Table of Contents
Journal of Discrete Mathematics
Volume 2014, Article ID 120342, 9 pages
http://dx.doi.org/10.1155/2014/120342
Research Article

Vague Filters of Residuated Lattices

Department of Mathematics, 22 Bahman Boulevard, Kerman 76169-133, Iran

Received 2 May 2014; Revised 7 August 2014; Accepted 13 August 2014; Published 10 September 2014

Academic Editor: Hong J. Lai

Copyright © 2014 Shokoofeh Ghorbani. 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

Notions of vague filters, subpositive implicative vague filters, and Boolean vague filters of a residuated lattice are introduced and some related properties are investigated. The characterizations of (subpositive implicative, Boolean) vague filters is obtained. We prove that the set of all vague filters of a residuated lattice forms a complete lattice and we find its distributive sublattices. The relation among subpositive implicative vague filters and Boolean vague filters are obtained and it is proved that subpositive implicative vague filters are equivalent to Boolean vague filters.