Investigating the Logical Structure of FUZZY IF-THEN Rule Bases using Concepts of Mathematical Logic and of Functional Analysis

Abstract

In developing a semantics for a Fuzzy If-Then Rule Base we in principle distinguish the following two approaches. Firstly, a Fuzzy If-Then Rule Base is considered as a Fuzzy Knowledge Base describing (time independent) situations by means of fuzzy logic. Secondly, a Fuzzy If-Then Rule Base describes the inner part of a fuzzy controller, therefore the conclusions of If-Then rules must be interpreted as assignments. In the paper presented we discuss only the first approach. To this end following TARSKI we define a suitable concept of model and semantic entailment for Fuzzy If-Then Rule Bases. Furthermore, we adopt the concept of fact from logic programming.