Constructing Abstract (Theoretical) Models of Actual (Material) Systems

Abstract

The world around us is a global system, therefore, it can be said that all its elements are interconnected. The strength of the connections between the system’s elements and their groups is not uniform. In some cases, we can observe the links very clearly, in other cases, we assume that they exist, while, sometimes, we are not even aware of their existence. The existence of the connections of various strength shows that the particular elements are of different nature and possess some specific features and capacity allowing them to interact with others and form the particular structures when the same goal is pursued. These structures differ from others and make the systems of a particular level. Therefore, the elements relevant for the considered problem should be identified (or formed if an artificial system is considered). In other words, we should identify or form a system for solving an arising problem. Another important aspect of investigating an existing or specially formed system is associated with its reflection. To change or to manage a social economic system, for example, the state of an enterprise should be measured. This may be achieved only if all major aspects of its performance are described by the particular criteria. The values of the criteria allow us to plan the measures to be taken for improving enterprise performance. The analysis of the literature shows that we can hardly find a generally accepted concept and definition of the word ‘system’. However, a lot of various definitions are suggested. This may be explained by the fact that either various features of the system are emphasized, or not all relevant features are considered. In some cases, a definition includes too many features, often duplicating each other. Some researchers base themselves on a very wide ‘system’s’ definition, while others prefer a short one, embracing its essential features. Various approaches depend on the research objective, ‘system’s’ perception, and, finally, the researcher’s ability to see the essential features and understand the nature of the considered phenomenon. In terms of the research objective, investigators usually search for a versatile ‘system’s’ definition, while others prefer a short one, embracing its essential features. Various approaches depend on the research objective, ‘system’s’ perception, and, finally, on the researcher’s ability to see the essential features and understand the nature of the considered phenomenon. In terms of the research objective, investigators usually search for a versatile system’s definition suitable for studying any phenomenon at any investigation level. However, they also may try to find a multifunctional approach, giving the priority to general features of the system, rather than to its basic, principal characteristics, thereby restricting themselves to a ‘narrow’ definition suitable for solving a particular problem and achieving a particular goal. The latter approach makes sense only if it does not contradict a universal system’s concept and definition. This means that a universal concept and definition of the word ‘system’, which could be used as a basis for possible interpretations should be developed. The analysis of the available ‘system’s’ definitions allows us to suggest the following basic definition – a system is the structured whole of interacting elements. A basic category of the theory of systems is structure, which marks the beginning of system’s stabilization. However, we can see that a generally accepted definition of the concept ‘structure’ is also lacking. On the other hand, all definitions emphasize the same, probably, most essential, structure’s feature – the connections between the elements. In addition, the existence of the system and structure representing it is closely connected to the aim (purpose) of the system. It is the structure that orients the system to pursuing a particular aim. In mathematical terms, the establishing of invariable relations between the elements is necessary but insufficient for system formation. These relations should be properly directed, i.e. oriented to achieving the system’s aim. This may be obtained only by establishing hierarchical relations between the interacting elements, i.e. by structuring the elements according to the type of their subordination. It is the process of structuring of a set of interacting elements that gives them a particular orientation and turns them into a system. The analysis of various ‘structure’s’ definitions allows us to define it as a whole of constant relations between the elements oriented to achieving the system’s aim. Now, when the concepts of system and structure are clear, it is possible to investigate them. Classification, i.e. their subdivision into separate groups, is an efficient tool in this process. The analysis of the literature on the problem shows that, in various system’s classifications, various attributes are considered. For the case investigated in the present paper, system’s classification into actual (material) and theoretical (abstract) systems is relevant. The first class embraces the systems of organic and inorganic nature, while the second includes hypotheses, theories, formalized models, etc. In fact, the latter may be deduced from the former. Therefore, they are aimed at reflecting actual (material) systems. Thus, it may be stated that theoretical (abstract) systems are the models of actual (material) systems. - 8 - The following steps may be identified in the process of reflecting actual (material) systems by theoretical (abstract) models. First, the problem situation associated with the actual (material) system is described, then, the problem and the aim of its solution are stated. The existence of the reflected system’s problem situation, the problem and the aim of its solution determine the problem situation, the problem and the aim of the reflecting model.