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Algebra and Discrete Mathematics, 2013, Volume 16, Issue 1, Pages 61–70
(Mi adm434)
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This article is cited in 2 scientific papers (total in 2 papers)
RESEARCH ARTICLE
$(\lambda,\mu)$-fuzzy interior ideals of ordered $\Gamma$-semigroups
Yuming Fengab, P. Corsinia a 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
Citation:
Yuming Feng, P. Corsini, “$(\lambda,\mu)$-fuzzy interior ideals of ordered $\Gamma$-semigroups”, Algebra Discrete Math., 16:1 (2013), 61–70
Linking options:
https://www.mathnet.ru/eng/adm434 https://www.mathnet.ru/eng/adm/v16/i1/p61
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