maksimov V.I., Kornoushenko E.K., Kachaev S.V., Grigoryan A.K. and others. On them scientific papers in the field of cognitive analysis and this lecture is based.

The technology of cognitive analysis and modeling (Figure 1) is based on cognitive (cognitive-targeted) structuring of knowledge about an object and its external environment.

Figure 1. Technology of cognitive analysis and modeling

Cognitive structuring of the subject area is the identification of future target and undesirable states of the control object and the most significant (basic) factors of control and the environment that affect the transition of the object to these states, as well as the establishment of cause-and-effect relationships between them at a qualitative level, taking into account mutual influence factors to each other.

The results of cognitive structuring are displayed using a cognitive map (model).

2. Cognitive (cognitive-targeted) structuring of knowledge about the object under study and its external environment based on PEST-analysis and SWOT-analysis

The selection of basic factors is carried out by applying PEST-analysis, which distinguishes four main groups of factors (aspects) that determine the behavior of the object under study (Figure 2):

P olicy - policy;

E economy - economy;

S ociety - society (sociocultural aspect);

T echnology - technology

Figure 2. PEST analysis factors

For each specific complex object, there is a special set of the most significant factors that determine its behavior and development.

PEST-analysis can be considered as a variant of system analysis, since the factors related to the listed four aspects are generally closely interconnected and characterize different hierarchical levels of society as a system.

In this system, there are determining links directed from the lower levels of the system hierarchy to the upper ones (science and technology affect the economy, the economy affects politics), as well as reverse and interlevel links. A change in any of the factors through this system of connections can affect all the others.

These changes may pose a threat to the development of the object, or, conversely, provide new opportunities for its successful development.

The next step is a situational problem analysis, SWOT analysis (Figure 3):

S trends- strengths;

W eaknesses - shortcomings, weaknesses;

O pportunities - opportunities;

T hreats - threats.

Figure 3. SWOT analysis factors

It includes an analysis of the strengths and weaknesses of the development of the object under study in their interaction with threats and opportunities and allows you to determine the actual problem areas, bottlenecks, chances and dangers, taking into account environmental factors.

Opportunities are defined as circumstances that contribute to the favorable development of an object.

Threats are situations in which damage to an object can be caused, for example, its functioning can be disrupted or it can lose its existing advantages.

Based on the analysis of various possible combinations of strengths and weaknesses with threats and opportunities, the problem field of the object under study is formed.

The problem field is a set of problems that exist in the modeled object and environment, in their relationship to each other.

The availability of such information is the basis for determining the goals (directions) of development and ways to achieve them, and developing a development strategy.

Cognitive modeling on the basis of the situational analysis carried out makes it possible to prepare alternative solutions to reduce the degree of risk in the identified problem areas, to predict possible events that may most severely affect the position of the object being modeled.

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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 cognitive structure of the learning space

I've done the work

V.A. Bakuridze

scientific adviser

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, which 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 description (labeling) of elements and integration (filters) of the corresponding background information contained in the states of knowledge.
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, i.e.
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; that is

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. Will also be considered different types relationships between skills and states. 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 "|" ("separator"). 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 is suggestive of more complex connection between questions and skills.

We postulate the existence of a function relating each question q to the set of all subsets of the set of skills 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 (because 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 say of such skill maps that they are essentially the same" with respect to any element of q. 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 of possible number 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. Ultimately, Theorems 3.3 and 5.3 are simply paraphrased 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 under 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.

Really, full list The 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 system distance learning ALEKS (see http://www.ales.com).

7.1 Marking examples

Let's assume that a large pool of questions is chosen, covering all the basic concepts of the mathematics program high school in some 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

Let's assume that at the beginning school year the teacher wants to know which class (maths, for example) is best for a student who has just arrived from foreign country. The knowledge assessment program used has 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 a education system reasonable, should 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, transfer, 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 lat. сognitio - 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 so-called "contextual knowledge" (abstractization and concretization), as well as in areas where concepts such as knowledge, skills or learning are considered.

The term "cognition" is also used in more broad sense, means the very "act" of knowledge or self-knowledge. 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 the 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 is key moment 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 the adoption management decisions in a complex and rapidly changing environment, saves the expert from "intuitive wandering", saves time for understanding and interpreting the events taking place 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 provides a determination of 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 various factors to the control object.

Cognitive analysis consists of several stages, each of which implements a specific task. Consistent solution of these tasks leads to the achievement main goal 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. For 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. Choosing a set of measures (a set of control factors), determining their possible and desired strength and direction of impact on the situation (concrete practical application of the cognitive model).

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.

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 in 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 cause-and-effect 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.

Similar schemes for representing cause-and-effect relationships are widely used for the analysis 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.

Individual work

Cognitive modeling

Introduction

1. Concepts and essence of "Cognitive modeling" and "Cognitive map"

2. Problems of the cognitive approach

Conclusion

List of used literature

INTRODUCTION

In the middle of the 17th century, the famous philosopher and mathematician René Descartes uttered an aphorism that has become a classic: "Cogito Ergo Sum" (I think, therefore I am). The Latin root cognito has an interesting etymology. It consists of the parts “co-“ (“together”) + “gnoscere” (“I know”). In English, there is a whole family of terms with this root: "cognition", "cognize", etc.

Cognitive analysis and modeling are fundamentally new elements in the structure of decision support systems.

Such technologies are gaining more and more confidence from structures involved in strategic and operational planning at all levels and in all areas of management. The use of cognitive technologies in the economic sphere allows in a short time to develop and justify the strategy for the economic development of an enterprise, bank, region or the whole state, taking into account the impact of changes in the external environment. In the field of finance and the stock market, cognitive technologies make it possible to take into account the expectations of market participants. In the military field and the field of information security, the use of cognitive analysis and modeling makes it possible to counter strategic information weapons, to recognize conflict structures without bringing the conflict to the stage of an armed clash.

1. Concepts and essence of "Cognitive modeling" and "Cognitive map"

Cognitive map (from Latin cognitio - knowledge, cognition) - an image of a familiar spatial environment.

The leading scientific organization in Russia engaged in the development and application of cognitive analysis technology is the Institute of Management Problems of the Russian Academy of Sciences, subdivision: Sector-51, scientists Maksimov V.I., Kornoushenko E.K., Kachaev S.V., Grigoryan A.K. and others. This lecture is based on their scientific works in the field of cognitive analysis.

The technology of cognitive analysis and modeling (Figure 1) is based on cognitive (cognitive-targeted) structuring of knowledge about an object and its external environment.

Figure 1. Technology of cognitive analysis and modeling

The results of cognitive structuring are displayed using a cognitive map (model).

2. Cognitive (cognitive-targeted) structuring of knowledge about the object under study and its external environment based on PEST-analysis and SWOT-analysis

The selection of basic factors is carried out by applying PEST-analysis, which distinguishes four main groups of factors (aspects) that determine the behavior of the object under study (Figure 2):

P olicy - policy;

E economy - economy;

S ociety - society (sociocultural aspect);

T echnology - technology

Figure 2. PEST analysis factors

For each specific complex object, there is a special set of the most significant factors that determine its behavior and development.

These changes may pose a threat to the development of the object, or, conversely, provide new opportunities for its successful development.

The next step is a situational problem analysis, SWOT analysis (Figure 3):

S trends - strengths;

W eaknesses - shortcomings, weaknesses;

O pportunities - opportunities;

T hreats - threats.

Figure 3. SWOT analysis factors

Opportunities are defined as circumstances that contribute to the favorable development of an object.

Threats are situations in which damage to an object can be caused, for example, its functioning can be disrupted or it can lose its existing advantages.

Based on the analysis of various possible combinations of strengths and weaknesses with threats and opportunities, the problem field of the object under study is formed.

The problem field is a set of problems that exist in the modeled object and the environment, in their relationship with each other.

The availability of such information is the basis for determining the goals (directions) of development and ways to achieve them, and developing a development strategy.

Stages of cognitive technology and their results are presented in Table 1:

Table 1

Stages of cognitive technology and results of its application

Stage name	Result Presentation Form
1. Cognitive (cognitive-targeted) structuring of knowledge about the object under study and its external environment based on PEST-analysis and SWOT-analysis: Analysis of the initial situation around the object under study with the allocation of basic factors that characterize the economic, political and other processes occurring in the object and in its macro-environment and influencing the development of the object. 1.1 Identification of factors characterizing the strengths and weaknesses of the object under study 1.2 Identification of factors characterizing the opportunities and threats from the external environment of the object 1.3 Construction of the problem field of the object under study	Report on a systemic conceptual study of an object and its problem area
2. Building a cognitive model of the development of an object - formalization of knowledge obtained at the stage of cognitive structuring 2.1 Identification and justification of factors 2.2 Establishing and justifying relationships between factors 2.3 Building a graph model	Computer cognitive model of an object in the form of a directed graph (and a matrix of factor relationships)
3. Scenario study of trends in the development of the situation around the object under study (with the support of the software systems "SITUATION", "KOMPAS", "KIT") 3.1 Determining the purpose of the study 3.2 Specifying study scenarios and modeling them 3.3 Identification of trends in the development of an object in its macroenvironment 3.4 Interpreting the results of the scenario study	Scenario study report, with interpretation and conclusions
4. Development of strategies for managing the situation around the object under study 4.1 Definition and justification of the control goal 4.2 Solution of the inverse problem 4.3 Selection of management strategies and ordering them according to criteria: the possibility of achieving the goal; the risk of losing control of the situation; risk of emergencies	Report on the development of management strategies with justification of strategies for various criteria of management quality
5. Search and justification of strategies for achieving the goal in stable or changing situations For stable situations: a) selection and justification of the control goal; b) the choice of measures (managements) to achieve the goal; c) analysis of the fundamental possibility of achieving the goal from current state situations with the use of selected activities; d) analysis of real restrictions on the implementation of selected activities; e) analysis and justification of the real possibility of achieving the goal; f) development and comparison of strategies for achieving the goal by: the proximity of the results of management to the intended goal; costs (financial, physical, etc.); by the nature of the consequences (reversible, irreversible) from the implementation of these strategies in a real situation; by risk of emergencies For changing situations: a) selection and justification of the current control goal; b) in relation to the current goal, the previous paragraphs b-e are valid; c) analysis of changes occurring in the situation and their display in the graph model of the situation. Go to step a.	Report on the development of strategies to achieve the goal in stable or changing situations
6. Development of a program for implementing the development strategy of the object under study based on dynamic simulation modeling (with the support of the Ithink software package) 6.1. Distribution of resources by directions and in time 6.2 Coordination 6.3 Follow-up	The program for the implementation of the development strategy of the facility. Computer simulation model of object development

2. Problems of the cognitive approach

Today, many advanced countries are "promoting" an economy based on knowledge and effective management. Intellectual property is becoming the most valuable commodity of the state. The essence of modern future war becomes a confrontation between intellectuals. Under such conditions, indirect and non-traditional actions are the most appropriate ways to achieve geopolitical goals, and, therefore, information weapons are of great importance. There are two concepts for the development of strategic weapons with different roles in them of the Strategic Information Weapon (SW). The first generation SPI is integral part strategic weapons along with other types of strategic weapons and conventional weapons.

The second generation SIS is an independent, radically new type of strategic weapon that emerged as a result of the information revolution and is used in new strategic directions (for example, economic, political, ideological, etc.). The time of exposure to such weapons can be much longer - a month, a year or more. The second generation SIO will be capable of withstanding many other types of strategic weapons and will form the core of strategic weapons. The situations emerging as a result of the application of SIO-2 pose a threat to the security of Russia and are characterized by uncertainty, unclear and fuzzy structure, influence a large number heterogeneous factors and the presence of many alternative development options. This leads to the need to apply non-traditional methods that make it possible to study the geopolitical, informational and other processes taking place in Russia and the world, in aggregate and interaction both among themselves and with the external unstable environment. Cognitive modeling is intended for structuring, analyzing and making managerial decisions in complex and uncertain situations (geopolitical, internal political, military, etc.), in the absence of quantitative or statistical information about the ongoing processes in such situations.

Cognitive modeling allows in express mode

in a short time at a high quality level:

- assess the situation and analyze the mutual influence of the existing factors that determine possible scenarios for the development of the situation;

- identify trends in the development of situations and the real intentions of their participants;

- develop a strategy for using trends in the development of the political situation in the national interests of Russia;

- to determine the possible mechanisms of interaction between the participants in the situation to achieve its purposeful development in the interests of Russia;

- develop and substantiate directions for managing the situation in the interests of Russia;

- identify possible scenarios for the development of the situation, taking into account the consequences of making the most important decisions and compare them.

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

For tasks related to organizational systems, the problem of uncertainty in the description and modeling of the functions of participants is not methodological, but inherent in the subject of research itself. Possible various productions tasks of managing the situation depending on the completeness of the information available to the participants about the situation and about the other participants, in particular, to search for resonant and synergistic effects, when the improvement of the situation with the simultaneous impact of several participants on it is greater than the “combination” of positive effects from each of the participants separately.

From the point of view of management science, it is especially important today to use soft resonant management of complex socio-economic systems, the art of which lies in the methods of self-management and self-control of systems. Weak, so-called resonant phenomena, are extremely effective for "unwinding" or self-government, as they correspond to the internal trends in the development of complex systems. The main problem is how to push the system onto one of its own and favorable development paths with a small resonant impact, how to ensure self-government and self-sustaining development (self-promotion).

Conclusion

The use of cognitive modeling opens up new possibilities for forecasting and management in various areas:

in the economic sphere, this allows in a short time to develop and justify a strategy for the economic development of an enterprise, bank, region or even the whole state, taking into account the impact of changes in the external environment;

in the field of finance and the stock market - to take into account the expectations of market participants;

in the military field and the field of information security - to counter strategic information weapons, recognizing conflict structures in advance and developing adequate response measures to threats.

Cognitive modeling automates some of the functions of cognitive processes, so they can be successfully applied in all areas in which self-knowledge is in demand. Here are just a few of these areas:

1. Models and methods of intelligent information technologies and systems for creating geopolitical, national and regional strategies for socio-economic development.

2. Models of survival of "soft" systems in changing environments with a shortage of resources.

3. Situational analysis and management of the development of events in crisis environments and situations.

4. Information monitoring socio-political, socio-economic and military-political situations.

5. Development of principles and methodology for computer analysis of problem situations.

6. Development of analytical scenarios for the development of problem situations and their management.

8. Monitoring of problems in the socio-economic development of a corporation, region, city, state.

9. Technology of cognitive modeling of purposeful development of the region of the Russian Federation.

10. Analysis of the development of the region and monitoring of problematic situations in the targeted development of the region.

11. Models for the formation of state regulation and self-regulation of the consumer market.

12. Analysis and management of the development of the situation in the consumer market.

The technology of cognitive modeling can be widely used for unique projects for the development of regions, banks, corporations (and other objects) in crisis conditions after appropriate training.

List of used literature

1. http://www.ipu.ru

2. http://www.admhmao.ru

3. Maksimov V.I., Kornoushenko E.K. Knowledge is the basis of analysis. Banking technologies, No. 4, 1997.

4. Maksimov V.I., Kornoushenko E.K. Analytical foundations for the application of the cognitive approach in solving semi-structured problems. Proceedings of IPU, issue 2, 1998.

5. Maksimov V.I., Kachaev S.V., Kornoushenko E.K. Conceptual modeling and monitoring of problematic and conflict situations with the targeted development of the region. On Sat. " Modern technologies management for administrations of cities and regions". Fund "Problems of Management", M. 1998.

1. Concepts and essence of "Cognitive modeling" and "Cognitive map"

2. Cognitive (cognitive-targeted) structuring of knowledge about the object under study and its external environment based on PEST-analysis and SWOT-analysis

Individual work

1. Concepts and essence of "Cognitive modeling" and "Cognitive map"

2. Cognitive (cognitive-targeted) structuring of knowledge about the object under study and its external environment based on PEST-analysis and SWOT-analysis

2. Problems of the cognitive approach

Cognitive modeling allows in express mode

in a short time at a high quality level:

- assess the situation and analyze the mutual influence of the existing factors that determine possible scenarios for the development of the situation;

- identify trends in the development of situations and the real intentions of their participants;

- develop a strategy for using trends in the development of the political situation in the national interests of Russia;

- to determine the possible mechanisms of interaction between the participants in the situation to achieve its purposeful development in the interests of Russia;

- develop and substantiate directions for managing the situation in the interests of Russia;

- identify possible scenarios for the development of the situation, taking into account the consequences of making the most important decisions and compare them.

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

Conclusion

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