Ordering intuitionistic fuzzy numbers by a convex combination of values and multiple of ambiguity inclusion functions with ambiguities of membership and nonmembership functions

Abstract

Ranking methods of intuitionistic fuzzy numbers are abundant in literature. However, an adequately accepted approach of ordering intuitionistic fuzzy numbers is not apparent. This motivates to develop a new method of ordering intuitionistic fuzzy numbers. In many cases, studies of ranking intuitionistic fuzzy numbers do not investigate the reasonable properties that a ranking method should follow. Furthermore, the majority of existing methods do not meet the reasonable properties. Furthermore, investigating the consistency in image ordering was never a concern in previous studies of ranking intuitionistic fuzzy numbers. Hence, in this paper, an innovative method of ranking intuitionistic fuzzy numbers has been developed. The method is based on the index of optimism, that is, a convex combination of value and multiple of ambiguity inclusion function with ambiguity of membership function and value and multiple of ambiguity inclusion function with ambiguity of nonmembership function. The present method exclusively complies with the reasonable properties as it satisfies all the reasonable properties of a ranking method. Further, newer properties that depicts the consistency in ranking the intuitionistic fuzzy numbers with their corresponding images are also being developed in this study. It is worth mentioning that the present method consistently ranks the intuitionistic fuzzy numbers and their corresponding images.