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The Scientific World Journal
Volume 2014, Article ID 718972, 8 pages
http://dx.doi.org/10.1155/2014/718972
Research Article

On Some Fuzzy Filters in Pseudo-BCI Algebras

College of Arts and Sciences, Shanghai Maritime University, Shanghai 201306, China

Received 2 March 2014; Accepted 9 March 2014; Published 8 April 2014

Academic Editor: Wieslaw A. Dudek

Copyright © 2014 Xiaohong Zhang. 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

Some new properties of fuzzy associative filters (also known as fuzzy associative pseudo-filters), fuzzy p-filter (also known as fuzzy pseudo-p-filters), and fuzzy a-filter (also known as fuzzy pseudo-a-filters) in pseudo-BCI algebras are investigated. By these properties, the following important results are proved: (1) a fuzzy filter (also known as fuzzy pseudo-filters) of a pseudo-BCI algebra is a fuzzy associative filter if and only if it is a fuzzy a-filter; (2) a filter (also known as pseudo-filter) of a pseudo-BCI algebra is associative if and only if it is an a-filter (also call it pseudo- filter); (3) a fuzzy filter of a pseudo-BCI algebra is fuzzy a-filter if and only if it is both a fuzzy p-filter and a fuzzy q-filter.