Ranking of Alternatives Described by Atanassov’s Intuitionistic Fuzzy Sets – A Critical Review

Abstract

While making decisions its is often convenient to use Atanassov’s intuitionistic fuzzy sets (IFSs) which are a very suitable tool because they can express in a natural way a decision maker’s arguments and judgments for, against, and with hesitation. The IFSs attract much attention and find many applications though, obviously, there are still some conceptual and algorithmic open problems related to their use. One of such problems is the ranking of intuitionistic fuzzy alternatives. The problem is very important but not all known methods produce satisfactory results. In this paper, we recall and critically analyze several methods of ranking of the intuitionistic fuzzy alternatives. We analyze them from the point of view of the results they yield and compare them taking into account their very illustrative geometrical representations. It turns out that most of these methods, except for one, have similar geometrical representations. For this latter method, we augment the assumptions assumed in the original version with an additional assumption, a justified and natural one, though not explicitly included so far. We therefore obtain a clearer interpretation of formulas involved in the augmented version of the method since the arguments pro, against and the hesitation are explicitly accounted for. This transparency is relevant for the user because there is no intuitively appealing linear order among the intuitionistic fuzzy alternatives so that some additional assumptions are to be made while ranking the elements. These issues are dealt with, and examples are provided.