Application of various reasoning methods to fuzzy rules with numerical degrees of confidence and verification of a kind of equality between singleton rules and conventional rules
Tatsuya Nomura · Electronics and Communications in Japan (Part III Fundamental Electronic Science) · 1997
Some fuzzy expert systems have recently been developed that use fuzzy rules with either numerical values or fuzzy numbers representing the degrees of confidence for the rules. In this paper, we propose two interpretations of the numerical degrees of confidence for these types of rules, called “direct degrees” and “indirect degrees.” We apply Zadeh's, Baldwin's, and Tsukamoto's reasoning methods to the rules under the two interpretations using general T-norms, and verify their properties. Moreover, in cases where fuzzy sets in descendent parts of rules are defined in a finite set, we present conditions for equivalence between rules with numerical degrees of confidence where the descendent parts are in Singleton form and conventional rules, under usage of *-max or *-sum composition to determine the conclusions of reasoning. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(8): 46–55, 1997