e-mail: e-mail On the Semantics of Perception-Based Fuzzy Logic Deduction∗)

In this paper, we return to the problem of 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 paper, 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 appropriate model, we obtain a piece-wise con-tinuous and monotonous function. Though the method has already proved to work well in a lot of applications, the non-smoothness of the output may sometimes lead to problems. We propose in this paper a method how the resulting function can be made smooth so that the output preserves its good properties. The idea consists in post-processing the output using a special fuzzy approximation method called F-transform