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• W2044936618 abstract "Abstract. In this paper, the concept of (∈,∈∨q)-fuzzy hyper K-sub-algebras andfuzzyhyper K-subalgebraswiththresholds areintroduced,andrelatedpropertiesandcharacterizations arediscussed. 1. IntroductionThe hyperstructure theory (called also multialgebras) is introduced in 1934by Marty [26] at the 8th congress of Scandinavian Mathematicians. Aroundthe 40’s, several authors worked on hypergroups, especially in France and inthe United States, but also in Italy, Russia, Japan and Iran. Hyperstruc-tures have many applications to several sectors of both pure and applied sci-ences. Jun et al. [22] introduced and studied hyperBCK-algebra which is ageneralization of a BCK-algebra. Borzooei et al. constructed the hyper K-algebras, and studied (weak) implicative hyper K-ideals in hyper K-algebras(see [3, 4, 5]). Fuzzy sets and hyperstructures introduced by Zadeh and Marty,respectively, are now used in the real world, both from a theoretical point ofview and for their many applications. The relations between fuzzy sets and hy-perstructures have been already considered by several authors (for instance see[6, 7, 8, 9, 10, 11, 12, 17, 19, 20, 24, 25, 31]). Murali [27] proposed a definitionof a fuzzy point belonging to fuzzy subset under a natural equivalence on fuzzysubset. The idea of quasi-coincidence of a fuzzy point with a fuzzy set, which ismentioned in [28], played a vital role to generate some different types of fuzzysubsets. Using the “belongs to” relation (∈) and “quasi-coincident with” rela-tion (q) between a fuzzy point and a fuzzy set, the fuzzy set theory applied tomany algebraic structures (for instance see [1, 2, 13, 14, 15, 16, 18, 21, 29, 30]).As a generalizationof the notion of fuzzy hyper K-subalgebras, Kang [23] intro-duced the concept of fuzzy hyper K-subalgebrasof type (α,β) where α, β ∈ {∈,q, ∈∨q, ∈∧q} and α 6= ∈∧q. He investigated relations between each types,and discussed many related properties. In particular, he dealt with the no-tion of (∈, ∈∨q)-fuzzy hyper K-subalgebras, and considered characterizations" @default.
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• W2044936618 date "2013-10-31" @default.
• W2044936618 modified "2023-09-22" @default.
• W2044936618 title "A NEW TYPE OF HYPER K-SUBALGEBRAS" @default.
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• W2044936618 doi "https://doi.org/10.4134/ckms.2013.28.4.679" @default.
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