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The Scientific World Journal
Volume 2014 (2014), Article ID 697012, 6 pages
http://dx.doi.org/10.1155/2014/697012
Research Article

Fuzzy Upper Bounds in Groupoids

1Department of Mathematics Education, Dongguk University, Seoul 100-715, Republic of Korea
2Department of Mathematics, Chungbuk National University, Cheongju 361-763, Republic of Korea
3Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, USA

Received 14 March 2014; Accepted 14 May 2014; Published 28 May 2014

Academic Editor: Young B. Jun

Copyright © 2014 Sun Shin Ahn 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

The notion of a fuzzy upper bound over a groupoid is introduced and some properties of it are investigated. We also define the notions of an either-or subset of a groupoid and a strong either-or subset of a groupoid and study some of their related properties. In particular, we consider fuzzy upper bounds in , where is the collection of all groupoids. Finally, we define a fuzzy- -subset of a groupoid and investigate some of its properties.