RANKING OF FUZZY-SETS BASED ON THE CONCEPT OF EXISTENCE

Various approaches have been proposed for the comparison or ranking of fuzzy sets. However, due to the complexity of the problem, a general method which can be used for any situation still does not exist. This paper formalizes the concept of existence for the ranking of fuzzy sets. Many of the existing fuzzy ranking methods are shown to be some application of this concept. An improved fuzzy ranking method is then introduced, based on this concept. This newly introduced method is expanded for treating both normal and nonnormal, convex and nonconvex fuzzy sets. Emphasis is placed on the use of the subjectivity of the decision maker, such as the optimistic or the pessimistic view points. An improved procedure for obtaining linguistic conclusions is also developed. Finally, some numerical examples are given to illustrate the approach.