Optimal Fuzzy Modus Ponens and Tollens Algorithm Based on KSI Principle

L. A. Zadeh has proposed the Compositional rule of inference (CRI) in fuzzy reasoning in 1975. But Zadeh’s CRI has some shortcomings that do not satisfy the reductive property. To overcome the shortcomings of the CRI, Compensating Fuzzy Reasoning (CFR) method was proposed by [15]. Its idea is called KSI Principle, which does satisfy the reductive property. In this paper we propose a new optimal approximate reasoning method based on KSI principle. Our new method is based on obtaining fuzzy reasoning results based on moving difference obtained from a given fuzzy premise and fuzzy antecedents, obtaining new fuzzy premises from the moving difference of this reasoning results and the consequent fuzzy set, and then iteratively obtaining the new reasoning results different from the previous reasoning results by fuzzy moving difference obtained from these fuzzy premises and the antecedent fuzzy set until the objective function is satisfied. Proposed method is better in accordance with human thinking than the previous Zadeh’s CRI method.