International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 838392, 14 pages
doi:10.1155/2010/838392
Research Article

Generalized Fuzzy Interior Ideals in Abel Grassmann's Groupoids

Asghar Khan,1 Young Bae Jun,2 and Tahir Mahmood3

1Department of Mathematics, COMSATS Institute of Information Technology, 22060 Abbottabad, Pakistan
2Department of Mathematics Education and RINS, Gyeongsang National University, Chinju 660-701, South Korea
3Department of Applied Mathematics, International Islamic University, 45320 Islamabad, Pakistan

Received 27 August 2009; Accepted 24 February 2010

Academic Editor: Peter Basarab-Horwath

Copyright © 2010 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

Using the notion of a fuzzy point and its belongness to and quasicoincidence with a fuzzy subset, some new concepts of a fuzzy interior ideal in Abel Grassmann's groupoids S are introduced and their interrelations and related properties are invesitigated. We also introduce the notion of a strongly belongness and strongly quasicoincidence of a fuzzy point with a fuzzy subset and characterize fuzzy interior ideals of S in terms of these relations.