A New Approach of Centroid based Ranking Fuzzy Numbers and its Comparative Reviews

Abstract

The numeric values represented by fuzzy numbers are vague and ranking them according to their location on the real axis is not adequate and logical. Ranking of fuzzy numbers plays a vital role in measuring the degree of importance of different alternatives in decision-making under the fuzzy environment and the comparison of fuzzy numbers reflects that of alternatives. Although a lot of methods for ranking fuzzy numbers exist in the literature, even then none of them is superior to all others. This paper proposes a new method for ranking fuzzy numbers using the coordinates of the centroid point of the fuzzy numbers. It suggests a ranking score for the fuzzy number that multiplies the ordinate and the exponential value of the ratio of the ordinate to the abscissa of the centroid point. The proposed ranking score method can rank two or more fuzzy numbers simultaneously irrespective of their linear or non-linear membership functions. Furthermore, it consistently ranks symmetric fuzzy numbers of the same or different altitudes, images of fuzzy numbers, and the fuzzy numbers that describe the compensation of areas. Comparative reviews show an edge of the proposed method over several representative approaches.