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The concepts of (λ , µ)−fuzzy subsemigroup and various (λ , µ)−fuzzy ideals of a semigroup were introduced by generalizing (∈, ∈∨q)−fuzzy subsemigroup and (∈, ∈∨q)−fuzzy ideal. The regular semigroup was characterized by the properties of the middle parts of various (λ , µ)−fuzzy ideals, and several equivalence conditions of regular semigroups were obtained.
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