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By introducing element equivalence class that proposes dynamic characteristic into Pawlak Z rough sets theory, the first author of this paper improved Pawlak Z rough sets and put forward S-rough sets (singular rough sets). S-rough sets are defined by element equivalence class that proposes dynamic characteristic. S-rough sets have dynamic characteristic. By… (More)
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.