Abstract

Fuzzy control is at present still the most important application of fuzzy theory. It is a generalized form of expert control using fuzzy sets in the definition of vague/linguistic predicates, modeling a system by If... then rules. In the classical approaches (Zadeh, Mamdani) the essential idea is that a fact (observation) known concerning the actual state of the system will match with one or several rules in the model to some positive degree, the conclusion will be calculated by the evaluation of the degree of these matches, and the matched rules themselves. In these approaches, the rules contain linguistic terms, i.e., fuzzy sets in the consequent parts, and these terms, weighted with their respective degrees of matching, will be combined in order to obtain a fuzzy conclusion—from which the crisp action is obtained by defuzzification, as e.g. the center of gravity method. This paper summarizes these classical methods and turns attention to their weak point: the computational complexity aspect. As a partial solution, the use of sparse rule bases is proposed and rule interpolation as a fitting inference engine is presented. The problem of preserving or not preserving linearity is discussed when terms in the rules are restricted to piecewise linear.

Author Keywords: fuzzy control; rule interpolation; preservation of piecewise linearity; preservation of normality; hierarchical rule base

Article Outline

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Corresponding author. Address correspondence to Dr. László T. Kóczy, Department of Telecommunications and Telematics, Technical University of Budapest, Sztoczek u. 2, H-1111 , Budapest, , Hungary.

*1 This article contains partly the topics discussed at CIFT '93 in the author's plenary paper “State of the Art of Fuzzy Control Algorithms,” and in addition includes some further results on the linear interpolation algorithm.