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Fuzzy Reduced Hypergroups

Author

Listed:
  • Milica Kankaras

    (Department of Mathematics, University of Montenegro, 81000 Podgorica, Montenegro)

  • Irina Cristea

    (Centre for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Slovenia)

Abstract

The fuzzyfication of hypercompositional structures has developed in several directions. In this note we follow one direction and extend the classical concept of reducibility in hypergroups to the fuzzy case. In particular we define and study the fuzzy reduced hypergroups. New fundamental relations are defined on a crisp hypergroup endowed with a fuzzy set, that lead to the concept of fuzzy reduced hypergroup. This is a hypergroup in which the equivalence class of any element, with respect to a determined fuzzy set, is a singleton. The most well known fuzzy set considered on a hypergroup is the grade fuzzy set , used for the study of the fuzzy grade of a hypergroup. Based on this, in the second part of the paper, we study the fuzzy reducibility of some particular classes of crisp hypergroups with respect to the grade fuzzy set.

Suggested Citation

  • Milica Kankaras & Irina Cristea, 2020. "Fuzzy Reduced Hypergroups," Mathematics, MDPI, vol. 8(2), pages 1-12, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:263-:d:321533
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    Citations

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    Cited by:

    1. Christos Massouros & Gerasimos Massouros, 2021. "An Overview of the Foundations of the Hypergroup Theory," Mathematics, MDPI, vol. 9(9), pages 1-41, April.
    2. Christos G. Massouros & Naveed Yaqoob, 2021. "On the Theory of Left/Right Almost Groups and Hypergroups with their Relevant Enumerations," Mathematics, MDPI, vol. 9(15), pages 1-31, August.
    3. Irina Cristea & Milica Kankaraš, 2021. "The Reducibility Concept in General Hyperrings," Mathematics, MDPI, vol. 9(17), pages 1-14, August.

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