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Powerset Theory of Fuzzy Soft Sets
International Journal of Fuzzy Logic and Intelligent Systems 2020;20(4):298-315
Published online December 25, 2020
© 2020 Korean Institute of Intelligent Systems.

Jiří Močkoř

Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Ostrava, Czech Republic
Correspondence to: Jiří Močkoř (
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 ( which permits unrestricted non-commercial 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

December 2020, 20 (4)
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  • CrossMark
  • Science Central