A generalized model for ranking fuzzy sets

Ranking fuzzy numbers using similarity measure with centroid

“…Any generalized fuzzy numbers may be transformed into standardized generalized fuzzy numbers as depicted in (1). In 1998, [10] proposed a method of ranking fuzzy numbers using similarity measure. They utilized the Jaccard Index to obtain the similarity measure as well as the ranking of the fuzzy numbers.…”

“…In the existing ranking fuzzy numbers method using similarity measure, Jaccard Index was used. [10] used solely the Jaccard index to rank the fuzzy numbers, while [11] extended [10] method by introducing the function principle to Jaccard index to obtain the ranking. In [11], the concept of index of optimism ( β that represents decision makers' degree of optimism is incorporated in the decision making procedure.…”

“…In [11], the concept of index of optimism ( β that represents decision makers' degree of optimism is incorporated in the decision making procedure. Methods by [10] and [11] can only rank overlapping fuzzy numbers.…”

An Alternative Ranking Approach and Its Usage in Multi-Criteria Decision-Making

“…As it is seen, the area that is not overlapping is named For example, in Fig. 6 let the fuzzy numbers A % and B % take the following values, respectively: (2,3,4,8) and (1,5,6,7). Then, from Eq.…”

“…The third category differs substantially from the first two. In this category, a method for pair wise ranking or preference for all pairs of fuzzy numbers is determined and then based on these pair wise orderings, a final order of the n fuzzy numbers is attempted 3 . The investigation on ranking fuzzy numbers began early 70's.…”