Abstract. As a generalization of fuzzy subsemigroups, the notion of ε-generalized fuzzy subsemigroups is introduced, and several properties are investigated. A condition for an ε-generalized fuzzy subsemigroup to be a fuzzy subsemigroup is considered. Characterizations of ε-generalized fuzzy subsemigroups are established, and we show that the intersection of two ε-generalized fuzzy subsemigroups is also an ε-generalized fuzzy subsemigroup. A condition for an ε-generalized fuzzy subsemigroup to be ε-fuzzy idempotent is discussed. Using a given ε-generalized fuzzy subsemigroup, a new ε-generalized fuzzy subsemigroup is constructed. Finally, the fuzzy extension of an ε-generalized fuzzy subsemigroup is considered.
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