International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 814861, 14 pages
doi:10.1155/2009/814861
𝒩-Fuzzy Ideals in Ordered Semigroups
Asghar Khan1
, Young Bae Jun2
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
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.