Expert fuzzy modeling of dynamic properties of complex systems

Abstract

The purpose of this article is to represent an extension of the classical notion of fuzzy sets to estimate the condition of complex systems, which is based on the dynamic fuzzy sets concept. In this article, the authors prove the necessity to use dynamic fuzzy sets to estimate the condition of a complex system. Firstly, we present the basic definition and construction method of dynamic fuzzy sets. There are described analytical and graphical representations of dynamic fuzzy sets, which are represented by dynamic membership functions constructed in a three-dimensional coordinate system, where one of the axes in the graph captures the time variation of the properties of the economic objects expressed by a set of numbers with fuzzy function. We develop the simulation of dynamic membership functions by expressions of expert assessments on multilevel fuzzy description of the complex indicators, which are made in strict sequence from a reference point and bifurcation points, selection of functional dependencies, to build a static membership functions, and then the dynamic membership functions on the whole interval assessment. Finally, we develop a few software systems to interactive construction dynamic membership function. Thus, this paper can provide interactive process of expert assessment of complex dynamic systems, which include quantitative and qualitative indicators