Formation of the knowledge base on the basis of identification of typical states of complex system

Abstract

This article presents the approach to form a knowledge base that describes the behaviour of a complex system. A scorecard is introduced to describe this behavior. It is assumed that as a result of their observation, time series are formed. Such time intervals, within which the linear trends of time series do not change, are identified based on the piecewise linear approximation. These intervals determine some state of a complex system. For a formal description of states, code vectors are used, which are formed based on a linguistic scale. Its gradations determine the base directions of linear trends. Each base direction corresponds to an integer code. The proximity of the slope of the linear trend to the base direction is determined using the membership function. It is proposed to use a cluster procedure to identify typical states. The analysis of suitable methods made it possible to separate the decomposition tree method as such a procedure. Its advantage is that it allows us to generate all possible partitions of a given set of states. At this stage, the problem of choosing the optimal partition arises. In this paper, optimal partition is a partition that contains as many classes as possible in the decomposition tree. Such classes exhibit stability in some sense. The optimal partition corresponds to a certain level of the decomposition tree, and the partition classes correspond to the typical states of a complex system. Under the assumption that the system indicators depend on some set of factors, a base of production rules is formed. The conclusions of these rules contain terms or functions that correspond to factors. The proposed approach is tested in the FuzzyClips environment to analyze the investment portfolio.