Atanassov’s Intuitionistic Fuzzy Sets Demystified

To what extent can intuitionistic fuzzy options be ranked?

“…However, we can show also in another way that the answer obtained by Definition 1 is correct. To do so, we recall that the three term representation of IFSs can be expressed by two intervals, namely (Szmidt and Kacprzyk [33]:…”

“…In this paper, we stress when the proposed by us (see [27]) method of ranking should be used, and compare the results obtained by it with the results of other well-known and still cited methods of ranking. In our considerations, we make use of the scenarios (Szmidt and Kacprzyk [33]) which are possible to construct when we take into account all three terms describing the intuitionistic fuzzy alternatives, namely, membership values, non-membership values, and the hesitation margins. We recall the examples of not justified results given by other methods and compare them with the results by our method.…”

“…The two-term representation (without a hesitation margin) and the three-term representation (with a hesitation margin) of IFSs with some conceptual and analytic aspects were presented in [31][32][33]35].…”

Ranking of Alternatives Described by Atanassov’s Intuitionistic Fuzzy Sets – Reconciling Some Misunderstandings

“…The two-term representation (without a hesitation margin) and the three-term representation (with a hesitation margin) of the IFSs were presented in [9,10,11].…”

“…(cf. [26,27,28,29,30]), [31,32,33,34,35,36,37,38,39]. Sometimes the concept of the hesitation margin is just indispensable, for example, for a proper definition of the Hausdorff distance [40] or attribute selection [37,41,42].…”