On Interpreting Fuzzy IF-THEN Rule Bases by Concepts of Functional Analysis

Abstract

Starting with ZADEH's fundamental paper 'The Calculus of Fuzzy IF-THEN Rules' we mention five possible interpretations of a Fuzzy IF-THEN Rule Base. The interpretation of a given Fuzzy IF-THEN Rule Base strongly depends on the area where it is to be applied. In the paper presented we restrict this area to fuzzy control and approximate reasoning. Consequently, we interpret a Fuzzy IF-THEN Rule Base as a system of functional equations for determining a special functional operator. Then using the concepts of functional analysis and metric spaces we introduce the principles FATI and FITA and study their correctness and equivalence.