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On Intuitionistic Fuzzy Ideals of Semirings with Respect to Fuzzy Connectives

Saifur Rahman, Apil Uddin Ahmed

Abstract


Intuitionistic fuzzy prime and strongly irreducible ideals with respect to fuzzy connectives of a semiring are introduced and investigated some properties of these ideals. It is shown that if every cut of an intuitionistic fuzzy set of a semiring is an ideal, then the associated intuitionistic fuzzy set is both left and right ideal with respect to any t-norm , however, it is not necessarily an ideal with respect to . Finite intersection of intuitionistic fuzzy ideals (k-ideals) with respect to a t-norm is again is an intuitionistic fuzzy ideal (k-ideal) with respect to the t-norm is established.  It is also found that if an intuitionistic fuzzy set  is an ideal (k-ideal) with respect to the minimum t-norm, then its nonempty cut, strong cut and weak cut are ideals (k-ideals).

Keywords


Intuitionistic Fuzzy Set, Semiring, t-norm, t-conorm, Strong α-cut, weak α-cut.

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References


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