EXACT-SOLUTIONS FOR INTERACTING RULES IN GENERALIZED MODUS PONENS WITH PARAMETERIZED IMPLICATION FUNCTIONS

Many authors have presented exact analyses of the behavior of an isola ted fuzzy inference rule, and many have presented empirical studies of the behavior of multiple-rule systems. This paper presents an exact a nalysis of the behavior of a class of two-rule systems in which the an tecedent and consequent membership functions are trapezoidal and the i mplication operator is a strong implication (S-implication) or a resid uated implication (R-implication) formed by the Schweizer-Sklar family of parameterized T-norms. The two-rule system exhibits many emergent properties not found when a single rule is studied, and much of the be havior of many-rule systems is dominated by two-rule interactions.