Ranking intuitionistic fuzzy numbers at levels of decision‐making and its application.

Abstract: In this paper, a new method of ranking trapezoidal intuitionistic fuzzy numbers has been introduced based on the concept of value and ambiguity at different levels of decision‐making. The concept of decision levels α for the membership function and β for the non‐membership function called as the flexibility parameters have been introduced in ranking these types of fuzzy numbers. If the flexibility parameters α is close to maximum membership degree of the membership function and β close to minimum membership degree of non‐membership function, then a high‐level decision is made. Likewise, if the flexibility parameters α is close to minimum membership degree of membership function and β close to maximum membership degree of non‐membership function, then a low‐level decision is made. Again, if the flexibility parameters α and β lie between minimum membership degree of the membership function and maximum membership degree of the non‐membership function, then an intermediate decision is made. This phenomenon of the proposed method is an attractive feature as it allows the decision‐maker to make a choice on the levels of decision. Further, the rationality validation of the proposed method has been checked by proving some of the Wang and Kerre's reasonable properties on ordering fuzzy quantities. [ABSTRACT FROM AUTHOR]