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International Journal of Fuzzy Logic and Intelligent Systems 2020; 20(4): 298-315

Published online December 25, 2020

https://doi.org/10.5391/IJFIS.2020.20.4.298

© The Korean Institute of Intelligent Systems

Powerset Theory of Fuzzy Soft Sets

Jiří Močkoř

Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Ostrava, Czech Republic

Correspondence to :
Jiří Močkoř (Jiri.Mockor@osu.cz)

Received: May 28, 2019; Revised: December 8, 2020; Accepted: December 10, 2020

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Fuzzy powerset theory is defined by a monad, and therefore it can be applied in computer science. Fuzzy soft sets generalize fuzzy sets and have considerable application potential in, for instance, decision-making and optimization. In this study, we prove that fuzzy soft sets also give rise to a powerset theory, which is also defined by a monad. As in the case of fuzzy sets, in fuzzy soft set theory, it is possible to use several theoretical constructions requiring the existence of a powerset theory and monads. We describe the construction of fuzzy soft relations as an example of the use of monads in fuzzy soft sets.

Keywords: Fuzzy soft set, Monad powerset theory, Fuzzy soft relations

This research was partially supported by the ERDF/ESF project CZ.02.1.01/0.0/0.0/17-049/0008414.

No potential conflict of interest relevant to this article was reported.

Jiří Močkoř is a Professor of algebra at the University of Ostrava and Senior Researcher at the Institute for Research and Application of Fuzzy Modeling at this University. He has been working on research related to category theory with applications in fuzzy set theory and fuzzy logic. He is the author or co-author of 4 monographs on theoretical algebra and fuzzy logic and published more than 100 articles in peer-reviewed journals and conferences.

E-mail: mockor@osu.cz


Article

Original Article

International Journal of Fuzzy Logic and Intelligent Systems 2020; 20(4): 298-315

Published online December 25, 2020 https://doi.org/10.5391/IJFIS.2020.20.4.298

Copyright © The Korean Institute of Intelligent Systems.

Powerset Theory of Fuzzy Soft Sets

Jiří Močkoř

Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Ostrava, Czech Republic

Correspondence to:Jiří Močkoř (Jiri.Mockor@osu.cz)

Received: May 28, 2019; Revised: December 8, 2020; Accepted: December 10, 2020

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Fuzzy powerset theory is defined by a monad, and therefore it can be applied in computer science. Fuzzy soft sets generalize fuzzy sets and have considerable application potential in, for instance, decision-making and optimization. In this study, we prove that fuzzy soft sets also give rise to a powerset theory, which is also defined by a monad. As in the case of fuzzy sets, in fuzzy soft set theory, it is possible to use several theoretical constructions requiring the existence of a powerset theory and monads. We describe the construction of fuzzy soft relations as an example of the use of monads in fuzzy soft sets.

Keywords: Fuzzy soft set, Monad powerset theory, Fuzzy soft relations

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