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Semiring-Valued Fuzzy Sets and F-Transform

Author

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  • Jiří Močkoř

    (Centre of Excellence IT4Innovations, Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 30. Dubna 22, 701 03 Ostrava, Czech Republic)

Abstract

The notion of a semiring-valued fuzzy set is introduced for special commutative partially pre-ordered semirings, including basic operations with these fuzzy structures. It is showed that many standard M V -algebra-valued fuzzy type structures with standard operations, such as hesitant, intuitionistic, neutrosophic or fuzzy soft sets are, for appropriate semirings, isomorphic to semiring-valued fuzzy sets with operations defined. F-transform and inverse F-transform are introduced for semiring-valued fuzzy sets and properties of these transformations are investigated. Using the transformation of M V -algebra-valued fuzzy type structures to semiring-valued fuzzy sets, the F-transforms for these fuzzy type structures is introduced. The advantage of this procedure is, among other things, that the properties of this F-transform are analogous to the properties of the classical F-transform and because these properties are proven for any semiring-valued fuzzy sets, it is not necessary to prove them for individual fuzzy type structures.

Suggested Citation

  • Jiří Močkoř, 2021. "Semiring-Valued Fuzzy Sets and F-Transform," Mathematics, MDPI, vol. 9(23), pages 1-24, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3107-:d:693712
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    References listed on IDEAS

    as
    1. Pinaki Majumdar & S. K. Samanta, 2008. "Similarity Measure Of Soft Sets," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-12.
    2. Huimin Zhang, 2014. "Linguistic Intuitionistic Fuzzy Sets and Application in MAGDM," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-11, April.
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