On Intuitionistic Fuzzy Ideals of Semirings with Respect to Fuzzy Connectives

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 (α β) 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 τ, however, it is not necessarily an ideal with respect to τ. 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 α cut, strong cut and weak α cut are ideals (k-ideals).