General Forms of (α, β)-Fuzzy Subhypergroups of Hypergroups
Yunqiang Yin, Jianming Zhan, Violeta Leoreanu-Fotea and Saeed Rasouli
Based on the concepts of “γ -belongingness (∈γ)” and “δ-quasicoincidence (qδ)” of a fuzzy point with a fuzzy set which generalize the concepts of “belongingness (∈)” and “quasi-coincidence (q)” of a fuzzy point with a fuzzy set introduced by Liu and Pu, this paper considers general forms of (α, β)-fuzzy subhypergroups of a hypergroup, where α, β ∈ {∈γ , qδ, ∈γ ∧qδ, ∈γ ∨qδ} and α =∈γ ∧qδ . The notion of (α, β)-fuzzy subhypergroups of a hypergroup is introduced, and several properties are investigated. A special attention is given to (∈γ , ∈γ ∨qδ)-fuzzy subhypergroups. Their characterizations and homomorphism properties are considered.
Keywords: Hypergroup, (α, β)-fuzzy subhypergroup, (∈γ , ∈γ ∨qδ )-fuzzy subhypergroup