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On Intuitionistic Fuzzy Ideals of Semirings with Respect to Fuzzy Connectives


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1 Department of Mathematics, Rajiv Gandhi University, Itanagar-791112, India
     

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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).

Keywords

Intuitionistic Fuzzy Set, Semiring, t-Norm, t-Conorm, Strong α-Cut, Weak α-Cut.
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  • On Intuitionistic Fuzzy Ideals of Semirings with Respect to Fuzzy Connectives

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Authors

Saifur Rahman
Department of Mathematics, Rajiv Gandhi University, Itanagar-791112, India
Apil Uddin Ahmed
Department of Mathematics, Rajiv Gandhi University, Itanagar-791112, India

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 (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).

Keywords


Intuitionistic Fuzzy Set, Semiring, t-Norm, t-Conorm, Strong α-Cut, Weak α-Cut.

References