Two types of MTL-L-filters in residuated lattices

Article type: Research Article

Authors: Ma, Zhen Ming

Affiliations: School of Science, Linyi University, Linyi Shandong, P.R. China

Note: [] Corresponding author. Zhen Ming Ma, School of Science, Linyi University, Linyi Shandong 276005, P.R. China. E-mail: [email protected]

Abstract: In this paper, MTL-L-filters of type I and type II in residuated lattices are proposed, some properties and alternative definitions of them are given. In particular, by the MTL-algebras derived from MTL-L-filters of type II, a one-to-one correspondence between the set of L-filters and the set of L-congruences is determined.

Keywords: Residuated lattice, L-filter, MTL-L-filter of type I, MTL-L-filter of type II

DOI: 10.3233/IFS-131026

Journal: Journal of Intelligent & Fuzzy Systems, vol. 27, no. 2, pp. 681-689, 2014