The Exact Defuzzification Method Under Polynomial Approximation of Various Fuzzy Sets

Abstract

This article deals with the new approach of finding the defuzzification / ranking index of various types of fuzzy sets. Traditionally, in most of the articles on fuzzy decision making the defuzzification methods are not justified with respect to that of highest aspiration levels. This study highlights an efficient defuzzification (ranking) method which links between the gaps on the defuzzified values obtained using α − cuts and without α − cuts of fuzzy numbers. Moreover, for a given problem different membership grades are found by different researchers which are confusing and contradicts the conceptual uniqueness of fuzzy set itself. To resolve these issues, first of all, we have studied a polygonal fuzzy set by means of an interpolating polynomial function. However, in fuzzy set theory we usually seek the highest membership grade for ranking any kind of decision- making problem therefore, maximizing the polynomial function, we get the index value of the proposed fuzzy set. An artificial intelligence (AI) based solution algorithm has also been developed to find the exact defuzzified value. Indeed, considering two numerical examples we have compared these ranking values with some of the existing state of- arts under higher aspiration levels. Finally, some graphical illustrations have also been done to justify the proposed approach.