On the Jaccard Index Similarity Measure in Ranking Fuzzy Numbers

Ranking fuzzy numbers play an important role in practical use and has become a prerequisite procedure for decision-making problem in fuzzy environment. Various techniques of ranking fuzzy numbers have been developed and one of them is based on the similarity measure technique. 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 study of Jaccard index similarity measure only focuses on the triangular fuzzy numbers and so far has not been utilized to other shapes of fuzzy numbers. Sometimes in some cases, it cannot discriminate the ranking between two different fuzzy numbers effectively. This paper extends the Jaccard index similarity measure in ranking all shapes of fuzzy numbers such as trapezoidal and general forms of fuzzy numbers. We have shown that when the degree of optimism concept is applied in determining the fuzzy total evidence, the ranking results has improved.