Ranking generalized fuzzy numbers based on centroid and rank index

Ranking fuzzy numbers is an increasingly important research issue in decision making, because it provides support for decision makers to select the best alternative under an uncertain environment. The recent ranking approach for generalized fuzzy numbers by Kumar et al. (Soft Computing, 15(7): 1373–1381, 2011) suffers from common shortcomings associated with discrimination, loss of information, and the inability to distinguish a group of fuzzy numbers. This study is divided into three stages. The first stage indicates the shortcomings through three cases: a group of four overlapping fuzzy numbers, two fuzzy numbers in a certain case, and fuzzy numbers that have the same mode but of different height. The second stage proposes an extended ranking approach for generalized fuzzy numbers integrating the concepts of centroid point, rank index value, height of a fuzzy number, and the degree of the decision maker’s optimism. The third stage investigates the three above-mentioned cases and the identical centroid point of two fuzzy numbers by the proposed method and compares them with previous studies. The results show that the proposed approach overcomes the above-mentioned shortcomings and provides a consistent ranking order for decision makers.