A Proposal of Interpretations on Numerical Degrees ofCon dence for Fuzzy If { Then

Some fuzzy expert systems have used fuzzy rules with numerical values which represent degrees of conndence for rules. We discuss two kinds of interpretations for these numerical degrees of conndence for rules, called "di-rect degrees " and "indirect degrees". Then, we apply Zadeh's, Baldwin's, and Tsukamoto's reasoning method to the rules under the two interpretations using general T-norms, and verify their properties. Moreover, in cases where fuzzy sets in descendant parts of rules are deened on a nite set, we present conditions for equivalence between rules with numerical degrees of conndence where descendant parts are singleton form and conventional rules, under usage of {max or {sum composition for conclusions of reasoning.