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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 736872, 8 pages
Research Article

Some Types of Generalized Fuzzy -Fold Filters in Residuated Lattices

School of Science, Linyi University, Linyi 276005, China

Received 3 November 2013; Accepted 18 December 2013

Academic Editor: Yansheng Liu

Copyright © 2013 Zhen Ming Ma. 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.


Fuzzy filters and their generalized types have been extensively studied in the literature. In this paper, a one-to-one correspondence between the set of all generalized fuzzy filters and the set of all generalized fuzzy congruences is established, a quotient residuated lattice with respect to generalized fuzzy filter is induced, and several types of generalized fuzzy -fold filters such as generalized fuzzy -fold positive implicative (fantastic and Boolean) filters are introduced; examples and results are provided to demonstrate the relations among these filters.