# Regularities of the theory of systems, Laws of interaction of...

## Regularities of the theory of systems

Regularities of the functioning and development of systems (in a shorter formulation - regularities of systems ) - system-wide regularities characterizing the fundamental features of the construction, functioning and development of complex systems.

Such patterns of L. von Bertalanfy at first called system parameters, and A. Hall - macroscopic properties, or regularities.

Regularities of systems can be divided into four groups (see Figure 3.17).

## Regularities of interaction of a part and a whole

In the process of studying the features of the functioning and development of complex open systems with active elements, a number of regularities have been revealed that help to better understand the dialectics of the part and the whole in the system in order to take them into account when making decisions. Consider the main of these patterns.

Integrity . The pattern of integrity (emergence) is manifested in the system in the appearance of (emerge - appear) in her new properties that are missing from the elements. Bertalanffy considered emergence as the main systemic problem.

Fig. 3.17. Groups of regularities of systems

The manifestation of this pattern can easily be explained by examples of the behavior of populations, social systems and even technical objects (the properties of the machine differ from the properties of the parts from which it is assembled).

In order to better understand the regularity of integrity, it is first of all necessary to take into account two sides:

1) the properties of the system (integer) Q s are not a simple sum of the properties of its constituent elements (parts) q :

2) the properties of the system (the whole) depend on the properties of its constituent elements (parts):

In addition to the two main sides, one should keep in mind one more:

3) the elements integrated in the system, as a rule, lose some of their properties inherent to them outside the system, i.e. the system seems to suppress a number of properties of elements; but, on the other hand, the elements, hitting the system, can acquire new properties.

The integrity property is related to the purpose for which the system is created. In this case, if the goal is not explicitly specified, and the displayed object has integral properties, one can try to determine the goal or expression connecting the goal with the means of achieving it (objective function, system-forming criterion) by studying the reasons for the appearance of the integrity law.

The study of the causes of the emergence of holistic properties in the theory of systems is given great attention. However, in a number of real situations, it is not possible to identify factors that cause the emergence of integrity. In this case, systemic representations become a means of investigation. Due to the fact that the display of an object in the form of a system implies, by virtue of the regularity of integrity, qualitative changes in the combination of elements in the system and in the transition from the system to the elements (and these changes occur at any level of the system's dismemberment), it is possible at least to represent the object or process for

(3.11)

(3.12)

study of which can not be immediately formed a mathematical model that requires the identification of exact, deterministic relationships between the elements of the system.

In other words, using the concepts system and structure can display problem situations with ambiguity, while separating large the uncertainty is more "small", which in some cases is easier to learn, which helps to identify the causes of qualitative changes in the formation of the whole of the parts. Separating the system, you can analyze the reasons for the emergence of integrity based on the establishment of cause-effect relationships of a different nature between parts, part and whole, identifying the causal conditionality of the whole environment.

Dual with respect to the regularity of integrity is the regularity of physical additivity, independence, summative, isolation.

The property of physical additivity is manifested in a system that, as it were, decays into independent elements; then it becomes fair:

(3.13)

In this last resort, you can not talk about the system. But, unfortunately, in practice there is a danger of artificial decomposition of the system into independent elements, even when they appear as elements of the system with an external graphic image.

Strictly speaking, any developing system is, as a rule, between the state of absolute integrity and absolute additivity, and the system state (its "slice") can be characterized by the degree of manifestation of one of these properties or tendencies to its growth or decrease.

To assess these trends, A. Hall introduced two conjugate regularities, which he called "progressive factorization - the desire of the system to a state with increasingly independent elements and progressive systematization - the desire of the system to a decrease in the independence of the elements; to greater integrity (Table 3.6).

Table 3.6

Regularities of interaction of part and the whole

 Regularities of the interaction of part and the whole Degree Integrity a Coefficient freedom elements β Integrity (emergence) 1 0 Progressive systematization α & gt; β Progressive factorization α & lt; β Additivity (summability) 0 1

In the following A. A. Denisov introduced comparative quantitative estimates of the degree of integrity a and the coefficient of using the properties of the elements of β as a whole, i.е. freedom of elements in the manifestation of their properties.

where Cc - system complexity or systemic meaning according to Denisov (1.7); Co is its own complexity; Sv - mutual complexity.

A. A. Denisov formulated the basic law of systemology: the sum of the relative connectivity of the elements a in the system and their relative freedom β is a logical constant 1:

AA Denisov's research shows that without integrity in the system, holistic, system-wide properties that are useful for its preservation and development can not arise. But in the case of great integrity, the system will suppress the properties of the elements and may lose some of them, including useful ones. Therefore, a real complex, evolving system must always be between two extreme states - integrity, stability and decay, chaos. And socio-economic systems (organizations, territorial entities, society as a whole) face a choice of the degree of integrity regulation.

Applied to public systems: the sum of relative justice and relative freedom in any social system is a constant value, so that freedom can be achieved only through justice and vice versa.

Integrativity . This term is often used as a synonym for integrity. However, some researchers (for example, VG Afanasyev ) single out this pattern as an independent one, trying to emphasize interest not to external factors of manifestation of integrity, but to deeper reasons causing the emergence of this property, to factors that ensure integrity.

Integrative are called system-forming, system-preserving factors, among which an important role is played by the heterogeneity and inconsistency of elements (investigated by the majority of philosophers), on the one hand, and their desire to join coalitions, > on the other, which drew attention to A. A. Bogdanov and researched his son A. A. Malinovsky and M. Mesarovic.

Regularities of hierarchical ordering of systems. This group of regularities is closely connected with the regularity of integrity, with the dismemberment of the whole into parts. However, it characterizes the interaction of the system with its environment - with the environment (significant or significant for the system), supersystem, subordinate systems. Therefore, the regularities considered below are separated into an independent paragraph.

Communicative . This pattern is the basis of the definition of B. N. Sadovskilg and E. G. Yudin , given in paragraph 3.1, from which it follows that the system is not isolated from other systems, it is connected by a set of communications with the environment, which in turn is a complex and heterogeneous formation containing subsystem (a system of higher order that specifies requirements and constraints to the system under study), subsystems <(i lower, subordinate systems) and systems of the same level with the system under consideration

Such a complex unity with the environment is called the regularity of communicativity, which, in turn, easily helps to move to hierarchy as the patterns of the construction of the whole world and any system selected from it.

Hierarchy . The regularity of hierarchy, or hierarchical ordering, was among the first laws of the theory of systems that singled out and investigated L. von Bertalanffy. He, in particular, showed the connection between the hierarchical orderliness of the world and the phenomena of differentiation and negentropic tendencies, i.e. with the laws of self-organization, the development of open systems, discussed below. On the allocation of levels of the hierarchy of nature, some classification of systems is based, in particular the considered classification of K. Boulding.

The need to take into account not only the external structural side of the hierarchy, but also the functional interrelations between the levels, Academician В drew attention. A. Engelhardt . On the examples of biological organizations, he showed that a higher hierarchical level exerts a directing influence on the underlying level subordinate to it, and this effect is manifested in the fact that the subordinate members of the hierarchy acquire new properties that they did not have in an isolated state (confirmation of the provision on the effect of the whole on elements listed above), and as a result of the appearance of these properties, a new, different "whole image" is formed; (the effect of the properties of the elements on the whole). The new whole that arises in this way acquires the ability to carry out new functions, which is the goal of the formation of hierarchies. In other words, we are talking about the law of integrity ( emergence) and its manifestation at each level of the hierarchy.

These features of the hierarchical structures of systems (or, as is sometimes said, hierarchical systems) are observed only at the biological level of the development of the universe, but also in social organizations, in the management of an enterprise, association, state, in the presentation of projects for complex technical complexes and

The study of hierarchical ordering in organizational systems using an information approach (see Chapter 3) made it possible to conclude that there are more complex interrelationships between levels and elements of hierarchical systems than it can be reflected in the graphical representation of the hierarchical structure. In particular, even if there are no explicit links between the levels of the hierarchy ("horizontal"), they are still interconnected through the higher level.

For example, in the production and organizational structures of an enterprise from a higher level, it depends which of these elements will be chosen for promotion (with the preferences of some excluding the encouragement of others) or, alternatively, which element will be entrusted with unrewarding or unprofitable work (again , it will free others from it.)

Thus, hierarchical representations help to better understand and explore the phenomenon of complexity.

Highlight the main features of hierarchical ordering from the point of view of the usefulness of using them as models of system analysis.

1. The pattern of communicativity manifests itself between the levels of the hierarchy of the system under study, and therefore each level of hierarchical ordering has complex interrelations with the higher and lower levels.

According to the metaphorical formulation used by A. By the Köstler , each level of the hierarchy has the property of the "two-faced Janus": the "face", directed towards the lower level, has the character of an autonomous whole (system), and the "face" directed to the node (top) of the higher level , shows the properties of the dependent part (the element of the superior system, which is the component of the higher level for which it is subordinate).

This specification of the regularity of hierarchy explains the ambiguity of the use in terms of complex organizational systems of concepts system and subsystem & quot ;, target and tool (the element of each level of the hierarchical structure of goals acts as a goal in relation to the underlying and as a "sub-goal", but starting with some level, and as a "means" in relation to the higher goal), which is often observed, as noted above, in real conditions and leads to incorrect terminological disputes.

2. The pattern of integrity (ie, qualitative changes in the properties of components of a higher level compared to the components of the underlying one) is manifested in it at each level of the hierarchy.

At the same time, the combination of elements in each node of the hierarchical structure leads not only to the appearance of new properties in the node and the loss of the manifestation of some of its properties by the unified components of freedom, but also to the fact that each subordinate member of the hierarchy acquires new properties that did not exist in the isolated state.

Thanks to this feature, hierarchical representations can be used to investigate systems and problem situations with uncertainty.

3. One and the same system can be represented by different hierarchical structures.

And it depends on: a) the purpose of the system, the goal (different hierarchical structures may correspond to different goal phrases); b) structuring techniques; c) prehistory of the development of the persons forming the structure: for the same purpose, if the structure is assigned to different persons, then depending on their previous experience, qualification and knowledge of the object, different structures can be obtained, e. differently reveal the uncertainty of the problem situation.

4. Owing to the considered features, hierarchical representations are a means of investigating systems with uncertainty: there is as it were a dismemberment large uncertainties are more "small", better amenable to research.

However, even if these small uncertainties can not be fully explained and explained, nevertheless hierarchical ordering partially removes the general uncertainty, provides at least controlled control over the decision making, for which a hierarchical representation is used.

In connection with what was said at the stage of structuring the system (or its purpose), it is possible (and necessary) to set the task of selecting a variant of the structure for further research or design of the system, for organizing the management of the technological process, enterprise, project, etc. In order to help in solving similar problems, we develop methods for structuring, evaluation methods and comparative analysis of structures, examples of which will be considered in later chapters.

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