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The Scientific World Journal
Volume 2013, Article ID 476057, 5 pages
http://dx.doi.org/10.1155/2013/476057
Research Article

On Abelian and Related Fuzzy Subsets of Groupoids

1Department of Physics, University of Michigan, Ann Arbor, MI 48109, USA
2Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Republic of Korea
3Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, USA

Received 12 August 2013; Accepted 15 September 2013

Academic Editors: M. Aiguier and M. I. Ali

Copyright © 2013 Seung Joon Shin 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 notion of abelian fuzzy subsets on a groupoid, and we observe a variety of consequences which follow. New notions include, among others, diagonal symmetric relations, several types of quasi orders, convex sets, and fuzzy centers, some of whose properties are also investigated.