IJPAM: Volume 92, No. 3 (2014)


Somsak Lekkoksung
Department of Mathematics
Faculty of Engineering
Rajamangala University of Technology Isan
Khon Kaen Campus, THAILAND

Abstract. In this paper we shows that in ordered groupoids the $Q$-fuzzy right (resp. $Q$-fuzzy left) ideals are $Q$-fuzzy quasi-ideals, in ordered semigroups the $Q$-fuzzy quasi-ideals are $Q$-fuzzy bi-ideals, and in regular ordered semigroups the $Q$-fuzzy quasi-ideals and the $Q$-fuzzy bi-ideals coincide and show that if $S$ is an ordered semigroup, then a $Q$-fuzzy subset $f$ is a $Q$-fuzzy quasi-ideal of $S$ if and only if there exist a $Q$-fuzzy right ideal $g$ and a $Q$-fuzzy left ideal $h$ of $S$ such that $f=g\cap h$.

Received: October 19, 2013

AMS Subject Classification: 06F05

Key Words and Phrases: ordered semigroup, regular ordered semigroup, $Q$-fuzzy left (right) ideal, $Q$-fuzzy quasi-ideal, $Q$-fuzzy bi-ideals

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DOI: 10.12732/ijpam.v92i3.5 How to cite this paper?

International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 92
Issue: 3
Pages: 369 - 379

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).