1. PRODUCT-SUM-GRAVITY METHOD = FUZZY SINGLETON-TYPE REASONING METHOD = SIMPLIFIED REASONING METHOD

Abstract

This paper shows that product-sum-gravity method whose consequent part consists of fuzzy set is reduced to fuzzy singleton-type reasoning method by regarding the area of fuzzy set of the consequent part as the weight of fuzzy singleton-type reasoning method. Moreover, it is shown that fuzzy singleton-type reasoning method is reduced to simplified reasoning method by multiplying fuzzy set in the antecedent part of simplified reasoning method by the weight of fuzzy singleton-type reasoning method. Therefore, these three fuzzy reasoning methods are found to be equivalent.