On Kleene-Diens inference

The Kleene-Diens implication operator is defined in terms of the min T-norm, which is the limit of the Schweizer-Sklar (1961) T-norm as the parameter p grows without bound. Consider a fuzzy rule-based system with trapezoidal antecedent and consequent fuzzy sets and mode defuzzification. The behavior of the system differs significantly depending on whether the Schweizer-Sklar parameter is taken to its limit before of after the inferencing and defuzzification. A four-rule knowledge base provides a simple benchmark to compare the behavior of the two versions of Kleene-Diens inference.