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Fuzzy Multi-Hypergroups
Open AccessArticle

Fuzzy Reduced Hypergroups

1
Department of Mathematics, University of Montenegro, 81000 Podgorica, Montenegro
2
Centre for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Slovenia
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Author to whom correspondence should be addressed.
Mathematics 2020, 8(2), 263; https://doi.org/10.3390/math8020263
Received: 10 January 2020 / Revised: 5 February 2020 / Accepted: 14 February 2020 / Published: 17 February 2020
(This article belongs to the Special Issue Hypercompositional Algebra and Applications)
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. View Full-Text
Keywords: fuzzy set; reducibility; grade fuzzy set fuzzy set; reducibility; grade fuzzy set
MDPI and ACS Style

Kankaras, M.; Cristea, I. Fuzzy Reduced Hypergroups. Mathematics 2020, 8, 263.

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