Affiliations: [a] Department of Mathematics, Rajiv Gandhi University, Rono Hills, Itanagar, India
| [b] Department of Mathematics, Yazd University, Yazd, Iran
Correspondence:
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Corresponding author. Saifur Rahman, Department of Mathematics, Rajiv Gandhi University, Rono Hills, Itanagar 791112, India. Tel.: +91 7308145302; Fax: +91 3602277889; E-mail: [email protected].
Abstract: We define intuitionistic fuzzy idempotent, prime, strongly irreducible and t-pure ideals on a semiring, and investigate some properties of such ideals. We show that all intuitionistic fuzzy ideals are idempotent in a fully idempotent semirings, and right weakly regular semirings. We establish that an intuitionistic fuzzy set of a semiring is an intuitionistic fuzzy ideal if and only if (α, β)-cut is an ideal. We prove that if all intuitionistic fuzzy ideals of a semiring are t-pure, then an intuitionistic fuzzy ideal is prime if and only if it is strongly irreducible. We also establish that for a fully idempotent semirings, an intuitionistic fuzzy ideal is prime if and only if it is strongly irreducible.
