International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 795934, 13 pages
http://dx.doi.org/10.1155/2011/795934
Research Article

Fuzzy Filter Spectrum of a BCK Algebra

Xiao Long Xin, Wei Ji, and Xiu Juan Hua

Department of Mathematics, Northwest University, Xi'an 710127, China

Received 14 October 2010; Accepted 22 December 2010

Academic Editor: Young Bae Jun

Copyright © 2011 Xiao Long Xin 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 fuzzy s-prime filters of a bounded BCK-algebra is introduced. We discuss the relation between fuzzy s-prime filters and fuzzy prime filters. By the fuzzy s-prime filters of a bounded commutative BCK-algebra 𝑋 , we establish a fuzzy topological structure on 𝑋 . We prove that the set of all fuzzy s-prime filters of a bounded commutative BCK-algebra forms a topological space. Moreover, we show that the set of all fuzzy s-prime filters of a bounded implicative BCK-algebra is a Hausdorff space.