## Classification of systems modeling methods

The statement of any problem is to translate its verbal or * verbal * description into * formal *

In the case of relatively simple tasks, such a transition takes place in the mind of a person who can not always even explain how he did it. If the formal model obtained (the mathematical relationship between the quantities in the form of a formula, equation, system of equations) is based on a fundamental law or is confirmed by experiment, then this proves its adequacy of the displayed situation, and the model is recommended for solving the problems of the corresponding class.

As the tasks become more complex, obtaining a model and proving its adequacy are complicated. Initially, the experiment becomes costly and dangerous (for example, when creating complex technical complexes, implementing space programs, etc.), and, as applied to economic objects, practically unrealizable. Then the problem goes into the class of * decision-making problems, * and the statement of the problem, the formation of the model, i.e. translation of a verbal description into a formal one, become an important part of the decision-making process. Moreover, this component can not always be identified as a separate stage, which, after completion, one can treat the received formal model in the same way as with the usual mathematical description, strict and absolutely fair. Most of the real situations of designing complex technical complexes and managing the economy need to be represented by a class of self-organizing systems, the models of which must be constantly adjusted and developed. In this case, it is possible to change not only the model, but also the modeling method, which is often a means of developing the DM representation about the simulated situation.

In other words, translating a verbal description of a problem or a problem situation into a formal, comprehension, interpretation of the model and the results obtained becomes an integral part of almost every stage of modeling a complex evolving system. Often, in order to more accurately characterize this approach to modeling decision-making processes, they speak of creating, as it were, the mechanism simulation, mechanism decision making (e.g., "business mechanism", "enterprise design and development mechanism", etc.).

The questions that arise from the researchers: "How to form such evolving models or" mechanisms "? How to prove the adequacy of models? - and are the main subject of system analysis.

To solve the problem of translating a verbal description or a problem situation into formal mapping, special techniques and methods began to develop in various fields of activity. So there were methods of "brainstorming", "scenarios", expert assessments, "goal tree" and the like.

In its turn, the development of mathematics was on the way of expanding the means of setting and solving difficultly formalizable problems.

Along with the deterministic, * analytical methods * of classical mathematics, * probability theory * and * mathematical statistics * (as a means of proving the adequacy of the model on the basis of a representative sample and concept probability of the legitimacy of the use of the model and the results of modeling). For problems with a greater degree of uncertainty, engineers began to attract * set theory, mathematical logic, mathematical linguistics, graph theory, * which largely stimulated the development of these directions. In other words, mathematics has gradually accumulated means of working with uncertainty, with a meaning that classical mathematics has excluded from its objects of consideration.

Thus, between the informal, imaginative thinking of man and the formal models of classical mathematics, the "spectrum" has developed. methods that help to obtain and refine (formalize) a verbal description of the problem situation, on the one hand, and to interpret formal models, to link them to reality, on the other. This spectrum methods is presented conditionally in Fig. 2.3, * a. *

The development of modeling methods, of course, did not proceed as consistently as shown in Fig. 2.3, * a *. The methods arose and developed in parallel. There are various modifications of similar methods. They were united in different ways into groups, i.e. the researchers proposed different classifications (mainly for formal methods, which is discussed in more detail in paragraph 2.3). Constantly there are new methods of modeling, as it were on the "intersection" already established groups. However, the basic idea is the existence of the spectrum methods between the verbal and formal representation of the problem situation - this figure illustrates.

Initially, researchers who developed the theory of systems, proposed classifications of systems, tried to put them in accordance with certain modeling methods that would best reflect the characteristics of a particular class. This approach to the choice of modeling methods is similar to the approach of applied mathematics. However, unlike the latter, which is based on the classes of applied problems, system analysis can represent the same object or the same problem situation (depending on the degree of uncertainty and as they are learned) to display different classes of systems and, accordingly, different models.

There is another point of view. If we successively change the methods of Fig. 2.3, and the spectrum (not necessarily using everything), then you can gradually, limiting the completeness of the description of the problem situation (which is inevitable in the formalization), but keeping the components and connections between them that are most significant from the point of view of the goal (goal structure), go to the formal model.

Such an idea was realized, for example, when creating computer software and automated information systems by sequentially translating the description of a task from natural language into a high-level language (task management language, information retrieval language, modeling language, design automation), and from it - to one of the programming languages suitable for the given task (PL/1, PASCAL, LISP, SI, PROLOG, etc.), which in turn is translated into machine instruction codes that activate the hardware part Computer.

At the same time, analysis of the processes of inventive activity, experience in the formation of complex models of decision-making showed that practice does not obey such a logic, i.e. the person does differently: he alternately chooses methods from the left and right parts of the "spectrum", shown in Fig. 2.3, * a. *

Therefore, it's convenient to break this spectrum methods in the middle, where the graphical methods are combined with the methods of structuring, i.e. to divide the methods of modeling systems into two large classes: * formalized systems representation methods * and * methods aimed at activating the use of intuition and expert experience. * The possible classifications of these two groups of methods are shown in Fig. 2.3, b. They are discussed in more detail in paragraphs 2.4 and 2.5.

This separation of methods is in accordance with the basic idea of system analysis, which consists in the combination of formal and informal representations in models and techniques, which helps in the development of methods, the choice of methods for gradual formalization of mapping and analysis of the problem situation. Possible variants of sequential use of methods from groups

Fig. 2.3

MAIS and IPPF in the examples of the techniques given in the subsequent chapters of the textbook (the corresponding references will be given) are shown in the figure as a solid and different dashed lines.

Note that in Fig. 2.3, b in the MAIS group, the methods are located from the bottom up in approximately the order of increasing formalization possibilities, and in the group of the IPPF, from the bottom up, attention is drawn to a meaningful analysis of the problem and more and more tools for such analysis appear. This ordering helps to compare methods and choose them in the formation of developing decision-making models, when developing methods of system analysis.

Classifications MAIS and especially IPPF can be different. In Fig. 2.3, b the IPPF classification proposed by * is given. E. Temnikov * [19] and considered in more detail in Section 2.4, which also gives other examples of IPPF classifications.

The proposed names of groups of methods are more preferable than the sometimes used * -quality * and * quantitative * terms, because, on the one hand, methods attributed to the MAIS group can use formalized representations (in the development of * scenarios *, statistical data can be used, some calculations can be made, formalization involves the acquisition and processing of expert assessments, morphological modeling methods), and on the other hand, by the * TO. Gödel * about incompleteness in the framework of any formal system, however complete and consistent it may seem, there are propositions (relations, statements), the truth or falsity of which can not be proved by the formal means of this system, but to overcome an unsolvable problem It is necessary to expand the formal system, relying on a meaningful, qualitative analysis. Gödel's results were obtained for arithmetic, the most formal direction of mathematics, and allowed to assume that the process of logical, including mathematical proof, is not reduced to using only the deductive method, that it always contains informal elements of thinking. In the future, studies of this problem by mathematicians and logicians have shown that evidence does not possess absolute, timeless rigor at all, and are only culturally mediated means of persuasion.

In other words, there is no strict separation between formal and informal methods. One can speak only about a greater or lesser degree of formalization or, on the contrary, more or less reliance on intuition, "common sense".

The system analyst should understand that any classification is conditional. It is only a tool that helps to navigate in a huge number of different methods and models. Therefore, it is necessary to develop the classification, taking into account the specific conditions, the features of the modeling systems (decision-making processes) and the preferences of decision-makers who can be offered a classification.

New modeling methods are often created based on a combination of pre-existing classes of methods.

So, the methods named in Fig. 2.3 * complex * (combinatorics, topology), began to develop in parallel within the framework of linear algebra, set theory, graph theory, and then formed into independent directions.

There are also new methods based on the combination of MAIS and IPPF. This group of methods is shown in Fig. 2.3, b as an independent group of modeling methods, collectively called * special methods. * The arrows show what means of MAIS and IPPF were used to create these methods.

The following special methods of modeling systems are most widely used:

■ * System Dynamics Simulation Modeling *;

this method is proposed * J. Forrester * (USA) in the 50's. XX century, he uses a convenient language for the individual, helping to express the real relationships that display closed control loops in the system, and analytical representations (linear finite difference equations) that allow the formal analysis of the obtained models on a computer using a specialized language

*DYNAMO;*in this country, this direction is developed by Professor

*applied to the management systems of the university and other socio-economic objects [87, etc.];*

**A. V. Fedotov** ■ * situational modeling; *

The idea is suggested * D. A. Pospelov * [68] and implemented

*and*

**Yu. I. Klykov***(see [80, Chapter 7]); this direction is based on mapping in the computer memory and analysis of problem situations using a specialized language developed with the help of expressive means of set theory, mathematical logic and language theory;*

**L. S. Zagadskaya** ■ * structural-linguistic modeling; *

The approach arose in the 1970s. XX century. in engineering practice and is based on the use of combinatorics of structural representations of various kinds, on the one hand, and the means of mathematical linguistics on the other, for the realization of ideas; in the expanded understanding of the approach, other discrete mathematics methods are used as linguistic means (languages based on set-theoretical representations, on the use of means of mathematical logic, semiotics);

■ * cognitive approach * (from Latin * cognitio * - knowledge, knowledge)

The approach is based on the ideas of * cognitive psychology; * the origins of the cognitive approach are traced, beginning with the works of ancient Greek thinkers (the doctrine of Plato's universals); the design of the cognitive approach as a special discipline is associated with the name * U. Naisser , * published in 1967 a book outlining this approach, which became in a certain sense programmatic; At present, there is an abundance of models proposed for interpreting various aspects of the thought process; In this country, this direction is actively developed by the school of professor

*applied to the management systems of municipalities [28]. In the models of this school, graphical representations are combined with analytical methods for studying impulse processes.*

**G. V. Gorelova** ■ * an approach based on the idea of gradual formalization of decision-making models through the alternate use of MAIS and IPPF means *

This approach to the modeling of self-organizing (developing) systems was originally proposed by one of the authors of the textbook on the basis of the concept of structural-linguistic modeling [21, 25], and later became the basis for almost all methodologies of system analysis (more detail the approach and its use in developing techniques and modeling languages is considered in Chapter 4);

■ * the theory of information field and information chains (information approach to modeling and analysis of systems); *

the concept of the information field was proposed by one of the authors of this textbook and was first published in his pamphlet on the theoretical foundations of cybernetics [33]; The theory is based on the use of the laws of dialectics to activate the intuition of the decision maker, but as a means of formalizing the object or problem situation - the apparatus of mathematical field theory and the theory of chains; this approach is considered in Ch. 3, and examples of its application - in Ch. 6-8; for brevity, the approach is called * informational, * because it is based on the mapping of real situations using information models.

Classification of modeling methods, similar to the one considered, helps to consciously choose the modeling methods (see paragraph 2.7); it can develop, supplemented with specific methods, i.e. accumulate the experience accumulated in the design and management process.

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