International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 814861, 14 pages
doi:10.1155/2009/814861
Research Article

𝒩-Fuzzy Ideals in Ordered Semigroups

Asghar Khan,1 Young Bae Jun,2 and Muhammad Shabir3

1Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad 22060, Pakistan
2Department of Mathematics Education, Gyeongsang National University, Chinju 660-701, South Korea
3Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan

Received 9 July 2009; Accepted 26 October 2009

Academic Editor: David Dobbs

Copyright © 2009 Asghar Khan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We introduce the concept of 𝒩-fuzzy left (right) ideals in ordered semigroups and characterize ordered semigroups in terms of 𝒩-fuzzy left (right) ideals. We characterize left regular (right regular) and left simple (right simple) ordered semigroups in terms of 𝒩-fuzzy left (𝒩-fuzzy right) ideals. The semilattice of left (right) simple semigroups in terms of 𝒩-fuzzy left (right) ideals is discussed.