A Function Principle Approach to Jaccard Ranking Fuzzy Numbers

Abstract

Ranking of fuzzy numbers plays 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 the fuzzy maximum and fuzzy minimum are obtained by using the extension principle. However, this approach is only applicable to normal fuzzy numbers and therefore, fails to rank the non-normal fuzzy numbers. Besides that the extension principle does not preserve the type of membership function of the fuzzy numbers and also involves laborious mathematical operations. In this paper, a simple vertex fuzzy arithmetic operation namely function principle is applied in the Jaccard ranking index. This method is capable to rank both normal and non-normal fuzzy numbers in a simpler manner. It has also improved the ranking results by the original Jaccard ranking method and some of the existing ranking methods.