Basic issues on fuzzy rules and their application to fuzzy control

Abstract

Fuzzy logic controllers have encountered an extraordinary success in a great variety of industrial applications in the last few years, especially in Japan. The principle of fuzzy controllers, first outlined by Zadeh[31] and then successfully experimented by Mamdani and Assilian[20], consists of synthesizing a control law for a system from fuzzy rules, usually provided by experts, which state the action(s) to do in typical situations, in contrast with the standard approach to automatic control which requires a model of the system to control. Each rule more or less applies to a fuzzy class of situations and an interpolation operation is performed between the conclusion parts of the selected rules, on the basis of the degrees of compatibility between the condition parts of these rules and the current situation encountered by the system. The reader is referred to Mamdani[19], Sugeno[24] for introductions and to Lee[16] and Berenji[5] for surveys. The basic methodology of fuzzy logic controllers was empirically developed in the late seventies and early eighties and has not changed much since. Recently, a revival of rather theoretically-oriented studies has been observed in order to build a strong methodology for fuzzy logic controllers. Thus the analytical comparison between a fuzzy controller and a proportional-integral controller[30], the limit behavior of fuzzy controllers[6], the stability of fuzzy controllers[27], [26], adaptive techniques for fuzzy controllers, e.g. [22]; [1]; [13], and the use of neural network methods for learning fuzzy rules and implementation issues[17] [28] have been discussed.

In this paper we concentrate our methodological study on issues related to the modelling of the set of fuzzy rules and the associated interpolation techniques and we point out several directions for further research.