(A) study on fuzzy control method with possibly inconsistent rule base

Abstract

In this thesis is studied a method of fuzzy logic control based on possibly inconsistent if-then rules representing uncertain knowledge or imprecise data. In most cases of practical applications adopting fuzzy if-then rule bases, inconsistent rules have been considered as ill-defined rules and, thus, not allowed to be in the same rule base. Note, however, that, in representing uncertain knowledge by using fuzzy if-then rules, the knowledge sometimes can not be represented in literally consistent if-then rules. In this thesis, it is assumed that, as long as inconsistent rules are also heuristically meaningful, there can be a useful information in the set of inconsistent rules and we propose that we allow inconsistent rules in the rule base to deal with the situation where it is difficult to obtain the rule base in usual ways. In this thesis, we first design an inference scheme to deal with the difficulty in handling inconsistent rules which appears when we use conventional inference scheme. One of the major difficulties is that, if we use all the possibly obtained rules including inconsistent rules in the same rule base, those rules with fuzzier consequents are more influential in forming a conclusion than those with less fuzzier consequence. To overcome the difficulty, we first propose a new type of inference scheme in which a new concept of distance on fuzzy sets is introduced for its inference procedure so that the odd phenomenon of fuzzier fuzzy sets being dominant in the consequents of rules does not occur. The next study in this thesis is to answer the fundamental questions regarding whether it is justified to use all the rules including inconsistent rules for inference and how the useful informations can be extracted from the inconsistent rules via inference procedure. For this, we use a statistical concept to prove that the proposed inference scheme is suitable for dealing with inconsistent rules and we can extract useful informations from a rule base ...