# Concept of the system, Development of the definition...

## The concept of the system

We can assume that the concept of system arose in the ancient world when Aristotle drew attention to the fact that the whole (that is, 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 , large.

These include, for example, the solar system, the machine control system, the organizational management system 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 calculus system, 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 the system emphasizes order, integrity, the presence of certain patterns of its construction, functioning and development.

At the same time, for the use of the term system in research, design, or management, it is necessary to give this concept a more precise definition.

## 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 tens of definitions of this concept (see the reviews of VN Sadovskii, AI Uemov [73, 83]) and the team of authors in [80]. Their analysis shows that the definition of the concept system changed not only in form, but also in content.

The basic and fundamental changes that occurred with the definition of the system as the theory of systems developed and the use of this concept in practice are given in Table. 1.2.

Table 1.2

 NO п/п Classes Definitions Symbolic definition entry Examples of definitions I a) b) c) d) Elements (parts, components) A = U} and links (relations) A = {zA. Terms items - Components & quot ;, links - Relationships often used (especially in translations) as synonyms. However, strictly speaking, the components - a concept more general, "link"; and relation too, are not always identified (see the review by VN Sadovskii [73]) Fig. 1.1 If it is known that the elements are fundamentally heterogeneous, then it can be immediately taken into account in the definition, selecting different sets of elements. For example, include the sets (1.1a) If a kind of relationship r l is applicable only to the elements of different sets and is not used inside each of them, then (1.1b) where are the elements of the new system, formed from the elements of the original sets A and B. Other forms of the definition record are used (1.1c) or in other notations of the intersection operation (1.1g) L. von Bertalanffy defined the system as a "complex of interacting components" or "a collection of elements that are in a certain relationship with each other and with the environment" [17]. In the Great Soviet Encyclopedia, the system is defined by a direct translation from the Greek: συ-στημα & quot ;, composition, i.e. composed, joined from parts . M. Mesarovic [54] allocates a set of A-input objects (acting on the system) and a set of Υ output results, and between them - the generalizing ratio of the intersection. II a) b) Elements of A, connection R, properties of Q. Qa = W ~ properties of the elements; Qr = W - relationship properties In the definition of A. Hall [89], the properties (attributes) & lt; 2L complement the concept of an element (object). A. I. Uyomov [83] defined the system through the concepts of "things", "properties", "relations" and suggested dual definitions, in one of which the properties characterize the elements (things), and in the other - the relationship (relationship) III a) b) Elements of A, connection R, property Q, goal Z Refinement of pricing conditions In the definition of FE Temnikov [79.80] the system - organized set the goal appears when the concept is organized. The goal was also presented in the form of the final result, the system-forming criterion, the definitions of VI Vernadsky, UR Gibson, P, K. Anokhin, MG Gaase-Rapoport (see references in the book by VN Sadovsky [73]) (Sadovsky's not only a review). In the definition of VN Sagatovskii, the conditions for the target formation - medium SR, the time interval AT, , are specified. the period within which the system will exist and its goals: the system is a finite set of functional elements and the relationships between them, selected from the environment according to a specific goal within a certain time interval, [66, c . 13-14] IV a) b) c) Elements A, Q of property Q, goal Z, "observer" N, i.e. a person who represents an object or process in the form of a system when they study or make a decision The necessity of taking into account the interaction between the studied system and the researcher was first pointed out by WR Ashby [103]. The first definition, in which the observer is explicitly included, was given by I. I. Chernyak: "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, [92, p. 22]. Chernyak began to take into account and the language of the observer Lv: "System - mapping in the observer's language of objects, relations and their properties in solving the research problem, cognition

In the table. 1.2 formalized definitions entries used different methods of set-theoretic representations: in I, II - different ways of specifying sets, the relationships between sets of elements and links are not taken into account; III reflects the fact that the system is not a simple collection of elements and connections of one kind or another, but includes only those elements and links that are in the intersection area (& amp;) with each other (Figure 1.1).

Definitions are classified on the basis of the principle of supplementing them with new components in the process of developing conceptions about the system: first, the definitions included only the elements and links, then the and in the future - and the observer (the person making the decision, the researcher, the designer, etc.).

In Table. 1.2, of course, not all definitions are presented. In works В. N. Sadovsky and A. I. Uyomov [73, 83] analyzed more than one hundred definitions and gave a different classification. In the papers A. I. Uyomov adopted and other symbols. In the definitions of the system there are more and more components, which is associated with the need for differentiation in specific conditions for the kinds of elements, connections, etc.

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

So, the dual definitions A. I. Uyomov used in the development of one of the first methods of structuring goals; definition of B. N. Sagatovsky [66] was used as the basis for the structuring technique, allowing to take into account the interaction of the system with the environment (see Chapter 5).

The goal can be represented in the definition not in an explicit form. For example, in the philosophical vocabulary the system is a set of elements that are in relationships and relationships with each other and form some integral unity, , ie, the goal is hidden in the concept of "holistic unity".

Comparing the evolution of the definition of the system ( the elements and of the connection, then the target, then the observer) and the evolution of the use of categories of the theory of knowledge in research activities , we can find a similarity: at first, models (especially formal ones) were based on taking into account only elements and interactions, interactions between them, then - began to pay attention to the goal, search for methods of its formalized representation (objective function, performance criterion, etc.), and, starting from the 60s. XX century. more and more attention is paid to the observer , the person who performs the simulation or conducts the experiment (even in physics), i.e. the person making the decision.

A look at the definition of the system as a means of its investigation made it possible to realize the expediency of determining in which the object is not divided into elements, i.e. is destroyed, which is done in the above definitions, but is represented as a set of enlarged components that are fundamentally necessary for the existence and functioning of the system being studied or created:

(1.5)

where - the totality or structure of the goals; - realizing the goals ( - production, - organizational, etc.); TECH = { meth , means, alg, ... } is a collection of technologies ( meth means - means, alg - algorithms, etc.) that implement the system; - the conditions for the existence of the system, ie . factors affecting its creation and functioning ( - external, - internal); N - Observers (in accordance with P. Ashby and I. I. Chernyak ), 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 was proposed by one of the authors of the textbook and was initially unconsciously used as the basis for a methodology based on the concept of activity (see Chapter 5).

Based on a deeper analysis of the essence of the concept of the system as a category of the reflection of objects, it seems, to treat this concept as a category of the theory of knowledge, the theory of reflection. In this regard, it is interesting to pay attention to the question of the materiality or immateriality of the system.

On the one hand, trying to emphasize the materiality of systems, some researchers in their definitions replaced the term element with terms thing, object, object and although the latter can be treated as abstract objects or subjects of research, nevertheless the authors of these definitions clearly wanted to pay attention to the materiality of the system, the materiality of the system.

On the other hand, in the definitions of C. (the "system is the means by which the problem solving process is performed" [65, p.51]) and 10. I. Chernyaka ("the system is a way to solve the problem", and system thinking is the "ability to find simple in complex" [93, p. 9]), the system can be treated only as a mapping, i.e. as something that exists only in the consciousness of the researcher, the designer.

Any specialist who understands the laws of reflection theory should seem to object: but it is obvious that the idea (ideal representation of the system) will then exist in a material embodiment, and for decision-making tasks it is important to emphasize that the notion of the system can be a means of investigating the problem, solving the problem. Nevertheless, the above definitions were criticized by the adherents of the materiality of systems, especially philosophers.

The meaninglessness of the dispute about the materiality and immateriality of the system showed В. G. Afanasyev (Figure 1.2): "... objectively existing systems - and the concept of the system; the concept of a system used as an instrument of knowledge of the system, - and again the real system, the knowledge of which is enriched by our systemic representations - is the dialectic of the objective and subjective in the system .

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