BASIC CONCEPTS AND DEFINITIONS of decision theory — system, control and situation

The concept of a system

At present there is still no established concept of «system», since its content has gradually grown more complex and continues to do so.

At first a system was understood as only a complex of interacting elements. Later this concept became more complex through the inclusion, in its content, of relations or interconnections between the elements making up the system . Still later, to more fully describe the elements of a system and their interconnections, another parameter describing the system was introduced – the properties or characteristics of the system . R. A. Fatkhutdinov described a system as a set of elements that are in relations and connections with each other and with the external environment and that form a certain integrity, a unity .

The next evolutionary step in filling out the content of the concept of «system» is the introduction into it of such a parameter as «the purpose of creating or operating the system».

As the specific needs for using this concept arose, it was supplemented with the necessary parameters.

Specialists comment on the situation that has developed as follows.

• • The selection of parameters that additionally describe the concept of «system» is related to the specifics of the situation under study and the goals of the research, and is therefore subjective and not mandatory.
• • The definition of this concept can be arbitrary, but it must necessarily include the following defining parameters: the elements of the system, the interconnection of the elements of the system, the characteristics (parameters, properties) describing the elements of the system and their interconnection" , as well as the purpose of creating and (or) operating the system. This is especially important when considering socio-economic systems, where the role of the human factor in making managerial decisions is very significant.

• Since a system is created and (or) operates in order to achieve a specific purpose, it is possible, for the sake of monitoring the achievement of the purpose and managing the system when necessary, to have a subject — the person, making the decision (DM).

In the text of this textbook the following definition of the concept of a system is used.

Definition

A system is a set of interconnected elements that ensure its functioning and are directed toward achieving the goals of its creation and (or) functioning.

The set of elements and their interconnections that define a system can be represented by the values of the characteristics corresponding to them. The set of values of these characteristics at any given moment in time determines the state of the system at that specific moment in time.

Pay attention!

The state of a system is determined by the list and the values of the characteristics (i.e., a certain set of data) describing the elements of the system and their interconnection.

The definition of a system presented here proceeds from the fact that it represents a set of elements, that these elements are interconnected with one another, and that the elements of the system and their interconnections are described by certain characteristics. A system is created and functions for the purpose of achieving certain goals.

Note that what is meant, first and foremost, is the goals of the DM with respect to this system.

The state of a system at any moment in time is represented by the set of values of the characteristics describing the elements of the system and their interconnections at that moment in time.

The assessment of whether the goals of creating and (or) operating any system under study have been achieved is carried out by the DM. If the system does not achieve its goals, the task of the DM is to develop a managerial decision aimed at achieving the goals of creating and (or) operating the system .

Since the state of a system is determined by a set of characteristics describing the composition of the system and their interconnections, the achievement of the goals of creating and (or) operating the system can be accomplished through the following variants:

• • by changing the values of the characteristics describing the given system. In this case the system itself remains unchanged; only its state changes;
• • by changing the set of the elements of the system themselves and (or) their interconnections and the corresponding characteristics. In this case the originally studied system becomes transformed (changed or refined).

Definitions

• 1. Change of the state of a system is a change in the values of the characteristics describing the elements of the system and their interconnection.
• 2. Transformation of the system under study is its alteration through the expansion or change of the composition of the elements of the system, and (or) their interconnections and the characteristics used to describe them.
• 3. The achievement of a new state of a system is possible on the basis of a change in its previous state or on the basis of its transformation.

In the event that the system under study does not ensure the goals of its creation and (or) operation (from the standpoint of the DM), it must either be transferred to a new state or transformed in such a way that the goals set are achieved.

Here it must be kept in mind that transferring the system under study to an optimal state through a change in its state or through its transformation can be iterative and can be carried out:

• • by repeatedly transferring the system from one state to another. Here, the transfer of the system from the analyzed state of the system to the subsequent one is conditioned by unsatisfactory results of checking the attainability of the goals of creating and (or) operating the system in its analyzed state. In this case, the next state of the system, one that already ensures the achievement of the stated goals of creating and (or) operating the system, will already be optimal;
• • by transforming the system, which can likewise be repeated more than once. Here, the next transformation of the system will be conditioned by unsatisfactory results of the previous transformation, in which the goals of creating and (or) operating the system were not achieved. In this case, the next transformation of the system, one that ensures the achievement of the stated goals, will already be optimal;
• • by a joint, repeated transformation of the system together with a repeated transfer of the system from one state to another within the transformed system. Here, the choice of the next change of the state of the system or of its transformation is conditioned by unsatisfactory results of the previous step. And only in the case where the next state of the transformed system ensures the achievement of the goals of its creation and (or) operation will the transformed system and its corresponding state already be optimal.

Pay attention!

Transferring a system to an optimal state is possible through a change in its state or through its transformation.

It is necessary to distinguish between newly created systems and already operating, functioning systems. The creation of a new system necessitates the adoption and development of a managerial decision, implemented on the basis of a project for creating this new system. It presupposes that the system being created will immediately correspond to its optimal state — the state in which the values of the characteristics describing the elements of the system and their interrelation will ensure the realization of the goals for its creation.

With regard to operating systems, the following can be noted.

First of all, static and dynamic systems must be distinguished.

Static systems presuppose, firstly, the constancy of the values of the characteristics describing the elements of the system and their interrelation, and, secondly, the correspondence of the values of these characteristics to the goals for which the system was created.

Dynamic systems presuppose the possibility of changing, over time, the values of the characteristics describing the elements of the system and their interrelation. However, any change in the values of these characteristics must correspond to the goal of the creation and functioning of the operating system.

In the event that the functioning of any system (created or operating) does not realize the goals of its creation and (or) functioning, it becomes an object of management aimed at achieving these goals.

Note!

A system becomes an object of management when, from the standpoint of the DM, its functioning does not correspond to the goals of its creation and (or) development.

The content of the concept of «management» has different shades of meaning depending on the context. At the very beginning, the goal of management was considered to be obtaining a desired result from human activity, and management was understood as purposeful, expedient actions aimed at coordinating people's opinions and the compatibility of their activities. In doing so, several main functions of management were distinguished: forecasting, planning, organization, control, coordination, activation and motivation, analysis .

A. I. Orlov describes management as the process of a subject acting on an object in order to transfer the object to a new qualitative state or to maintain it in an established regime. Here, the subject of management is the one who manages, while the object of management is the one who is managed .

When managing socio-economic systems, the human factor and its influence on decision-making are essential. In decision theory, for the subject of management, i.e. for the one who manages, there is a special term — the decision maker — the one who has the corresponding authority and who bears responsibility for the decision made, the one who signs the order or other document in which the decision is reflected. This is usually the general director or chairman of the board of a firm, the rector of a university, the commander of a military unit, the mayor of a city, and so on — in a word, an official vested with the corresponding authority. Sometimes a collective body, as in the case of a shareholders' meeting or the State Duma of the Russian Federation, may act as the DM.

The following definitions are used in the text of this textbook.

Definitions

By management of a system is understood a change in the state of the system or its transformation.

The person, making the decision, — is the subject of management, the one who manages, has the corresponding authority and who bears responsibility for the decision made.

In general, the DM is interested in the state of the system (the composition of its elements, the interrelation of the elements, and the values of the characteristics describing them) that ensures the realization of the goal of the system's creation and (or) functioning.

If the system under study does not realize the goals set, it must be transferred from an unsatisfactory state to a new (optimal) state that already ensures the achievement of the goals set for the system. It must be remembered here that the transfer of the system into the optimal state may be carried out in several steps.

The non-optimal state of a system may be represented by unsatisfactory values of the characteristics describing both the elements of the system and their interrelation. To ensure the transfer of the system into the optimal state, it is necessary to manage the elements of the system and (or) their interrelations in such a way that the values of the corresponding characteristics are changed appropriately, i.e. they must be changed so that they ensure the system's realization of its goals. This means that if the system under study requires management, i.e. requires its transfer into an optimal system, the specific objects of management within it may be the elements of the system and their interrelations.

Note!

• 1. By optimal is understood the state of a system in which the values of the characteristics describing the elements of the system and their interrelation ensure the system's realization of the goals of its creation and functioning.
• 2. If the system under study does not ensure the realization of the goals of its creation, the specific objects of management within it become those elements of the system, their interrelations, and (or) the characteristics describing them, that take on unsatisfactory values — those that do not ensure the system's realization of its goals.

Here, for static systems under study, the transfer of the system into the optimal state can be carried out in a finite number of steps, at each of which the system must change its state, coming ever closer to the optimal one. A special case is also possible — the transfer of a static system into the optimal state in a single step.

For dynamic systems implementing a certain process, the need to transfer the system into the optimal state may arise at any moment in time, since the very course of the process over time, implemented by the dynamic system, presupposes the possibility of changing the values of the characteristics describing the elements of the system and their interrelation at any moment in time.

Here, the need for managing such a system arises whenever any of the characteristics takes on a value that contradicts the goal of the system's functioning.

Note!

If the system under study is static — the values of the characteristics describing the elements of the system and their interrelation must be constant — then the need for managing it arises in the event that, for some reason, the values of the characteristics describing the elements of the system and their interrelation become unsatisfactory.

If, however, the system under study is dynamic — that is, it implements a certain process unfolding over time, and the values of the characteristics describing the system's elements and their interrelations change over time — then the need to control it, i.e., the need to transfer the system from an unsatisfactory state to an optimal one that ensures the realization of the system's goals, arises in the course of the process every time one of the characteristics describing the system's elements and their interrelations becomes unsatisfactory, i.e., no longer meets the goal of the system's functioning.

Technical and socio-economic systems are among the systems that most often become objects of control in everyday life.

The most complex of these from the standpoint of control is the socio-economic system, which has the following specific feature.

One of the elements that make it up is a person (a group of people) who may have their own interests with respect to the whole system or its subsystems, elements, characteristics and parameters describing the state of the system.

These interests of the person are determined by his social and (or) economic status in society, and they determine the person's behavior, which, in turn, becomes a subjective factor influencing the behavior of the entire system from within — from the side of its elements.

Note!

One of the elements of a socio-economic system is a person who may have his own interests, determined by his social and economic status.

A person's interests determine his behavior, which becomes a subjective factor influencing the development of the system itself from within.

It is precisely this factor — the presence in the system of people with their own interests — that must be taken into account when controlling a socio-economic system.

It should be noted that for technical systems as well, the presence of a human is often the case. But unlike a socio-economic system, he (the human) is not an internal element of the system that determines the development of the technical system from within. He and his behavior can influence the functioning of such a technical system, but only his activity is an external factor influencing the system. An example is technical systems operating in autonomous mode. And although a person may intervene in the operation of such a system, his intervention will be a manifestation of the influence of an external, rather than internal, factor determined by the nature of the system itself.

Next, let us discuss the subjects who make decisions in technical and socio-economic systems.

A decision by the DM regarding a control object that is an element of a technical system is a decision of a subject who is not an element of that system. As for the DM in relation to a control object of a socio-economic system, two situations are possible: the control subject (DM) either is or is not an element of that socio-economic system.

Any acquaintance with the system under study on the part of the decision maker begins with the study of a certain situation that has developed in the specific subject area to which the system under study itself belongs.

The term «situation» is usually used in two variants:

• • as a broad concept, the content of which is a description of the environment in which the system under study is or finds itself located;
• • as a specific concept, the content of which influences the DM's decision about preserving, improving, or changing it.

If the object of study is a system, the first variant of using this term is usually applied.

The DM's assessment of the situation comes down to assessing how, in the current specific situation, the system under study is realizing the goals of its creation and (or) functioning. If everything is going normally, i.e., the system meets the set goals, no change of the situation is required and, as a consequence, no transfer of the system to a new state is required, since it is already in an optimal state.

In the opposite case, when for some reason the goals of creation and (or) functioning are not being realized, the DM assesses the situation that has developed as unsatisfactory, requiring control of the system — its transfer to an optimal state.

Changing the situation with a view to improving it is possible through controlling the system under study — transferring it from one state to another on the basis of the development, adoption and implementation of managerial decisions.

In this connection, the demand for applying the procedure of constructing a managerial decision is influenced by the following factors.

• • The characteristic of the system's static/dynamic nature. If the system is static, then in the case of an unsatisfactory situation, when the system is not realizing the goals of its creation, managerial decisions are associated with transferring the system from one state to another. Once the system reaches an optimal state, the need for further managerial decisions disappears until a new unsatisfactory situation arises. If, however, the system is dynamic, the need to apply the procedure of constructing a managerial decision arises every time an unsatisfactory situation develops in the functioning of the system, when it (the system) no longer meets the goals set.
• • The variant of transferring the system to an optimal state. If the situation is unsatisfactory — the system is not realizing the goals of its creation or functioning — the DM can make various decisions. This may be a sequential transfer of the system from one state to another until the system arrives at an optimal state. In this case, the demand for the procedure of constructing a managerial decision will be determined by the specific number of transfers of the system from one state to another. But the DM may also decide to transform the system, in which case the composition of the system's elements and their interrelations is additionally clarified. In doing so, within each possible transformation of the system, simple transfers of the system from one state to another are also possible, characterized by the fact that the transfer of the system to a new state will be determined only by a change in the values of the characteristics describing the system's elements and their interrelations. In this case, the demand for the procedure of constructing a managerial decision will be determined by the number of both transformations of the system and transfers of it from one state to another.

Note that with respect to the operating system under study, the following is also possible. The system under study realizes the goals of its creation, yet the DM believes that the situation can be or should be improved. This presupposes a clarification of the goal of the operating system under study, in accordance with which further control of the system is then built.