On the semantics of perception-based fuzzy logic deduction

Abstract

In this article, we return to the problem of the derivation of a conclusion on the basis of fuzzy IF–THEN rules. The so-called Mamdani method is well elaborated and widely applied. In this article, we present an alternative to it. The fuzzy IF–THEN rules are here interpreted as genuine linguistic sentences consisting of the so-called evaluating linguistic expressions. Sets of fuzzy IF–THEN rules are called linguistic descriptions. Linguistic expressions derived on the basis of an observation in a concrete context are called perceptions. Together with the linguistic description, they can be used in logical deduction, which we will call a perception-based logical deduction. We focus on semantics only and confine ourselves to one specific model. If the perception-based deduction is repeated and the result interpreted in an appropriate model, we obtain a piecewise continuous and monotonous function. Though the method has already proved to work well in many applications, the nonsmoothness of the output may sometimes lead to problems. We propose in this article a method for how the resulting function can be made smooth so that the output preserves its good properties. The idea consists of postprocessing the output using a special fuzzy approximation method called F-transform. © 2004 Wiley Periodicals, Inc. Int J Int Syst 19: 1007–1031, 2004.