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Approximations of fuzzy soft sets by fuzzy soft relations with image processing application

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Abstract

Fuzzy soft sets represent a generalization of fuzzy sets with considerable application potential in decision-making problems, optimization, and computer science. In the paper, we use the fact that the fuzzy soft sets powerset theory is defined by the monad and, using this theory, we introduce the concept of fuzzy soft relations defined by the monad. Using that general method, we can also introduce the fuzzy soft approximation of fuzzy soft sets defined by fuzzy soft relations. We show that fuzzy soft sets and fuzzy soft approximations can be naturally used in selective color segmentation problem, where reliable and fully automated methods do not yet exist.

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Acknowledgements

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

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Authors and Affiliations

  1. Centre of Excellence IT4Innovations, Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 30. dubna 22, Ostrava, Czech Republic

    Jiří Močkoř & Petr Hurtík

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  1. Jiří Močkoř
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  2. Petr Hurtík
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Correspondence to Jiří Močkoř.

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Močkoř, J., Hurtík, P. Approximations of fuzzy soft sets by fuzzy soft relations with image processing application. Soft Comput 25, 6915–6925 (2021). https://doi.org/10.1007/s00500-021-05769-3

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