Classification of systems, Examples of systems classification...

Classification of systems

System classification examples

Systems are divided into classes according to different characteristics, and depending on the problem being solved, different classification principles can be chosen.

There have been attempts to classify systems according to the following criteria:

by the type of the displayed object (technical, biological, economic, etc. systems)

type of scientific direction, used for their modeling (mathematical, physical, chemical, etc.);

interactions with the environment (open and closed);

magnitude and complexity.

It was also suggested to distinguish the following types of systems:

deterministic and stochastic;

abstract and material (existing in objective reality); and so on

Classifications are always relative. So, in the deterministic system, we can find stochasticity elements , and, on the contrary, the deterministic system can be considered a special case of stochastic (with probability equal to one).

Similarly, if we take into account the dialectics of the subjective and objective in the system, then the relativity of the separation of systems into abstract and objectively existing: this can be the stages of development of one and the same same system.

Indeed, natural and artificial objects, reflected in the mind of a person, act as abstractions, concepts, and abstract projects of the created systems are embodied in real objects that can be felt, and when reflected in the study again reflected as an abstract system.

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However, the relativity of classifications should not stop researchers. The goal of any classification is to limit the choice of approaches to the system's mapping, to compare selected techniques and methods of system analysis to selected classes, and to give recommendations on the choice of methods for the corresponding class of systems. In this case, the system, in principle, can be simultaneously characterized by several features, i.e. It can be found simultaneously in different classifications, each of which can be useful in selecting modeling methods.

Consider some of the most important classifications of systems.

Open and closed systems. The concept of open system introduced L. von Bertalanffy [16, 17, 107]. The main distinguishing features of open systems are the ability to exchange mass, energy and information with the environment. In contrast, it is assumed that closed systems (of course, to the accuracy of the accepted sensitivity of the model) are completely deprived of this ability, i.e. isolated from the environment.

Special cases are possible: for example, gravitational and energy processes are not taken into account, and in the model of the system only information exchange with the environment is reflected; then talk about information-permeable or, respectively, information-impenetrable systems.

With the model of the open system Bertalanffy can be found in his books on the general theory of systems [16,17]. There are also some interesting features of open systems.

One of the most important is as follows. In open systems, thermodynamic regularities appear that seem paradoxical and contradict the second law of thermodynamics [17, p. 42]. Recall that the second law of thermodynamics ("the second beginning"), formulated for closed systems, characterizes the system as entropy growth, aspiration for disorder, destruction.

This law manifests itself in open systems (for example, the aging of biological systems). However (in contrast to closed systems), in open systems, the entropy entropy is possible, its decrease; "Similar systems can maintain their high level and even evolve towards increasing order of complexity [17, p. 42], i.e. in them the regularity of self-organization considered in the next paragraph (although Bertalanffy has not yet used this term) appears. That is why it is important for the management system to maintain a good exchange of information with the environment.

Purposeful, purposeful systems. When studying economic, organizational objects, it is important to distinguish a class of purposeful or purposeful systems [91, 92, etc. .

In this class, in turn, you can select systems in which targets are set from outside (usually this is the case in closed systems), and systems in which the targets are formed inside (which is typical for open, self-organizing systems).

The patterns of goal-forming in self-organizing systems are discussed below. Techniques that help shape and analyze the structure of goals are described in Ch. 7.

Classification of systems by complexity. There are several approaches to separating systems by complexity.

In the beginning, the terms large system and the complex system are used as synonyms.

Some researchers have linked complexity to the number of elements.

Example

Mr. N. Povarov , depending on the number of elements entering the system, allocates four of their classes: small systems (10-103 elements), complex (104-106 elements), ultrasolid (107-1030 elements), super-systems (1030-10200 elements).

Have. R. Ashby believed that the system is large from the point of view of the observer, whose possibilities it surpasses in some aspect important for achieving goals.

In this case, the same material object, depending on the purpose of the observer and the means at his disposal, can be displayed or not displayed by the large system, and, in addition, the physical dimensions of the object are not a criterion the assignment of an object to the class of large systems.

N . P. Buslenko suggested (by virtue of the lack of a clear definition of the classification of the system as a category of large and relative conventionality of this concept) to associate the concept of "large system" with what role in the study of the system complex system-wide issues, , which, naturally, depends on the properties of systems and classes of problems to be solved.

This point of view is also shared by the authors of the first in our country of the textbook on the theory of large control systems A. A. Denisov and D. N. Kolesnikov [5].

For the spheres of biological, economic, social systems, sometimes the notion of a large system was associated, to a large extent, with the important concepts "emergence", "openness", "activity of the elements". As a result, such a system has, as it were, "free will", unstable and unpredictable behavior and other characteristics of developing, self-organizing systems.

At the same time, there are other points of view: since these are different words in natural language, then they need to be used as different concepts.

However, some authors link the concept of "large system" with the size of the system, the number of elements (often relatively homogeneous), and the concept of "complex system" - with the complexity of relations, algorithms. As a basis for the classification of B. C. Fleishman takes the complexity of the behavior of the system [85].

There are more convincing justifications for the difference between the concepts large system and complex system .

In particular, Yu. I. Chernyak suggests calling a large system one that can not be explored except by subsystems & quot ;, and complex - such a system that is built to solve a multi-task, multidimensional task. " [91, p. 22].

Explaining these concepts on the examples, Yu. I. Chernyak emphasizes that in the case of large systems, the object can be described as if it were in one language, ie. using a single method of modeling, albeit in parts, subsystems (Figure 1.20, a). A complex system reflects the object "from different sides in several models, each of which has its own language", and to reconcile these models a special metalanguage is needed (Figure 1.20, b ).

The notion of a large and complex system Chernyak associates with the concept of "observer" (in Figure 1.20, the "observers" are represented by rectangles): to study the large of the system, you need one "observer" (we do not mean the number of people taking part in the research or design of the system, but the relative homogeneity of their qualifications: for example, an engineer or an economist), and for understanding an complex system, you need several observers, fundamentally different qualifications (for example, a mechanical engineer, a programmer, a computer engineer, an economist, and possibly a lawyer, a psychologist, etc.).

Fig. 1.20

It emphasizes the presence of complex system "complex, compound goal" or even different targets and at the same time many structures at the same system (for example, technological, administrative, communication, functional, etc.) [92, p. 22].

In the following Chernyak refines these definitions. In particular, when defining a large system, it introduces the concept of & apos; a priori dedicated subsystems [91, p. 28-29], and in the definition of complex - the concept of incomparable aspects of the characteristic of the object, and includes in the definition the necessity of using several languages ​​and different models [92, p. 32].

One of the most complete and interesting classifications by complexity levels is offered To. Boulding [38, p. 106-124; 108]. The levels identified in it are given in Table. 1.4.

Table 1.4

Type

Difficulty level

Examples

Non-living systems

Static structures (skeletons).

Simple dynamic structures with a prescribed law of behavior.

Cybernetic systems with controlled feedback loops

Crystals. Clockwork. Thermostat

Live

Systems

Open systems with a self-preserving structure (the first stage, on which separation into living and non-living is possible).

Cells, homeostat.

Living organisms with low ability to perceive information.

Plants.

Living organisms with a more developed ability to perceive information, but not possessing self-awareness.

Animals.

Systems characterized by self-awareness, thinking and non-trivial behavior.

People.

Social systems.

Transcendental systems or systems that are currently outside our cognition

Social

Organization

In the K classification. Boulding each subsequent class includes the previous one, characterized by a greater manifestation of the properties of openness and stochastic behavior, more pronounced manifestations of the regularities of hierarchy and historicity (discussed in paragraph 1.6), although this is not always noted, but also more complex mechanisms functioning and development.

Evaluating classifications from the point of view of their use when choosing methods for modeling systems, it should be noted that such recommendations (up to the choice of mathematical methods) are available only for classes of relatively low complexity (in the classification K. Boulding , for example, -for the level of inanimate systems). For more complex systems, it is stipulated that it is difficult to give such recommendations. Therefore, further on, a classification is considered in which an attempt is made to relate the choice of modeling methods to all classes of systems. The basis of this classification is the degree of organization.

Classification of systems by degree of organization. The separation of systems by degree of organization is suggested in continuation of the idea of ​​their division into well-organized and poorly organized, or diffuse . To these two classes, another class of developing, or self-organizing systems was added. These classes are summarized in Table. 1.5.

Table 1.5

Class

Systems

Brief description

Features

Applications

1. Well organized

The representation of the object or decision-making process in the form of a well-organized system is possible in those cases when the researcher can determine all its elements and their interrelations with each other and with the purposes of the system in the form of deterministic (analytical, graphical) dependencies.

This class of systems includes most models of physical processes and technical systems.

When an object is represented by this class of systems, the tasks of selecting purposes and determining the means of achieving them (elements, links) are not separated. The problem situation can be described in the form of expressions linking the target to the means (ie, in the form of a criterion of functioning, a criterion or an efficiency measure, an objective function, etc.) that can be represented by an equation, formula, system of equations

This class of systems is used in those cases where a deterministic description can be offered and experimentally shown the legitimacy of its application, i.e. experimentally proved the adequacy of the model to a real object or process. Attempts to apply this class of systems to represent complex multicomponent objects or multicriteria tasks that have to be solved when developing technical complexes, improving the management of enterprises and organizations, etc., are practically unsuccessful. This requires an unacceptably high time consuming to model the model, and in addition, as a rule, it is not possible to put an experiment proving the adequacy of the model

2. Poorly organized, or diffuse

When presenting an object in the form of a poorly organized, or diffuse, system, it is not the task to determine all the components and their connections to the purposes of the system. The system is characterized by a certain set of macroparameters and regularities, which are revealed on the basis of an investigation of a sufficiently representative sample of components that represent the object or process that is determined by means of some rules.

Based on such, selective, studies receive characteristics or regularities (statistical, economic, etc.), and distribute these patterns to the behavior of the system 8 as a whole with some probability (statistical or broad sense of the use of this term)

The display of objects in the form of diffuse systems is widely used in determining the capacity of systems of all kinds, in determining the number of states in the servicing, for example, repair shops of the enterprise, in servicing institutions (for solving similar problems, methods of queuing theory are used) and other. When applying this class of systems, the main problem is the proof of the adequacy of the model.

In the case of statistical patterns, adequacy is determined by the representativeness of the sample. For economic patterns, the methods of proving adequacy are not investigated.

3. Self-organizing, or evolving

Class of self-organizing, or developing, systems is characterized by a number of features, features that approximate them to real developing objects (for more details see Table 1.6). When studying these features, an important difference between developing systems and active elements from closed ones is revealed - the fundamental limitation of their formalized description.

This feature leads to the need for a combination of formal methods and methods of qualitative analysis. Therefore, the basic idea of ​​mapping a projected object by the class of self-organizing systems can be formulated as follows. A sign system is developed that fixes the currently known components and relationships, and then by transforming the resulting mapping using the selected or accepted approaches and methods ( structuring, or decomposition, composition, of the search for proximity measures on the state space, etc.) receive new, previously unknown components, relationships, dependencies that can either serve as the basis for decision-making, or suggest further steps in the preparation of a solution. Thus, it is possible to accumulate information about an object, fixing all new components and connections (rules of interaction of components), and applying them, to obtain maps of successive states of the developing system, gradually forming an increasingly adequate model of the real, studied or created object. At the same time, information can come from specialists in various fields of knowledge and accumulate in time as it occurs (in the process of knowing the object)

The mapping of the studied object as a system of this class makes it possible to study the least studied objects and processes with great uncertainty at the initial stage of setting the problem. Examples of such problems are the problems arising in the design of complex technical complexes, research and development of organizational management systems.

Most of the models and techniques of system analysis are based on the representation of objects in the form of self-organizing systems, although this is not always specified. In the formation of such models, the usual notion of models, typical for mathematical modeling and applied mathematics, changes. The idea of ​​the adequacy of such models also changes. The adequacy of the model is proved, as it were, consistently (as it is formed) by estimating the correctness of the reflection in each subsequent model of the components and connections necessary to achieve the set goals.

When an object is represented by a class of self-organizing systems, the tasks of determining goals and selecting funds are usually divided. In this case, the tasks of determining goals, selecting funds, in turn, can be described in the form of self-organizing systems, i.e. the structure of the main directions of the development of the organization, the structure of the functional part of the automated control system, the structure of the part of the automated control system, the organizational structure of the enterprise, etc. should also be seen as developing systems

In the proposed classification of systems used by the mid-70's. XX century. terms, but they are combined into a single classification in which the selected classes are viewed as approaches to the object mapping or problem solving and their characteristics are proposed, which allows choosing a class of systems for the object display depending on the stage of its cognition and the possibility of obtaining information about it. >

Problem situations with a large initial uncertainty correspond more closely to the representation of the object in the form of a third-class system. In this case, the simulation becomes, as it were, a kind of "mechanism" development of the system. The practical implementation of this mechanism is connected with the need to develop the order of building a model of the decision-making process. The construction of the 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 modeling, etc. .). When modeling the most complex processes (for example, the processes of forming goal structures, improving organizational structures, etc.), the "mechanism" development (self-organization) can be implemented in the form of an appropriate methodology of system analysis. The method of gradual formalization of the decision-making model, characterized in Chap. 5, is based on the idea of ​​mapping an object in the process of its representation by a class of self-organizing systems. 4.

The class of self-organizing, or developing, systems is characterized by a number of features or features that approximate them to real developing objects (Table 1.6).

The listed characteristics of self-organizing, or developing, systems 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 useful for the existence of the system, its adaptation to changing environmental conditions, but at the same time cause uncertainty, make it difficult to manage the system.

We did not provide detailed explanatory examples, as each student can easily discover most of the above features by the example of his own behavior or the behavior of his friends, the collective in which he studies.

Some of the features considered are typical for diffuse systems ( stochastic behavior, instability of individual parameters ), but most of them are specific features that significantly differentiate this class of systems from others and make them difficult to model. >

At the same time, when creating and organizing management, enterprises often seek to present them using the theory of automatic regulation and management developed for closed, technical systems and significantly distorting the understanding of systems with active elements, which can harm the enterprise, make it lifeless mechanism, "unable to adapt to the environment and develop options for its development.

Such a situation became, in particular, observed in the former USSR in the 60-70-ies. XX century, when too rigid directives began to restrain the development of industry.

Table 1.6

Feature

Brief description

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 stochastic behavior

Uniqueness and unpredictability of system behavior under 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 manifests as "freedom of will", but at the same time, there are limiting possibilities defined available resources (elements, their properties) and structural bonds characteristic for a certain type of system

Ability to adapt to changing environmental conditions and interference

This property, it would seem, is very useful. However, adaptivity can be manifested not only in relation to interference, but also in relation to control actions, which makes it very difficult to manage the system

Principal

nonequilibrium

In exploring the differences between living, developing objects and inanimate biologists, Erwin Bauer hypothesized that the living entity is fundamentally in an unstable, nonequilibrium state and, moreover, uses its energy to sustain itself in a non-equilibrium state (which is actually life itself). This hypothesis is increasingly confirmed in modern studies. This raises the problem of maintaining the stability of the system

Ability to withstand entropy (destroying system) tendencies and manifest negentropic tendencies

It is caused by the presence of active elements, stimulating the exchange of material, energy and information products with the environment and showing their own initiatives, active principle. Due to this, in such systems, the law of increasing entropy (analogous to the second law of thermodynamics acting in closed systems, the so-called "second start") is violated, and even negentropic tendencies, i.e. actually self-organization, development, including "free agency"

Ability to develop behaviors and change their structure

This property can be provided with the help of various methods allowing to form various models of decision-making options, to enter a new level of equifinality, while preserving the integrity and basic properties

Ability and aspiration for goal-setting

In contrast to closed (technical) systems, to which targets are set from outside, in systems with active target elements are formed inside of the system (for the first time this feature was applied to economic systems Yu. I. Cherniak [92]); goal-formation - the basis of negentropic processes in socio-economic systems

Ambiguity

Usage

concepts

For example, the target means & quot ;, system-subsystem etc. This feature is manifested in the formation of target structures, the development of projects of complex technical complexes, automated control systems, etc., when the persons forming the structure of the system, calling some part of it a subsystem, after a while start talking about it as a system, without adding prefixes "under", or subgoals begin to be called means for achieving higher goals. Because of this, often there are protracted discussions that are easily resolved with the help of the regularity of communicativity, the properties of the "two-faced Janus" (see details in section 1.6)

These features are contradictory. In most cases, they are both positive and negative, desirable and undesirable for the system being created. Signs of systems can not immediately be understood and explained, to choose and create the required degree of their manifestation. Investigations of the reasons for the manifestation of such features of complex objects with active elements are dealt with by philosophers, psychologists, system theory specialists who, in order to explain these features, propose and investigate the regularities of systems. The main regularities of the construction, functioning and development of systems , explaining these features, will be considered in the next paragraph.

The manifestation of the contradictory features of developing systems and the explanation of their regularities on the example of real objects must be studied, constantly monitored, reflected in models and sought 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 and active elements from closed ones: trying to understand the fundamental features of modeling such systems, the first researchers noted that starting from a certain level of complexity, the system is easier to manufacture and put into operation, and change what to display with a formal model.

With the accumulation of experience in research and transformation of such systems, this observation was confirmed, and their main feature was recognized - the fundamental limitation of the 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 for most models and methodologies of system analysis. In the formation of such models, the usual notion of models, typical for mathematical modeling and applied mathematics, changes. The representation of the adequacy of such models also changes.

The basic constructive idea of ​​modeling in the mapping of an object by the class of self-organizing systems can be formulated as follows.

A sign system is being developed that fixes the currently known components and relationships, and then by transforming the already existing mapping using the established rules (structuring rules or decomposition; of the composition rules, of the proximity measures on the state space), new components unknown earlier, relationships, dependencies that can either serve as the basis for decision-making, or prompt subsequent ones Steps to prepare a solution.

Thus, it is possible to accumulate information about an object, fixing all new components and connections (rules of interaction of components), and applying them, to obtain maps of 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 different fields of knowledge and accumulate in time as it occurs (in the process of knowing the object).

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

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

When modeling the most complex processes (for example, goal-building processes, improving organizational structures, etc.) mechanism development (self-organization) can be implemented in the form of appropriate methodology of system analysis (examples of which are considered in the applied chapters of the textbook).

The considered class of systems can be divided into subclasses, selecting adaptive or self-adapting systems, self-learning systems, self-healing, self-reproducing etc. classes of systems in which the properties considered above and those 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 selecting funds are usually divided. In this case, the tasks of determining goals, in turn, can be described in the form of self-organizing systems, i.e. the structure of the main directions of the development of the enterprise, the plan, the structure of the functional part of the automated control system, etc.) should develop (and even here it is necessary to include the "development mechanism" more often), as well as the tasks of selecting the means, developing the structure of the providing part of the ACS, the organizational structure of the enterprise and e.

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

The considered classes of systems are convenient to use as approaches at the initial stage of modeling any problem. These classes are associated with the methods of formalized representation of systems (Chapter 2), and thus, by defining the class of the system, one can give recommendations on the choice of a method that will allow it to be more adequately displayed.

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