A New Study Based on Fuzzy bi-Γ-ideals in Ordered-Γ-semigroups
Keywords:ordered Γ-semigroups, fuzzy subsets, (∈, ∈ ∨(κ∗ , qκ))-fuzzy bi-Γ-ideals
In this paper, using the notion of (k∗ , q)-quasi-coincident of an ordered fuzzy point with a fuzzy set of the support, the concept of (∈, ∈ ∨(κ∗ , qk))-fuzzy bi-Γ-ideals in ordered Γ-semigroups is defined. We prove that intersection of (∈, ∈ ∨(κ∗ , qk))-fuzzy bi-Γ-ideals of S is an (∈, ∈ ∨(κ∗ , qk))-fuzzy bi-Γ-ideal but the statement does not hold for union, and in this aim an example is provided. Moreover, we present correspondence between bi-Γ-ideals and (∈, ∈ ∨(κ∗ , qk))-fuzzy bi-Γ-ideals of ordered Γ-semigroups based on level subset and (∈ ∨(κ∗ , qκ))-level subset of fuzzy sets.
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