2000 Volume 12 Issue 1 Pages 114-126
The main difficulty in applying a fuzzy modeling method based on fuzzy if-then rules to a nonlinear system with many input variables is the exponential increase in the number of fuzzy if-then rules with the number of the input variables. For avoiding the exponential increase without losing a clear linguistic interpretation of each fuzzy if-then rule, we need to utilize general fuzzy if-then rules with only a few antecedent conditions. Such a general fuzzy if-then rule, which has many "don't care" conditions in the antecedent part, covers a large area of the multi-dimensional input space of the nonlinear system. Thus the entire input space can be covered by a small number of general fuzzy if-then rules. Since there may exist some complicated parts of the nolinear system that can not be captured by the general fuzzy if-then rules, specific fuzzy if-then rules with many linguistic conditions may be required in the fuzzy modeling of the nonlinear system. As a result, our fuzzy model is a mixture of general and special fuzzy if-then rules. Some fuzzy if-then rules have many antecedent conditions and others have only a few conditions. In this paper, we first discuss the fuzzy reasoning for fuzzy if-then rules with different specificity levels. Next we propose a fuzzy reasoning method for realizing implicit hierarchies of fuzzy if-then rules where specific rules have priority over general rules in the fuzzy reasoning. Then we demonstrate that fuzzy reasoning results by the proposed method coincide with our intuitive understanding of fuzzy if-then rules. Finally we demonstrate that a small number of fuzzy if-then rules can be found from numerical data by genetic algorithms and the proposed fuzzy reasoning method.
