Statistical analysis of the formation mechanism of concepts-representations in organizational and technical systems
Authors: Solodov Alexander A. 
Published: September 2018

The aim of the research is the analytical description of one of the modules of the organizational and technical system, designed for the formation of sensual images and their transformation into concepts-representations. Within the framework of the computer paradigm in organizational and technical systems, such obvious principles as digital representation of information and its processing with the use of algorithms implemented by computing means are used. The success of the computer paradigm application is certainly impressive, but there are clearly situations in which human consciousness operates much more efficiently, interpreting the unconventional, the new situation with the aim of formulating an adequate response. In this regard, attempts to model some mechanisms of human consciousness within the framework of the cognitive approach are of great interest. In accordance with the ideas of cognitive theory in the human brain, images (schemes, categories, gestalts, systems, archetypes, etc.) are formed and then are processed. It is assumed that the resulting images are those effects that are then processed, perceived, used by the organizational and technical system for the formation of concepts-representations. Concept representation is a generalized sensual-visual image of the object or phenomenon and is characterized by a number of features, the number of which may vary in the course of the system operation.

The method of Markov chains is used to study the statistical characteristics of the mechanism of formation of concepts-representations. It is assumed that the formation of sensual images and their transformation into concepts-representations occurs at random moments of time. The module of concept-representation formation can be in one of two states that correspond to the logic of its functioning – either its state does not change, or when a new concept-representation is formed, the state of the module changes. A stochastic matrix of one step transient probabilities, characterizing changes in the module states and corresponding initial probabilities of states is introduced. Because of application of the theory of Markov chains with two states, the relations for the probabilities of the module states through an arbitrary number of steps, as well as asymptotic expressions for the probabilities of states are given. The graphs of the module state probabilities change depending on the number of circuit steps, initial probabilities, probabilities of one-step transitions of the stochastic matrix are presented.

Analytical expressions and corresponding graphs for the average number of stays in the module of a particular state are obtained, which are interpreted as the average number of corrections of essential features of concepts-representations. The asymptotic relations for the number of corrections are obtained, and the error of the approximate asymptotic relations is estimated.

Thus, the paper formulates a very general model of the random process of formation of sensual images and their transformation into concepts-representations. The key task of the practical application of the model is to analyze the logic of the functioning of a particular organizational and technical system and to determine on this basis the parameters appearing in the model.