This article is cited in 3 papers

Intuitionistic fuzzy semisimple ideals in ordered semigroups

A. Khan^a, M. Shabir<sup>b

a</sup> Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad, Pakistan
^b Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan

Abstract: We give characterizations of different classes of ordered semigroups by using intuitionistic fuzzy ideals. We prove that an ordered semigroup is regular if and only if every intuitionistic fuzzy left (respectively, right) ideal of $S$ is idempotent. We also prove that an ordered semigroup $S$ is intra-regular if and only if every intuitionistic fuzzy two-sided ideal of $S$ is idempotent and give further characterizations of regular and intra-regular ordered semigroups in terms of intuitionistic fuzzy left (respectively, right) ideals. In the last part of this paper we prove that an ordered semigroup $S$ is left weakly regular if and only if every intuitionistic fuzzy left ideal of $S$ is idempotent.

Keywords: intuitionistic fuzzy sets, intuitionistic fuzzy ideals, regular (respectively, intra-regular and left weakly regular) ordered semigroups.

UDC: 512.53+536.5

Received: 30.04.2008

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2010, 54:5, 56–67

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