Classification of systems: open - closed, according to the complexity of structure and behavior. Classification of information The presence of what determines the degree of organization of the social system

The division of systems according to the degree of organization is proposed in continuation of the idea of their division into well organized and poorly organized, or diffuse. To these two classes, another class has been added developing (self-organizing) systems. These classes are briefly characterized in Table. 1.4.

Table 1.4

System class	a brief description of	Application possibilities
1. Well organized	Representation of an object or decision-making process in the form of a well-organized system is possible in those cases when the researcher manages to determine all its elements and their interconnections with each other and with the goals of the system in the form deterministic(analytical, graphical) dependencies. This class of systems includes most models physical processes and technical systems. When an object is represented by this class of systems, the tasks of choosing goals and determining the means to achieve them (elements, links) are not separated	This class of systems is used in cases where a deterministic description can be proposed and the validity of its application has been experimentally shown, i.e. experimentally proved the adequacy of the model to a real object or process
2. Poorly organized (diffuse)	When presenting an object as a poorly organized (diffuse) system, the task is not to determine all the components and their connections with the goals of the system. The system is characterized by a certain set of macro-parameters and regularities that are revealed on the basis of a study of a fairly representative sample of components determined with the help of certain rules that reflect the object or process under study. On the basis of such selective, studies obtain characteristics or patterns (statistical, economic, etc.), and extend these patterns to the behavior of the system as a whole with some probability (statistical or in the broad sense of using this term)	Displaying objects in the form of diffuse systems is widely used in determining the throughput of systems of various kinds, in determining the number of staff in service, for example, repair shops of an enterprise, in service institutions (methods of queuing theory are used to solve such problems), etc. When applying this class of systems, the main problem is to prove the adequacy of the model
3. Self-organizing (developing)	Class self-organizing (developing), systems are characterized by a number of features, features that bring them closer to real developing objects (see details in Table 1.5). In the study of these features, an important difference between developing systems with active elements and closed systems was revealed - fundamental limitation of their formalized description. This feature leads to the need to combine formal methods and methods qualitative analysis. Therefore, the main idea of displaying the designed object as a class of self-organizing systems can be formulated as follows. A sign system is being developed, with the help of which known this moment components and relationships, and then by transforming the resulting mapping using the chosen or accepted approaches and methods ( structuring, decomposition; compositions, searching for measures of proximity on the state space, etc.) receive new, previously unknown components, relationships, dependencies, which can either serve as the basis for making decisions or suggest the next steps towards preparing a solution. Thus, it is possible to accumulate information about the object, while fixing all the new components and connections (rules of interaction between components), and, applying them, obtain mappings of the successive states of the developing system, gradually forming an increasingly adequate model of a real, studied or created object.	Displaying the object under study as a system of this class allows you to explore the least studied objects and processes with a large uncertainty at the initial stage of the problem statement. Examples of such tasks are the tasks that arise in the design of complex technical complexes, research and development of management systems for organizations. Most of the models and techniques system analysis is based on the representation of objects in the form of self-organizing systems, although this is not always specifically stipulated. When such models are formed, the usual idea of models, which is characteristic of mathematical modeling and applied mathematics. The idea of proving the adequacy of such models also changes.

In the proposed classification of systems, the systems that existed by the mid-70s of the twentieth century were used. terms, but they are combined into a single classification, in which the distinguished classes are considered as approaches to displaying an object or solving a problem, and their characteristics are proposed, which allows choosing a class of systems for displaying an object, depending on the stage of its cognition and the possibility of obtaining information about it.

Problem situations with a large initial uncertainty are more consistent with the representation of an object in the form of a third-class system. In this case, modeling becomes, as it were, a kind of “mechanism” for the development of the system. The practical implementation of such a "mechanism" is associated with the need to develop a procedure for building a model of the decision-making process. Building a model begins with the use of a sign system (modeling language), which is based on one of the methods of discrete mathematics (for example, set-theoretic representations, mathematical logic, mathematical linguistics) or special methods of system analysis (for example, simulation dynamic simulation etc.). When modeling the most complex processes (for example, the processes of forming goal structures, improving organizational structures, etc.), the “mechanism” of development (self-organization) can be implemented in the form of an appropriate methodology for system analysis. On the considered idea of displaying an object in the process of representing it by a class of self-organizing systems, the method of gradual formalization of the decision-making model is also based, which is characterized in Ch. four.

Class self-organizing (developing), systems are characterized by a number of features or features that bring them closer to real developing objects (Table 1.5).

Table 1.5

Peculiarity	a brief description of
Non-stationarity (variability, instability) of parameters and stochastic behavior	This feature is easily interpreted for any systems with active elements (living organisms, social organizations, etc.), causing their behavior to be stochastic.
The uniqueness and unpredictability of the system behavior in specific conditions	These properties are manifested in the system due to the presence of active elements in it, as a result of which the system, as it were, manifests "free will", but at the same time, but at the same time, there is also the presence limits, determined by the available resources (elements, their properties) and structural connections characteristic of a certain type of systems
Ability to adapt to changing environmental conditions and interference	This property seems to be very useful. However, adaptability can manifest itself not only in relation to interference, but also in relation to control actions, which makes it very difficult to control the system.
Fundamental disequilibrium	When studying the differences between living, developing objects and non-living ones, biologist Erwin Bauer hypothesized that the living is fundamentally in an unstable, non-equilibrium state and, moreover, uses its energy to maintain itself in a non-equilibrium state (which is actually life). This hypothesis is increasingly supported by modern research. In this case, problems of maintaining the stability of the system arise.
Ability to resist entropic (system-destroying) tendencies and exhibit negentropic tendencies	It is due to the presence of active elements that stimulate the exchange of material, energy and information products with the environment and show their own "initiatives", an active principle. Due to this, in such systems, the pattern of entropy increase is violated (similar to the second law of thermodynamics, acting in closed systems, the so-called "second law"), and even observed negentropic trends, i.e. actually self-organization, development, including "free will"
The ability to develop behaviors and change your structure	This property can be provided using various methods that allow you to form a variety of models of decision-making options, reach a new level equifinality while maintaining the integrity and basic properties
Ability and desire for goal setting	In contrast to closed (technical) systems, for which goals are set from the outside, in systems with active elements, goals are formed inside the system (for the first time, this feature in relation to economic systems was formulated by Yu. I. Chernyak); goal setting is the basis of negentropic processes in socio-economic systems
Ambiguity in the use of concepts	For example, "goal - means", "system - subsystem", etc. This feature is manifested in the formation of goal structures, the development of projects for complex technical complexes, automated control systems, etc., when the persons who form the structure of the system, calling some part of it a subsystem, after a while begin to talk about it as a system, without adding the prefix “under”, or sub-goals begin to be called means to achieve higher goals. Because of this, protracted discussions often arise, which are easily resolved using the patterns of communication, the properties of the "two-faced Janus"

The listed signs of self-organizing (developing) systems have various manifestations, which can sometimes be distinguished as independent features. These features, as a rule, are due to the presence of active elements in the system and are of a dual nature: they are new properties that are useful for the existence of the system, its adaptation to changing environmental conditions, but at the same time cause uncertainty and make it difficult to control the system.

Some of the features considered are characteristic of diffuse systems ( stochastic behavior, instability of individual parameters), but most of them are specific features that significantly distinguish this class of systems from others and make their modeling difficult.

At the same time, when creating and organizing enterprise management, they often try to represent them using the theory of automatic regulation and control, which was developed for closed, technical systems and significantly distorts the understanding of systems with active elements, which can harm the enterprise, make it an inanimate "mechanism", unable to adapt to the environment and develop options for their development.

The considered features are contradictory. In most cases, they are both positive and negative, desirable and undesirable for the system being created. It is not immediately possible to understand and explain the signs of systems, to select and create the required degree of their manifestation. Philosophers, psychologists, specialists in systems theory are studying the reasons for the manifestation of such features of complex objects with active elements, who, in order to explain these features, propose and investigate patterns of systems.

The manifestation of contradictory features of developing systems and the explanation of their patterns on the example of real objects must be studied, constantly monitored, reflected in models, and search for methods and means to regulate the degree of their manifestation.

At the same time, one should keep in mind the important difference between developing systems with active elements and closed ones: trying to understand the fundamental features of modeling such systems, the first researchers already noted that starting from a certain level of complexity, the system is easier to manufacture and put into operation, transform and change than to be represented by a formal model.

With the accumulation of experience in the study and transformation of such systems, this observation was confirmed, and their main feature was realized - fundamental limitation of a formalized description of developing (self-organizing) systems.

This feature, i.e. the need to combine formal methods and methods of qualitative analysis, and is the basis of most models and methods of system analysis. When forming such models, the usual idea of models, which is characteristic of mathematical modeling and applied mathematics, changes. The idea of proving the adequacy of such models also changes.

The degree of organization of the system

The organization or orderliness of the organization of the system R is estimated by the formula

R \u003d 1-E real / E max, (2.3)

where Ereal- real or current value of entropy,

Emax- the maximum possible entropy or uncertainty in the structure and functions of the system.

If the system is completely deterministic and organized, then E real = 0 and R = 1. Reducing the entropy of the system to zero means the complete "overorganization" of the system and leads to the degeneration of the system. If the system is completely disorganized, then R=0 and E real = E max.

A qualitative classification of systems according to the degree of organization was proposed by V. V. Nalimov, who singled out a class of well-organized and a class of poorly organized, or diffuse systems. Later, a class of self-organizing systems was added to these classes. It is important to emphasize that the name of a system class is not its evaluation. First of all, it can be considered as approaches to displaying an object or a problem being solved, which can be chosen depending on the stage of cognition of the object and the possibility of obtaining information about it.

Well organized systems

If the researcher manages to determine all the elements of the system and their relationship with each other and with the goals of the system and the type of deterministic (analytical or graphical) dependencies, then it is possible to represent the object as a well-organized system. That is, the representation of an object in the form of a well-organized system is used in cases where a deterministic description can be proposed and the validity of its application has been experimentally shown (the adequacy of the model to a real object has been proved).

This representation is successfully used in modeling technical and technological systems. Although, strictly speaking, even the simplest mathematical relationships that reflect real situations are also not absolutely adequate, since, for example, when adding apples, it is not taken into account that they are not exactly the same, and weight can only be measured with some accuracy. Difficulties arise when working with complex objects (biological, economic, social, etc.). Without significant simplification, they cannot be represented as well-organized systems. Therefore, in order to display a complex object in the form of a well-organized system, it is necessary to single out only the factors that are essential for the specific purpose of the study. Attempts to apply models of well-organized systems to represent complex objects are practically often unrealizable, since, in particular, it is not possible to set up an experiment that proves the adequacy of the model. Therefore, in most cases, when representing complex objects and problems at the initial stages of the study, they are displayed by the classes discussed below.

Poorly organized (or diffuse) systems

If the task is not set to determine all the considered components and their connections with the goals of the system, then the object is presented as a poorly organized (or diffuse) system. To describe the properties of such systems, two approaches can be considered: selective and macroparametric.

With a selective approach, regularities in the system are revealed on the basis of studying not the entire object or class of phenomena, but by studying a fairly representative (representative) sample of components that characterize the object or process under study. The sample is determined using some rules. The characteristics or patterns obtained on the basis of such a study are extended to the behavior of the system as a whole.

Example. If we are interested in the average price of bread in a certain city, then we could sequentially go around or call all the outlets of the city, which would require a lot of time and money. Or you can go the other way: collect information in a small (but representative) group of outlets, calculate the average price and generalize it to the whole city.

At the same time, we must not forget that the obtained statistical regularities are valid for the entire system with some probability, which is estimated using special techniques studied by mathematical statistics.

With the macroparametric approach, the properties of the system are evaluated using some integral characteristics (macroparameters).

Examples:

1. When using a gas for applied purposes, its properties are not determined by an accurate description of the behavior of each molecule, but are characterized by macro parameters - pressure, temperature, etc. Based on these parameters, devices and devices are developed that use the properties of the gas, without examining the behavior of each molecule.

2. When assessing the quality level of the health care system of the state, the UN uses as one of the integral characteristics the number of children who die before the age of five per thousand newborns.

Displaying objects in the form of diffuse systems is widely used in determining the throughput of systems of various kinds, in determining the number of staff in service, for example, repair shops of an enterprise and in service institutions, in the study of documentary information flows, etc.

Self-organizing systems

The class of self-organizing, or developing, systems is characterized by a number of features, features, which, as a rule, are due to the presence of active elements in the system that make the system purposeful. This implies the features of economic systems, as self-organizing systems, in comparison with the functioning of technical systems:

non-stationarity (variability) of individual parameters of the system and the stochasticity of its behavior;

uniqueness and unpredictability of the system behavior in specific conditions. Due to the presence of active elements of the system, a kind of "free will" appears, but at the same time, its possibilities are limited by the available resources (elements, their properties) and structural connections characteristic of a certain type of systems;

the ability to change its structure and form behaviors while maintaining integrity and basic properties (in technical and technological systems, a change in structure, as a rule, leads to a disruption in the functioning of the system or even to the cessation of existence as such);

the ability to resist entropic (system-destroying) tendencies. In systems with active elements, the regularity of the increase in entropy is not observed, and even negentropic tendencies are observed, i.e., self-organization proper;

The ability to adapt to changing conditions. This is good in relation to disturbing influences and interference, but it is bad when adaptability also manifests itself in relation to control actions, making it difficult to control the system;

ability and desire for goal setting;

fundamental imbalance.

It is easy to see that although some of these features are also characteristic of diffuse systems (stochastic behavior, instability of individual parameters), however, for the most part they are specific features that significantly distinguish this class of systems from others and make their modeling difficult.

The considered features are contradictory. In most cases, they are both positive and negative, desirable and undesirable for the system being created. They can not immediately be understood and explained in order to select and create the required degree of their manifestation.

At the same time, one should keep in mind the important difference between open developing systems with active elements and closed ones. Trying to understand the fundamental features of modeling such systems, the first researchers already noted that, starting from a certain level of complexity, the system is easier to manufacture and put into operation, transform and change than to be displayed by a formal model. With the accumulation of experience in the study and transformation of such systems, this observation was confirmed, and their main feature was realized - the fundamental limitation of a formalized description of developing, self-organizing systems.

On this occasion, von Neumann expressed the following hypothesis: “We do not have complete confidence that in the field of complex problems a real object cannot be the simplest description of itself, that is, that any attempt to describe it using ordinary verbal or formal logical method will not lead to something more complex, confusing and difficult to implement ... ".

The need to combine formal methods and methods of qualitative analysis is the basis of most models and methods of system analysis. When forming such models, the usual idea of models, which is characteristic of mathematical modeling and applied mathematics, changes. The idea of proving the adequacy of such models also changes.

The main constructive idea of modeling when displaying an object by a class of self-organizing systems can be formulated as follows: by accumulating information about the object, fixing all the new components and connections and applying them, you can get mappings of the successive states of the developing system, gradually creating an increasingly adequate model of the real, studied or created object. In this case, information can come from specialists various areas knowledge and accumulate over time as it arises (in the process of knowing the object).

The adequacy of the model is also proved, as it were, sequentially (as it is formed) by evaluating the correctness of the reflection in each subsequent model of the components and relationships necessary to achieve the goals.

Open and closed systems

The concept of an open system was introduced by L. von Bertalanffy. Main distinctive features open systems- the ability to exchange mass, energy and information with the environment. In contrast, closed or closed systems are assumed to be completely devoid of this ability, isolated from the environment.

Members of the "Society for the Development of OTS" A. Hall and I "Fagin, based on their own definition of the system, give the following classification of systems: If a change in each individual part of the system causes a change in all other parts and in the whole system, then in this case the system is holistic. If a change in each part of the system does not cause a change in other parts, then the system is called summative. It is quite clear that, thanks to this division, Hall and Fagin are able to cover in their theory a much wider range of systems than Bertalanffy.

Despite the fact that the classification of Hall and Fagin systems is more detailed than the Bertalanffy classification, and their definition of the system is wider than the definition of the Bertalanffy system, nevertheless, these modifications do not introduce fundamental changes into the essence of the “general systems theory”. Both Bertalanffy and Hall - Fagin we are talking about the construction of a certain mathematical apparatus capable of describing the "behavior" of a fairly large class of system objects.

Other signs

By homogeneity or diversity of structural elements systems are homogeneous or homogeneous and heterogeneous or heterogeneous, as well as mixed type . In homogeneous systems, such as gases, liquids, or populations of organisms, the structural elements of the system are homogeneous and therefore interchangeable. Heterogeneous systems consist of heterogeneous elements that do not have the property of interchangeability.

By balance systems are divided into equilibrium or balanced and nonequilibrium or unbalanced. In equilibrium systems, if there are changes simultaneously in two opposite directions (opposite processes), then they are mutually compensated or neutralized at some level. Each of the emerging changes is balanced by another, opposite to it, and the system remains in an equilibrium state. An example of equilibrium systems is an organism, society, ecosystem, etc. In unbalanced systems, on the contrary, if changes occur simultaneously in two opposite directions, then one of them prevails, the system is transformed in this direction and the balance is disturbed. However, this disturbance of the equilibrium can sometimes occur so slowly that the system gives the impression of being in equilibrium (false equilibrium). Flame is an example of a false balance.

Systems are divided into classes according to various characteristics, and depending on the problem being solved, different classification principles can be chosen. In this case, the system can be characterized by one or more features:

· in appearance scientific direction - mathematical, physical, chemical, etc.;

· by the form of a formalized representation apparatus systems - deterministic and stochastic;

· by degree of organization- well organized, poorly organized (diffuse), self-organizing systems.

· by conditionality of action distinguish between deterministic and stochastic (probabilistic) systems.

· by origin distinguish between natural systems, created in the course of natural evolution and generally not subject to human influence (cell), artificial, created under the influence of man, due to his interests and goals (machine) and virtual (imaginary and, although they do not really exist, but functioning in the same way as if they actually existed).

· by main elements systems can be divided into abstract, all elements of which are concepts (languages, philosophical systems, number systems), and concrete, in which there are material elements.

· on interaction with the environment Distinguish between closed and open systems. Most of the studied systems are open, i.e. they experience and react to the environment and, in turn, affect the environment.

· by degree of difficulty distinguish between simple, complex and very complex systems.

· by natural separation systems are divided into: technical, biological, socio-economic.

· by description system variables : with qualitative variables (having only a meaningful description); with quantitative variables (having discretely or continuously quantitatively described variables).

· according to the type of description of the law (laws) of the functioning of the system: type “Black box” (the law of the system functioning is not completely known; only input and output messages of the system are known); not parameterized (the law is not described, we describe it using at least unknown parameters, only some a priori properties of the law are known); parameterized (the law is known up to parameters and it is possible to carry it from ADE to a certain class of dependencies); type “White (transparent) box” (the law is fully known).

· By the method of system management (in the system): externally controlled systems (without feedback, regulated, structurally, informationally or functionally controlled); managed from within (self-managing or self-regulating - programmatically controlled, automatically regulated, adaptable - adaptable with the help of controlled changes in states and self-organizing - changing their structure in time and space in the most optimal way, ordering their structure under the influence of internal and external factors); with combined control (automatic, semi-automatic, automated, organizational).

deterministic A system is called if its behavior can be predicted with absolute certainty. A system whose state depends not only on controlled, but also on uncontrolled influences, or if there is a source of randomness in it, is called stochastic. Let's give an example of stochastic systems, these are factories, airports, networks and computer systems, shops, consumer services, etc.

Dynamic systems are characterized by the fact that their output signals at a given time are determined by the nature of the input actions in the past and present (depending on the prehistory). Otherwise, the systems are called static.

An example of dynamic systems is biological, economic, social systems; such artificial systems as a factory, enterprises, a production line, etc.

Distinguish systems linear and non-linear. For linear systems the response to the sum of two or more different influences is equivalent to the sum of the responses to each perturbation separately, for non-linear ones this is not true.

If the parameters of the systems change over time, then it is called non-stationary, the opposite concept is the concept stationary systems.

An example of non-stationary systems are systems where processes, for example, aging, are significant in a given time interval.

If the input and output of the system is measured or changed in time discretely, through a step, then the system is called discrete. The opposite concept is the concept continuous systems. For example: computer, electronic clock, electric meter - discrete systems; hourglass, sundial, heating appliances, etc. are continuous systems.

Rice. 2.3 Classification of systems according to their properties.

(Arrows indicate a possible set of system properties)

Recently, so-called "hard" and "soft" systems have begun to be distinguished, mainly according to the criteria used for consideration.

The study of "hard" systems is usually based on the categories: "design", "optimization", "implementation", "goal function" and others. For "soft" systems, the following categories are used more often: "possibility", "desirability", "adaptability", "common sense", "rationality" and others. The methods are also different: for "hard" systems - optimization methods, probability theory and mathematical statistics, game theory and others; for "soft" systems - multicriteria optimization and decision making (often under uncertainty), Delphi method, catastrophe theory, fuzzy sets and fuzzy logic, heuristic programming, etc.

For the "transfer" of knowledge, systems invariants and system isomorphism are widely used. It is important not to violate the emergence property of the system in such a transfer.

test questions

1. How are systems classified?

2. What system is called big? complicated?

3. What determines the computational (structural, dynamic) complexity of the system? Give examples of such systems.

Theme 3

"Patterns of systems"

General system regularities are considered

Regularities of systems (in a more complete formulation - regularities of functioning and development of systems) - general system regularities that characterize the fundamental features of the construction, functioning and development of complex systems.

If the law is absolute and does not allow any exceptions, then the regularity is less categorical.

A regularity is a frequently observed, typical property (relationship or dependence) inherent in objects and processes, which is established by experience.

For us, the system-wide regularity is of the greatest interest.

System-wide patterns are patterns that characterize the fundamental features of the construction, functioning and development complex systems.

These patterns are inherent in any system, whether it be an economic, biological, social, technical or other system.

Such regularities L. von Bertalanffy initially called system parameters or principles, and A. Hall - macroscopic regularities.

one of the first regularity classifications proposed by V. G. Afanasiev. He divided patterns into 4 groups:

1. Patterns of interaction between the part and the whole: integrity or emergence, additivity, progressive systematization, progressive factorization, integrativity.

2. Patterns of hierarchical ordering: communication, hierarchy.

3. Patterns of systems feasibility: W. Ashby's law of "necessary diversity", equifinality, pattern of potential efficiency by B. S. Fleishman.

4. Patterns of systems development: historicity, self-organization.

Using the laws of construction, functioning and development of systems helps to clarify the idea of the object being studied or designed, allows you to develop recommendations for improving organizational systems, system analysis techniques.

1.3.2. Classification of systems according to the degree of organization and its role in the choice of methods for modeling systems

For the first time, the division of systems according to the degree of organization by analogy with the classification of G. Simon and A. Newell (well-structured, poorly structured and unstructured problems) was proposed by V.V. Nalimov, who singled out the class well organized and class poorly organized or probabilistic systems.

Later, to these two classes, another class was added self-organizing, complex, systems, which includes the classes of self-regulating, self-learning, self-tuning, etc., sometimes considered separately in the literature. systems.

The distinguished classes can practically be considered as approaches to modeling an object or a problem to be solved, which can be selected depending on the stage of cognition of the object and the possibility of obtaining information about it.

Below is a brief description of these classes.

1. Well organized (deterministic) systems - systems for which the researcher manages to determine all the elements and their relationships with each other and with the goals of the system in the form of deterministic (analytical, graphical) dependencies.

To display a complex object in the form of a deterministic system, it is necessary to single out the essential ones and not take into account the components that are relatively insignificant for a specific purpose of consideration.

Representation of an object in the form of a well-organized system is used in cases where a deterministic description can be proposed and the validity of its application has been experimentally shown, i.e., the adequacy of the model to a real object or process has been experimentally proven.

2. Poorly organized (probabilistic) systems. Such systems are characterized by probabilistic (stochastic) parameters defined by statistical methods on a fairly representative sample of factors representing the object or process under study.

Modeling of objects in the form of probabilistic systems is widely used in determining the throughput of systems of various kinds, in determining the number of staff in service, for example, repair shops of an enterprise and in service institutions (methods of queuing theory are used to solve such problems), in the study of documentary information flows etc.

3. Self-organizing (developing or complex) systems are characterized by a number of features, features that bring them closer to real developing objects.

These features, as a rule, are due to the presence of active elements (human) in the system, which, on the one hand, are a source of development and adaptability of the system during external environment, but on the other hand, it is a source of uncertainty and unpredictability of behavior that makes management difficult. Complex systems are characterized by non-stationary parameters and stochastic behavior.

These features are explained with the help of regularities of systems, the main groups of which are listed above.

An analysis of the activities of enterprises shows that if you do not create conditions for the development of an enterprise, such as the ability to adapt, develop behavior options, formulate goals, change the structure, etc., then the enterprise will not survive in an unstable environment. And the realization of these properties can be ensured by studying and using the patterns of functioning and development of self-organizing systems.

With the accumulation of experience in the study and transformation of systems with similar properties, their main feature was realized - fundamental limitation of a formalized description of developing, self-organizing systems. This feature, i.e., the need to combine formal methods and methods of qualitative analysis, is the basis of most models and methods of system analysis. When forming such models, the usual idea of models, which is characteristic of mathematical modeling and applied mathematics, changes. The idea of proving the adequacy of such models also changes.

The adequacy of the model is proved, as it were, sequentially (as it is formed) by evaluating the correctness of the reflection in each subsequent model of the components and relationships necessary to achieve the goals. In other words, such modeling becomes, as it were, a kind of “mechanism” for the development of the system.

The practical implementation of such a "mechanism" is associated with the need to develop a language for modeling the decision-making process. Such a language can be based on one of the systems modeling methods: for example, set-theoretic representations, mathematical logic, mathematical linguistics, simulation dynamic modeling, informational approach, etc. As the model evolves, methods may change.

The representation of an object in the form of a self-organizing system is used to solve the most complex problems inherent in decentralized systems with large initial uncertainty and unpredictability of the behavior of agents of economic relations. At the same time, the systemic "mechanism" of development (self-organization) can be implemented in the form of an appropriate approach (see Fig. Gradual formalization of the decision-making model. Graphosemiotic modeling or system analysis techniques) using various methods to implement its steps.

It is convenient to use the briefly described classes of systems as approaches at the initial stage of modeling any problem. These classes are assigned methods of formalized representation of systems Having determined the class of the system, it is possible to give recommendations on the choice of a method that will allow it to be displayed more adequately.

If a preliminary analysis of the problem situation shows that it can be represented as deterministic systems, then you can choose modeling methods from classes analytical and graphic methods. If experts in systems theory and systems analysis recommend representing the situation in the form poorly organized or probabilistic systems, you should first of all refer to statistical modeling .

When the situation is represented by a class self-organizing systems methods of discrete mathematics, fuzzy logic and cognitive modeling should be applied, in particular, set-theoretic representations, mathematical logic, mathematical linguistics.

The division of systems according to the degree of organization is proposed in continuation of the idea of dividing systems into well organized and poorly organized, or diffuse. To these two classes, another class has been added developing, or self-organizing systems. These classes are briefly characterized in Table. 3.4.

The classification under consideration uses the terms that existed at that time, but they are combined into a single classification, in which the selected classes are considered as approaches to displaying an object or a problem being solved, and their characteristics are proposed, which allows choosing a class of systems for displaying an object, depending on the stage of its cognition and the possibility getting information about it.

Table 3.4

Classification of systems according to F. E. Temnikov - V. N. Volkova

System class	a brief description of	Application possibilities
Well organized system	Representation of an object or decision-making process in the form of a well-organized system is possible in those cases when the researcher manages to determine all the elements of the system and their relationship with each other and with the goals of the system in the form deterministic(analytical, graphical) dependencies. This class is represented by most models of physical processes and technical systems. When an object is represented by this class of systems, the selection problems goals and definitions funds their achievements (elements, connections) are not shared. The problem situation can be described as expressions linking the end with the means(i.e. in the form of a performance criterion, criterion or performance indicator, objective function, etc.), which can be represented by an equation, formula, system of equations	It is used in those cases when a deterministic description can be proposed and the validity of its application has been experimentally shown, i.e. experimentally proven adequacy model of a real object or process. Attempts to apply this class of systems to represent complex multi-component objects or multi-criteria tasks that have to be solved when developing technical complexes, improving the management of enterprises and organizations, etc., are practically futile, since this requires an unacceptably large amount of time to form a model, and, in addition, as a rule, it is not possible to set up an experiment proving the adequacy of the model
Poorly organized, or diffuse, system	When presenting an object as a poorly organized, or diffuse, system, the task is not to determine all the components and their connections with the goals of the system. The system is characterized by a certain set of macro parameters and regularities that are revealed on the basis of a study of a fairly representative system defined using certain rules. samples components that display the object or process under study. On the basis of such selective studies receive characteristics, or patterns(statistical, economic, etc.) and extend these patterns to the behavior of the system as a whole from some probability(statistical or in the broad sense of the use of the term)	Displaying objects in the form of diffuse systems is widely used in determining the throughput of systems of various kinds, in determining the number of staff in service, for example, repair shops of an enterprise, in service institutions (methods of queuing theory are used to solve such problems), etc. When applying this class of systems, the main problem is to prove the adequacy of the model. When statistical regularities adequacy is determined by the representativeness of the sample. For economic regularities methods of proving the adequacy ns investigated
self-organizing, or developing, systems	Class self-organizing or developing, systems are characterized by a number of features, features that bring them closer to real developing objects (see paragraph 1.3 for more details). In the study of these features, an important difference between developing systems with active elements and closed systems was revealed - fundamental limitation of their formalized description. This feature leads to the need to combine formal methods and methods of qualitative analysis. Therefore, the main constructive idea of modeling when displaying an object by a class of self-organizing systems can be formulated as follows. A sign system is being developed, with the help of which the currently known components and relationships are fixed, and then, by transforming the resulting display using the selected or accepted approaches and methods (structuring or decompositions", compositions, search proximity measures on the state space, etc.), receive new, previously unknown components, relationships, dependencies, which can either serve as a basis for decision-making, or suggest subsequent steps towards preparing a decision. Thus, it is possible to accumulate information about the object, while fixing all the new components and connections (the rules for the interaction of components), and, using them, to obtain mappings of the successive states of the developing system, gradually forming an increasingly adequate model of a real, studied or created object. At the same time, information can come from specialists in various fields of knowledge and accumulate over time as it arises (in the process of knowing an object)	The mapping of systems by this class allows one to study the least studied objects and processes with a large uncertainty at the initial stage of the problem statement. Examples of such tasks are the tasks that arise in the design of complex technical complexes, in the study and development of management systems for organizations. Most of the models and methods of system analysis are based on the representation of objects in the form of self-organizing systems, although this is not always specifically stipulated. When forming such models, the usual idea of models, which is characteristic of mathematical modeling and applied mathematics, changes. The idea of proving the adequacy of such models also changes. The adequacy of the model is proved, as it were, sequentially (as it is formed) by evaluating the correctness of the reflection in each subsequent model of the components and relationships necessary to achieve the goals. When an object is represented by a class of self-organizing systems, the tasks of determining goals and choosing means are, as a rule, separated. At the same time, the tasks of determining goals and choosing means, in turn, can be described as self-organizing systems, i.e. development of the structure of the main directions of development of the organization, the structure of the functional part of the automated control system, the structure of the supporting part of the automated control system, the organizational structure of the enterprise, etc. should also be seen as developing systems

Class self-organizing or developing, systems is characterized by a number of specific features, features (Table 3.5). The table first shows the features that bring them closer to real developing objects, and the last three features are the payment for these, which are important for the development of systems.

Table 3.5

Features of developing systems with active elements

Peculiarity	a brief description of
Ability adapt to changing environmental conditions and interference	This property seems to be very useful. However, adaptability can manifest itself not only in relation to interference, but also in relation to control actions, which makes it very difficult to control the system.
Fundamental disequilibrium	When studying the differences between living, developing objects and non-living ones, biologist Erwin Bauer hypothesized that the living is fundamentally in an unstable, non-equilibrium state, and moreover, it uses its energy to maintain itself in a non-equilibrium state (which is life itself). This hypothesis is increasingly supported by modern research. In this case, problems of maintaining the stability of the system arise.
Ability resist entropy(destroying the system) trends and show negentropic tendencies	It is due to the presence of active elements that stimulate the exchange of material, energy and information products with the environment and show their own "initiatives", an active principle. Due to this, in such systems, the regularity of the increase in entropy (similar to the second law of thermodynamics, acting in closed systems, the so-called "second law") is violated, and even negentropic trends, i.e. actually self-organization, development, including " free will"
The ability to produce behavior options and change your structure	This property can be provided using various methods that allow you to form a variety of models of decision-making options, reach a new level equifinality while maintaining the integrity and basic properties
Ability and desire to goal setting	Unlike closed (technical) systems, in which goals are set from the outside in systems with active elements, goals are formed inside systems (for the first time this feature in relation to economic systems was formulated Yu. I. Chernyak, goal setting is the basis of negentropic processes in socio-economic systems
Ambiguity concepts	For example, "goal" - "means", "system" - "subsystem", etc. This feature is manifested in the formation of goal structures, in the development of projects for complex technical complexes, automated control systems, etc., when the persons who form the structure of the system, calling some part of it a subsystem, after a while begin to talk about it as a system , without adding the prefix "under", or subgoals begin to be called means to achieve higher goals. Because of this, protracted discussions often arise, which are easily resolved with the help of the communicative pattern, the property of "two-faced Janus" (see paragraph 1.5)
non-stationarity(variability, instability) of parameters and stochasticity behavior	This feature is easily interpreted for any systems with active elements (living organisms, social organizations, etc.), causing their behavior to be stochastic.
Uniqueness and unpredictability system behavior in specific conditions	These properties are manifested in the system due to the presence of active elements in it, as a result of which the system, as it were, manifests "free will", but at the same time, there is also the presence limit possibilities, determined by the available resources (elements, their properties) and structural connections characteristic of a certain type of systems

These features have a variety of manifestations, which can sometimes be distinguished as independent features. These features, as a rule, are due to the presence of active elements in the system and are of a dual nature: they are new properties that are useful for the existence of the system, its adaptability to changing environmental conditions, but at the same time cause uncertainty and make it difficult to control the system.

Some of the features considered are characteristic of diffuse systems (stochastic behavior, instability of individual parameters), but most of the features are specific features that significantly distinguish this class of systems from others and make their modeling difficult.

At the same time, when creating and organizing enterprise management, they often seek to display them using the theory of automatic regulation and control, which was developed for closed technical systems and significantly distorts the understanding of systems with active elements, which can harm the enterprise, make it an inanimate "mechanism", not able to adapt to the environment and develop options for their development.

Such a situation began, in particular, to be observed in our country in the 1960s and 1970s, when too strict directives began to hinder the development of industry.

The considered features are contradictory. In most cases, they are both positive and negative, desirable and undesirable for the system being created. It is not immediately possible to understand and explain them, to select and create the required degree of their manifestation. Philosophers, psychologists, specialists in systems theory are studying the reasons for the manifestation of such features of complex objects with active elements, who, in order to explain these features, propose and investigate patterns of systems. The main regularities of the construction, functioning and development of systems that have been studied so far and explain these features will be considered in the next paragraph.

The manifestation of contradictory features of developing systems and the laws that explain them in real objects must be studied, constantly monitored, reflected in models, and search for methods and means to regulate the degree of their manifestation.

At the same time, one should keep in mind the important difference between developing systems with active elements and closed ones. Trying to understand the fundamental features of modeling such systems, the first researchers already noted that, starting from a certain level of complexity, the system is easier to manufacture and put into operation, transform and change than to be displayed by a formal model.

With the accumulation of experience in the study and transformation of such systems, this observation was confirmed and their main feature was realized - the fundamental limitation of a formalized description of developing, self-organizing systems.

This feature, i.e. the need to combine formal methods and methods of qualitative analysis is the basis of most models and methods of system analysis. When forming such models, the usual idea of models, which is characteristic of mathematical modeling and applied mathematics, changes. The idea of proving the adequacy of such models also changes.

The main constructive idea of modeling when displaying an object as a class of self-organizing systems can be formulated as follows.

A sign system is being developed, with the help of which the currently known components and connections are fixed, and then, by transforming the resulting display using the established (accepted) rules (rules structuring, or decomposition, rules compositions, search proximity measures on the state space), receive new, previously unknown components, relationships, dependencies, which can either serve as a basis for decision-making, or suggest the next steps towards preparing a decision.

Thus, it is possible to accumulate information about the object, while fixing all the new components and connections (rules of interaction between components), and, applying them, obtain mappings of the successive states of the developing system, gradually creating an increasingly adequate model of a real, studied or created object. At the same time, information can come from specialists in various fields of knowledge and accumulate over time as it arises (in the process of knowing an object).

In other words, such modeling becomes, as it were, a kind of "mechanism" for the development of the system. The practical implementation of such a "mechanism" is associated with the need to develop a language for modeling the decision-making process. Such a language (sign system) can be based on one of the systems modeling methods (for example, set-theoretic representations, mathematical logic, mathematical linguistics, simulation dynamic modeling, information approach, etc.), but as the model develops, the methods can change.

Problem situations with a large initial uncertainty are more consistent with the representation of an object by a third class of systems. In this case, modeling becomes, as it were, a kind of "mechanism" for the development of the system. The practical implementation of such a "mechanism" is associated with the need to develop a language for modeling the decision-making process.

Such a language (sign system) can be based on one of the systems modeling methods (for example, set-theoretic representations, mathematical logic, mathematical linguistics, simulation dynamic modeling, etc.). When modeling the most complex processes (for example, the processes of goal formation, improvement of organizational structures, etc.), the "mechanism" of development (self-organization) can be implemented in the form of an appropriate methodology for system analysis. On the considered idea of modeling when displaying an object by a class of self-organizing systems, the one proposed in Chap. 4 method of gradual formalization of the decision-making model.

When modeling the most complex processes (for example, goal-setting processes, improving organizational structures, etc.), the "mechanism" of development (self-organization) can be implemented in the form of an appropriate system analysis methodology (examples are discussed in the textbook and reference books).

The considered class of systems can be divided into subclasses, highlighting adaptive, or self-adjusting, systems, self-learning systems, self-healing, self-reproducing and similar classes in which the features considered above and not yet studied (for example, for self-reproducing systems) are realized to varying degrees.

When an object is represented by a class of self-organizing systems, the tasks of determining goals and choosing means are, as a rule, separated. At the same time, the tasks of determining goals and choosing means, in turn, can be described as self-organizing systems, i.e. the structure of the main directions of the plan, the structure of the functional part of the automated control system should develop in the same way (and even here it is necessary to include the "mechanism" of development more often), as well as the structure of the supporting part of the automated control system, organizational structure enterprises, etc.

Most of the examples of methods, models and techniques of system analysis considered in the following chapters are based on the representation of objects in the form of self-organizing systems, although this will not always be specifically stipulated.

It is convenient to use the considered classes of systems as approaches at the initial stage of modeling any problem. These classes can be associated with methods of formalized representation of systems, and thus, having determined the class of the system, it is possible to give recommendations on choosing a method that will allow it to be displayed more adequately.

Volkova V. N. Approach to the choice of the method of formalized representation of systems / V. II. Volkova, F. E. Temnikov // Modeling of complex systems. M.: MDNTP, 1978. S. 38-40.
Nalimov V. V. Influence of ideas of cybernetics and mathematical statistics on the methodology scientific research// Methodological problems of cybernetics: materials for the All-Union Conference. T. 1. M.: 1970. S. 50-71.

The division of systems according to organization corresponds to their characteristics. These are such systems as: well organized; poorly organized; developing or self-organizing.

K good organized systems we relate objects with well-defined elements, relationships between them, clearly set goals and objectives associated with the means. Well-organized systems are characterized by systems of performance indicators, performance indicators, tools for implementing management, control and feedback.

When presenting an object as a poorly organized, or diffuse, system, the task is not to determine all the components and their connections with the goals of the system. The system is characterized by a certain set of macro-parameters and regularities that are revealed on the basis of a study of a fairly representative sample of components determined with the help of certain rules that reflect the object or process under study. On the basis of such a selective study, characteristics or patterns are obtained that apply to the behavior of the system as a whole with some probability.

The class of self-organizing or developing systems is characterized by a number of features, features, which, as a rule, are due to the presence in the system of active elements that are of a dual nature, being at the same time useful for the existence of the system with their properties of good adaptation to changing environmental conditions, but at the same time causing uncertainty making it difficult to control the system. The class of systems under consideration can be divided into subclasses, identifying adaptive or self-adapting systems, self-learning systems, self-healing, self-reproducing classes of systems.

Patterns of system processes

The patterns of functioning and development of systems that characterize the fundamental features of the construction, functioning and development of complex systems can be conditionally divided into four groups:

Regularities of interaction of the part and the whole;

· Patterns of hierarchical ordering;

· Patterns of feasibility of systems;

· Patterns of systems development.