This article is cited in 2 papers

RESEARCH ARTICLE

$(\lambda,\mu)$-fuzzy interior ideals of ordered $\Gamma$-semigroups

Yuming Feng^ab, P. Corsini<sup>a

a</sup> Dipartimento di Ingegneria Civile e Architettura dell’Universita’ degli Studi di Udine, Via delle Scienze, 206, 33100 Udine, Italy
^b School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou, Chongqing, 404100, P.R. China

Abstract: For all $\lambda,\mu\in [0,1]$ such that $\lambda<\mu$, we first introduced the definitions of $(\lambda,\mu)$-fuzzy ideals and $(\lambda,\mu)$-fuzzy interior ideals of an ordered $\Gamma$-semigroup. Then we proved that in regular and in intra-regular ordered semigroups the $(\lambda,\mu)$-fuzzy ideals and the $(\lambda,\mu)$-fuzzy interior ideals coincide. Lastly, we introduced the concept of a $(\lambda,\mu)$-fuzzy simple ordered $\Gamma$-semigroup and characterized the simple ordered $\Gamma$-semigroups in terms of $(\lambda,\mu)$-fuzzy interior ideals.

Keywords: $\Gamma$-semigroup; $(\lambda,\mu)$-fuzzy interior ideal; $(\lambda,\mu)$-fuzzy simple; regular ordered $\Gamma$-semigroup; intra-regular ordered $\Gamma$-semigroup.

Received: 13.02.2011
Revised: 01.03.2012

Language: English

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