Representation and ranking of fuzzy numbers with heptagonal membership function using value and ambiguity index

Abstract

In many real life problems, the parameters used to characterize the uncertainty or vagueness or impreciseness in information are either triangular or trapezoidal fuzzy numbers. But it is not always possible to restrict the membership function to either triangular or trapezoidal form. In this paper, a new form of non-normal fuzzy number named as Heptagonal fuzzy number is introduced and its arithmetic operations are defined. Further, an attempt has been made to give a new version of definition for value and ambiguity of non-normal fuzzy numbers and based on this new definition a parametric ranking method is proposed for ordering Heptagonal fuzzy numbers. Finally, an application of Heptagonal fuzzy number in fuzzy assignment problem is given and it is proved that the optimal value obtained using Heptagonal Fuzzy number is more optimal than the solution obtained by using Trapezoidal fuzzy numbers.