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W. A. Dudek, M. Shabir and M. Irfan Ali discussed the properties of ()-fuzzy ideals of hemirings in [9]. In this paper, we discuss the generalization of their results on ()-fuzzy ideals of hemirings. As a generalization of the notions of -fuzzy left (right) ideals, -fuzzy h-ideals and -fuzzy k-ideals, the concepts of -fuzzy left (right) ideals, -fuzzy h-ideals and -fuzzy k-ideals are defined, and their characterizations are considered. Using a left (right) ideal (resp. h-ideal, k-ideal), we construct an -fuzzy left (right) ideal (resp. -fuzzy h-ideal, -fuzzy k-ideal). The implication-based fuzzy h-ideals (k-ideals) of a hemiring are considered.

GENERAL TYPES OF (α,β)-FUZZY IDEALS OF HEMIRINGS