A Tutorial on Fuzzy Rule-Based Expert System (Frbes) Models. 1: Mathematical Foundations

Article type: Research Article

Authors: Vadiee, Nader | Jamshidi, Mohammad

Affiliations: CAD Laboratory for Intelligent & Robotic Systems, Department of Electrical & Computer Engineering, University of New Mexico, Albuquerque, NM 87131

Abstract: In this article, the general problems of system identification and control system design are formulated and the concept of control or decision surface is described. The article shows that a collection of fuzzy conditional restrictive rules can be used to model complex or ill-defined processes (fuzzy systems), and some simple canonical formats for the production rule sets are given. It is shown that a system of fuzzy relational equations could be obtained from a set of IF-THEN production rules. A fuzzy system transfer relation based on a system of fuzzy relational equations is defined. The article also shows how a variety of fuzzy implication relations or Zadeh's extension principle might be used to derive the fuzzy relational equations. Various methods for obtaining the solution of these equations are studied based on a number of composition of relations techniques. Finally, two of the most commonly used solution techniques in fuzzy control applications, that is, Max-Min and Max-Product methods, are described.

DOI: 10.3233/IFS-1993-1206

Journal: Journal of Intelligent and Fuzzy Systems, vol. 1, no. 2, pp. 171-188, 1993