On the Jaccard Index with Degree of Optimism in Ranking Fuzzy Numbers

Ranking of fuzzy numbers plays an important role in practical use and has become a prerequisite procedure for decision-making problems in fuzzy environment. Jaccard index similarity measure has been introduced in ranking the fuzzy numbers where fuzzy maximum, fuzzy minimum, fuzzy evidence and fuzzy total evidence are used in determining the ranking. However, the fuzzy total evidence is obtained by using the mean aggregation which can only represent the neutral decision maker's perspective. In this paper, the degree of optimism concept winch represents all types of decision maker's perspectives is applied in calculating the fuzzy total evidence. Thus, the proposed method is capable to rank fuzzy numbers based on optimistic, pessimistic and neutral decision maker's perspective. Some properties which can simplify the ranking procedure are also presented.