# Basic terminology of the theory of systems, Concept of the system...

## The concept of the system

We can assume that the concept of system arose in the ancient world, when Aristotle paid attention to the fact that the whole (ie the system) is irreducible to the sum of the parts that make it up.

The need for the use of this term arises when it is impossible to demonstrate something, to represent it, to represent it with a mathematical expression, and it needs to be emphasized that it will be big, complex, not completely immediately understandable (with uncertainty), while a single, unified .

For example, the solar system, the system of organizational management of an enterprise (city, region, etc.), the economic system, the circulatory system, etc.

In mathematics, the term system use to display a collection of mathematical expressions or rules: a system of equations, a system of measures, etc. It would seem that in these cases it would be possible to use the terms set or aggregate & quot ;. However, the concept of systems emphasizes the orderliness, integrity, manifestation of the regularity of emergence (the appearance of a whole new properties in comparison with the properties of elements) and other patterns of their construction, functioning and development.

To apply the term system when researching, designing, or managing, it is necessary to give a more precise definition to this concept.

## Development of the system definition

The term system and related concepts of a complex, systemic approach, philosophers, biologists, psychologists, cybernetics, physicists, mathematicians, economists, engineers of various specialties are exploring and analyzing.

There are several dozen definitions of this concept. Their analysis shows that the definition of the concept system changed not only in form, but also in content.

In the first definitions, the system was considered as a collection of only elements a i and links r j between them:

(3.1)

In the above formalized definition records, various methods of set-theoretical representations are used.

With such formalized records, the definition of L. von Bertalanffy's system can be displayed: the complex of interacting components .

In the Great Soviet Encyclopedia, the system is defined by a direct translation from the Greek σύστημα, which means συ-στημα - co-become & quot ;, i.e. composed, connected from parts.

Terms elements - Components & quot ;, links - Relationships are commonly used as synonyms (especially in definitions translations). However, strictly speaking, the components - a concept more general than the "elements". Concerning the concepts connection and relation there are also different points of view.

If the elements are fundamentally non-uniform, sometimes this was immediately taken into account in the definition, distinguishing different sets of elements A = { a i} and B = {b k }. In the definition of M. Mesarowicz . for example, a set of X input objects (affecting the system) and a set of Y output results, and between them a generalizing intersection relation is established, which can be displayed either as the author of the definition:

(3.16)

or using other notation of intersection:

(3.1c)

Then the definitions began to take into account the properties of Q ( A. Hall , AI Uyomov, etc.):

(3.2)

A. Hall calls properties attributes.

A. I. Uyomov, defining the system through the concepts of things, properties, relations, proposed dual definitions, in one of which the properties q i, are characterized by the elements (things) a i, and in the other - the properties q j characterize the relations (relations) r j.

(3.2, a)

In the future, in the definitions of the system appears the notion the goal. » At first - in an implicit form: in the definition of FE Temnikov, the system - organized (in which the goal appears when the concept of is organized »is opened). Then - in the form of the final result, the system-forming criterion, the function (for more details, see [1,19]), and later - and in an explicit form:

(3.3)

where Z is the goal, aggregate or structure of goals.

In the definition of In. N. Sagatovsky the goal-setting conditions are specified - medium SR, time interval ΔТ, ie. the period within which the system will exist and its purposes: the system - the " finite set of functional elements and the relationships between them , selected from the environment in accordance with a specific goal within a certain time interval :

(3.3, a)

In the following, the definition suggests taking into account the observer N.

(3.4)

The necessity of taking into account the interaction between the studied system and the researcher was originally indicated by WR Ashby. Yu. I. Chernyak gave the first definition, in which the observer was explicitly included: "The system is a reflection in the consciousness of the subject (researcher, observer) of the properties of objects and their relations in solving the problem of research, cognition" .

(3.5)

In the following variants of this definition, I. I. Chernyak began to take into account the observer's language L N : The system is a mapping in the observer's language of objects, relations and their properties in solving the problem of research, cognition .

(3.5, a)

In the expressions (3.5) and (3.5, a) the complex concept of the goal is replaced by a more concrete notion - the Z problem.

In a number of definitions, the main components - the elements, the relationships (relations) are detailed taking into account the specific features of the spheres of activity, include the transformation rules in the form of functions, operations, models.

There were definitions in which there were even more components, which helped in the study and design of systems of a certain physical nature.

Of course, from the very beginning, the definitions implied that the system is something whole. In the philosophical vocabulary, the system is the "set of elements that are in relationships and relationships with each other and form some integral unity" . Therefore, some researchers first of all defined the system on the basis of its separation from the environment and determining the relationship with it.

A particular case of system isolation from the environment is its definition through inputs and outputs by means of which the system communicates with the environment. In cybernetics, such a representation of the system is called the "black box & quot ;. On this model, the initial definition of the W.R. Ashby system was based.

In one of the works of L. von Bertalanffy defined the system as "a collection of elements that are in a certain relationship with each other and with the environment" .

The complex interaction of the system with its environment is reflected in the definition of В. N. Sadovsky and E. G. Yudin : "... 2) it forms a special unity with the environment; 3) as a rule, any investigated system is an element of a system of a higher order; 4) the elements of any system under investigation, in turn, usually act as systems of lower order. "

This definition is the basis of the regularity of communicability (see the essence of this regularity in paragraph 3.4). Consistent with this definition and develops it and the definition of VN Sagatovsky, which proposes the separation of a complex environment into subsystem, or higher systems underlying, or subordinate systems, systems of the actual or essential environment.

The relationship between the system and the environment is dynamic: some parts of the environment become parts of the system, and some are transferred to the environment. The problems of interaction of the system with the environment remain relevant at the present time.

The problem of reflection in determining the regularity integrity, emergence remains also relevant (see paragraph 3.4). The definition, which includes conditions that ensure the integrity of the system, gives P. Ackoff :

The system is an integer consisting of two or more parts that satisfies the following six conditions: :

(3.6)

where Q 1 - an integer has one or more defining properties or functions; Q 2 - Each part in this set can affect the behavior or properties of the whole; Q 3 - there is a subset of parts that is sufficient in one or more external conditions to perform the defining function of the whole, each of these parts is necessary, but not sufficient to fulfill this defining function; Q 4 - the way any significant part affects the behavior or properties of a system depends on the behavior or properties of at least one other significant part of the system; Q5 - the impact of any subset of essential parts on the system as a whole depends on the behavior of at least one other subset; Q 6 - the system is an integer that can not be divided into independent parts without losing its essential properties or function.

In the definition of F. P. Tarasenko takes into account not only the static properties of the system (integrity, openness, internal heterogeneity, structuredness), but also dynamic (functionality, stimulability, time variability, existence in a changing environment), and synergetic (emergence, isolation from integrity, which is understood statically, inseparable, ingerent from the English ingerent, ie being an integral part of something), and expediency.

Comparing the evolution of the definition of the system (the and links), then the properties, then the target, then the observer) and the evolution of the use of the categories of the theory of knowledge, research activity, one can find a similarity: at first, models (especially formal ones) were based on taking into account only elements and interactions, interactions between them, attention was paid to goals, the search for methods of its formalized representation (objective function, performance criterion, etc.), and from the 1960s on, increasingly Maintenance refers to the face (of Ashby - Observer), carrying out simulation or conducting an experiment (even in physics), ie the person making the decision.

In the period of the development of system studies, one of the first definitions of the system was the definition of C. Optner : System - there is a method or solution to the problem i.e. means of cognition, object mapping.

However, in the 1960-1970's. quite often there were discussions about whether the system is material or immaterial, and the definitions of Yu. I. Chernyak and S. Optner were criticized for idealism, because the system in them can only be treated as a mapping, i.e. as something that exists only in the consciousness of the researcher, the designer.

The meaninglessness of the dispute about the materiality and immateriality of the system showed В. G. Afanasyev: ... objectively existing systems - and the concept of the system; the concept of a system used as an instrument of cognition of the system - and again the real system, the knowledge of which has been enriched by our systemic notions; - such is the dialectic of the objective and subjective in the system ... .

Thus, in the concept of system (like any other category of cognition) the objective and subjective make up the dialectical unity, and one should not speak of the materiality or immateriality of the system, but of approaching the objects of research as systems, about their different representation at different stages of cognition or creation.

For example, Yu. I. Chernyak shows that the same object at different stages of its consideration can be represented in various aspects, and accordingly, it offers the same system to display at different levels of existence: philosophical (theoretic-cognitive), research, design, engineering , etc. - up to material embodiment.

The above classification principles definitions are aimed at helping in the selection of the definition for the study of specific classes of systems. On these definitions are based methods of structuring the goals and functions of management systems.

Thus, AI Uyomov's ambiguous definitions were used in the development of one of the first methods of structuring goals; the definition of VN Sagatovskii was used as the basis for a structuring technique that allows for the interaction of the system with the environment (see Chapter 5).

With this in mind and relying on a deeper analysis of the essence of the concept of the system, it seems that this concept should be referred to as the category of the theory of knowledge, the theory of reflection as a means to start its research and design.

Therefore, it is interesting to look at the definitions of the system from the point of view of approaches to representation (mapping), analysis and design of systems.

The traditional approach used in mathematical research is to define the variable elements and associate them with the appropriate relationship (formula, equation, system of equations) that reflects the principle of the interaction of elements.

When the tasks became more complicated, and such a relationship could not be immediately found, it was suggested to form the "state space" elements and enter proximity measures between the elements of this space. This approach was first applied to the study of complex systems. However, the very first attempts to apply it to the study of complex technical complexes and management systems of enterprises and organizations have shown that it is practically impossible to determine all the elements and connections between them in a complex system.

Given the difficulties enumerations (establishing the composition of the system), from the very beginning of the emergence of systemic theories, the researchers sought approaches to its analysis and creation (see paragraph 3.3).

Analysis of the definitions of the system shows that the first definitions relied on an approach to the study and design of the system, based on the mapping of the state space (elements, connections, their properties) and the search for proximity measures on this space (this approach in the theory of systems < strong> M. Mesarovic calls the terminal, and J. I. Chernyak - the linguistic or method of the "language" system); for brevity, in the theory of systems, a simplified term is adopted-an approach to the investigation or design of a system from elements, i.e. as it were from below & quot ;.

At the same time, subsequent studies have shown that when investigating complex systems with active elements, and especially socio-economic objects, an axiological approach is preferable - from goals, needs (ie "from above").

Therefore, the author of this textbook was asked to define a system in which the system-target approach is implemented:

(3.7)

where Z = {z} - the aggregate or structure of the goals; STR = {STR np , STR opg, ...} is the set of structures that implement the (STR IIS - production, STR opg - organizational, etc.); TECH = {meth, means , alg, ...} is a collection of technologies (methods - meth, means - means, algorithms - alg , etc.) that implement the system; COND = {φex, φin} - conditions for the existence of the system, i.e. factors affecting its creation and functioning (φхх - external, φ, • "- internal); Ν - Observers (by WR Ashby), i.e. persons who take and execute decisions, carry out the structuring of goals, adjust the organizational and production structure, implement the choice of methods and tools for modeling, etc.

This definition is based on the concept of a multi-level structure of the organization's information system, discussed in Ch. 8.

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