On the interpretation of fuzzy if then rules

摘要

The basic algorithm for reasoning in the fuzzy systems modeling method is introduced. Two classes of operators for interpreting the rules in these models are described, the Mamdani-Zadeh operator and the logical operator. The basic characteristics of these operators are presented and it is shown that the two classes of operators are distinguished by their response to a zero firing level. A class of Mamdani-Zadeh operators based upon the residuation operation is presented. A comparison is made between the performance of these residuation based Mamdani-Zadeh operators and the standard Mamdani-Zadeh operators derived from the t-norm. A new class of Mamdani-Zadeh operators based upon a generalization of the bounded difference is presented.