<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Atanassov’s intuitionistic fuzzy sets (IFSs) are a very convenient tool for describing alternatives/options while making decisions because they make it possible to naturally represent the pros, cons, and hesitation. The IFSs have attracted a significant interest and have been applied in various fields. Of course, their use poses some challenges. One of the main challenges is the ranking of alternatives/options described by the intuitionistic fuzzy sets, to be called for brevity the intuitionistic fuzzy alternatives. This is a crucial issue, notably for the applications, for instance, in decision making. We first present in detail and analyze the benefits of a method we introduced previously (cf. Szmidt and Kacprzyk [<xref ref-type="bibr" rid="j_jaiscr-2024-0013_ref_001">1</xref>]). For this method, we augment the original assumptions with an additional assumption, which is justified and inherently reasonable. As a result, we obtain formulas which are better justified than those previously used as they explicitly consider the arguments in favor (pro), against (con), and hesitance. Since the intuitionistic fuzzy alternatives can not be linearly ranked, then the additional assumptions during the ranking process are necessary. We address these issues and analyze examples to clarify our new approach. We examine some other methods discussed in the literature and analyze their results, and show that the new assumptions reconcile some misconceptions raised by those other papers.</p>
</abstract>

Atanassov’s intuitionistic fuzzy sets (IFSs) are a very convenient tool for describing alternatives/options while making decisions because they make it possible to naturally represent the pros, cons, and hesitation. The IFSs have attracted a significant interest and have been applied in various fields. Of course, their use poses some challenges. One of the main challenges is the ranking of alternatives/options described by the intuitionistic fuzzy sets, to be called for brevity the intuitionistic fuzzy alternatives. This is a crucial issue, notably for the applications, for instance, in decision making. We first present in detail and analyze the benefits of a method we introduced previously (cf. Szmidt and Kacprzyk [1]). For this method, we augment the original assumptions with an additional assumption, which is justified and inherently reasonable. As a result, we obtain formulas which are better justified than those previously used as they explicitly consider the arguments in favor (pro), against (con), and hesitance. Since the intuitionistic fuzzy alternatives can not be linearly ranked, then the additional assumptions during the ranking process are necessary. We address these issues and analyze examples to clarify our new approach. We examine some other methods discussed in the literature and analyze their results, and show that the new assumptions reconcile some misconceptions raised by those other papers.

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

Department of Intelligent Computer Systems

Journal of Artificial Intelligence and Soft Computing Research

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Atanassov’s intuitionistic fuzzy sets (IFSs) are a very convenient tool for describing alternatives/options while making decisions because they make it...

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

Pubblicato online: 11 giu 2024

Pagine: 237 - 250

Ricevuto: 03 dic 2023

Accettato: 25 feb 2024

DOI: https://doi.org/10.2478/jaiscr-2024-0013

Parole chiave
Atanassov’s intuitionistic fuzzy sets, intuitionistic fuzzy options, ranking, geometrical representations

© 2024 Eulalia Szmidt et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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

Pubblicato online: 11 giu 2024

Pagine: 237 - 250

Ricevuto: 03 dic 2023

Accettato: 25 feb 2024

DOI: https://doi.org/10.2478/jaiscr-2024-0013

Parole chiaveAtanassov’s intuitionistic fuzzy sets, intuitionistic fuzzy options, ranking, geometrical representations

© 2024 Eulalia Szmidt et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Parole chiave
Atanassov’s intuitionistic fuzzy sets, intuitionistic fuzzy options, ranking, geometrical representations