On intuitionistic fuzzy idempotent, prime, strongly irreducible and t-pure ideals of semirings

被引：4

作者：

Ahmed, Apil Uddin ^{[1
]}

Rahman, Saifur ^{[1
]}

Davvaz, Bijan ^{[2
]}

机构：

[1] Rajiv Gandhi Univ, Dept Math, Rono Hills, Itanagar 791112, India

[2] Yazd Univ, Dept Math, Yazd, Iran

来源：

JOURNAL OF INTELLIGENT & FUZZY SYSTEMS | 2017年 / 33卷 / 01期

关键词：

Intuitionistic fuzzy idempotent ideals; intuitionistic fuzzy t-pure ideals; intuitionistic fuzzy prime ideals; intuitionistic fuzzy strongly irreducible ideals; fully idempotent semirings; weakly regular semirings; WEAKLY REGULAR-RINGS; K-IDEALS;

D O I：

10.3233/JIFS-161747

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

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 (alpha, beta)-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.

引用

页码：433 / 443

页数：11

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