Amount of Information and Attitudinal-Based Method for Ranking Atanassov's Intuitionistic Fuzzy Values

Abstract

The ranking of Atanassov's intuitionistic fuzzy values (A-IFVs) is nontrivial because there is no natural linear order among them, as opposed to fuzzy sets. In this paper, we tackle this difficult problem and develop a new novel technique for ranking A-IFVs based on amount of information using the geometrical representation of Atanassov's intuitionistic fuzzy sets (A-IFSs), with the aim of overcoming some drawbacks and ambiguities in existing methods and to build a new ranking model in the A-IFS context from the viewpoint of amount of information. We prove that the order on nonempty A-IFVs induced by our function is admissible in the A-IFS context. Thus, our developed method provides a total order that extends the usual partial order between A-IFVs. Moreover, we discuss the role that a decision maker's attitude can play in decision making under uncertainty. This allows us to introduce the idea of attitudinal-based extension of our developed technique, which is much more useful and flexible in real-world applications. By this, we also provide a new idea and explanation to evaluate two special A-IFVs: the completely known opposition (0,1,0) and the completely unknown information (0,0,1). Finally, an effort is made to extend the applicability of the developed methods by considering the situation in which Atanassov's interval-valued intuitionistic fuzzy sets are involved. Experimental studies show the good performance of the developed methods in the A-IF and A-IVIF situations, respectively.Index Terms-Atanassov's intuitionistic fuzzy sets (A-IFSs), attitudinal character, decision making, ranking.

Priorities of Intuitionistic Fuzzy Preference Relation Based on Multiplicative Consistency

“…For the applications of A-IFS, there is required an order relation that should be fixed and that plays a crucial role for the proposed results [7], [41]. In order to rank IFVs, many scholars have proposed different procedures [3], [7], [41]- [43].…”

Preference Attitude‐Based Method for Ranking Intuitionistic Fuzzy Numbers and Its Application in Renewable Energy Selection

“…To analyze the fuzzy meaning of an intuitionistic fuzzy value, Yu et al [26] formalized an intuitionistic fuzzy value as a fuzzy subset and determined the dominance relation between two intuitionistic fuzzy values. Guo [27] built a new ranking model based on the viewpoint of amount of information. A total order which extended the usual partial order was analyzed in deep.…”

A novel group decision making method with intuitionistic fuzzy preference relations for RFID technology selection

“…It is impractical to express the evaluation information by accurate measurement and crisp numerical values. Since intuitionistic fuzzy set (IFS) [17] considers the membership and non-membership degrees simultaneously, it is flexible and practical in dealing with ambiguity and uncertainty [18][19][20][21][22][23][24][25][26][27][28][29][30][31].…”

“…In general, the tolerance parameters l ij  and l ij  should be chosen enough large that makes the optimal solution non-empty. (2) The pessimistic approachIn this approach, the linear membership function for intuitionistic fuzzy constraint ( ) 0l ij IF H   wis also Eq (19). while the non-membership function is constructed as…”