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

<p>We discuss some aspects of similarity measures in the context of Atanassov’s intuitionistic fuzzy sets (IFSs, for short). IFSs, proposed in 1983, are a relatively new tool for the modeling and simulation and, because of their construction, present us with new challenges as far the similarity measures are concerned. Specifically, we claim that the distances alone are not a proper measure of similarity for the IFSs. We stress the role of a lack of knowledge concerning elements (options, decisions, etc.) and point out the role of the opposing (complementing) elements. We also pay attention to the fact that it is not justified to talk about similarity when one has not enough knowledge about the compared objects/elements. Some novel measures of similarity are presented.</p>
</abstract>

We discuss some aspects of similarity measures in the context of Atanassov’s intuitionistic fuzzy sets (IFSs, for short). IFSs, proposed in 1983, are a relatively new tool for the modeling and simulation and, because of their construction, present us with new challenges as far the similarity measures are concerned. Specifically, we claim that the distances alone are not a proper measure of similarity for the IFSs. We stress the role of a lack of knowledge concerning elements (options, decisions, etc.) and point out the role of the opposing (complementing) elements. We also pay attention to the fact that it is not justified to talk about similarity when one has not enough knowledge about the compared objects/elements. Some novel measures of similarity are presented.

Similarity measures for Atanassov’s intuitionistic fuzzy sets: some dilemmas and challenges

Control and Cybernetics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

We discuss some aspects of similarity measures in the context of Atanassov’s intuitionistic fuzzy sets (IFSs, for short). IFSs, proposed in 1983, are a...

Similarity measures for Atanassov’s intuitionistic fuzzy sets: some dilemmas and challenges

Publicado en línea: 12 ago 2022

Páginas: 249 - 266

Recibido: 01 abr 2022

Aceptado: 01 abr 2022

DOI: https://doi.org/10.2478/candc-2022-0016

Palabras clave
similarity measures, Atanassov’s intuitionistic fuzzy sets, distances, complements

© 2022 Eulalia Szmidt et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Similarity measures for Atanassov’s intuitionistic fuzzy sets: some dilemmas and challenges

Publicado en línea: 12 ago 2022

Páginas: 249 - 266

Recibido: 01 abr 2022

Aceptado: 01 abr 2022

DOI: https://doi.org/10.2478/candc-2022-0016

Palabras clavesimilarity measures, Atanassov’s intuitionistic fuzzy sets, distances, complements

© 2022 Eulalia Szmidt et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Palabras clave
similarity measures, Atanassov’s intuitionistic fuzzy sets, distances, complements