Fuzzy dynamic models of situation analysis, decision support, and control in complex systems

Abstract

In this work we consider the theoretical foundations of building fuzzy models of system dynamics, analysis of situations, their development, and control in complex weakly-structured systems based on knowledge modeling and expert preferences. The proposed fuzzy models can serve as mathematical tool for analyzing the behavior of a system in various situations, as well as to serve as the basis of specialized computer simulation systems of decision support in unstructured fuzzy situations. As is known, decision making problems under uncertainty can be divided into two groups: decision making in static situations and decision making in dynamic situations. For decision making in static situations, the methods and models of decision support based on the theory of choice are developed. For decision-making in dynamic situations, the dynamic models, including those based on expert knowledge, are used. To build a dynamic model of a situation, the expert knowledge about physical, economic, or social processes occurring in a system, which are represented as a cognitive map, is employed. The models of analysis of static situations are focused on evaluation and ordering of alternatives, and models of analysis of dynamic situations are focused on generating of strategies (alternatives) to achieve the targets of control, that is, the desired target state of the situation. Thus, one of the aims of this paper is to develop mathematical methods for constructing integrated decision support models based on fuzzy models of hierarchical estimation, control, and fuzzy cognitive modeling.