IJPAM: Volume 92, No. 3 (2014)

ON $Q$-FUZZY IDEALS IN ORDERED SEMIGROUPS

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?

Source: 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).