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 with inconsistent rules.
In this thesis, the way of using inconsistent rules is also applied to the design of a new type of Fuzzy Neural Network(FNN). For this, we propose the qualitative model with inconsistent rules as a means to represent uncertain knowledge. The imprecise data can be converted into the possibly conflicting knowledge which can be effectively represented and dealt with by the proposed qualitative model and, thus the FNN based on the qualitative model is to be suitable for dealing with the imprecise data.
In order to show the effectiveness of the approach in this study, the overhead crane system is controlled based on the identical rule base containing the multiple groups of rules which are respectively obtained from contradictory control objectives. Then the truck and trailer backer-upper control is done by collecting all the possibly obtained control rules and using them in the same rule base. Also the proposed FNN is applied to control of the yo-yo system by using imprecise sampled I/O data possibly obtained from the actions of a human playing yo-yo. The results show that the approaches in this study is useful when we use uncertain knowledge or imprecise data for fuzzy control.
