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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, Number 5, Pages 65–78 (Mi ivm6737)  
This article is cited in 2 scientific papers (total in 2 papers)

Intuitionistic fuzzy semisimple ideals in ordered semigroups

A. Khana, M. Shabirb

a Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad, Pakistan
b Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan
Full-text PDF (224 kB) Citations (2)
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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.
Received: 30.04.2008
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2010, Volume 54, Issue 5, Pages 56–67
DOI: https://doi.org/10.3103/S1066369X10050087
Bibliographic databases:
UDC: 512.53+536.5
Language: Russian
Citation: A. Khan, M. Shabir, “Intuitionistic fuzzy semisimple ideals in ordered semigroups”, Izv. Vyssh. Uchebn. Zaved. Mat., 2010, no. 5, 65–78; Russian Math. (Iz. VUZ), 54:5 (2010), 56–67
Citation in format AMSBIB
\Bibitem{KhaSha10}
\by A.~Khan, M.~Shabir
\paper Intuitionistic fuzzy semisimple ideals in ordered semigroups
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2010
\issue 5
\pages 65--78
\mathnet{http://mi.mathnet.ru/ivm6737}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2779774}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2010
\vol 54
\issue 5
\pages 56--67
\crossref{https://doi.org/10.3103/S1066369X10050087}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78649609634}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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