A note on some filters in residuated lattices

Article type: Research Article

Authors: Xiao, Lei | Liu, Lianzhen^*

Affiliations: School of Science, Jiangnan University, Wuxi, China

Correspondence: [*] Corresponding author. Lianzhen Liu, School of Science, Jiangnan University, 214122 Wuxi, China. Tel.: +86 18915328585; Fax: +86 051085910532; E-mail: zhen712000@126.com.

Abstract: Recently, the notions of EIMTL-filters, associative filters, t-filters and I-filters were introduced in MTL-algebras and residuated lattices, respectively. In this paper, we consider these filters in residuated lattices and study some properties of them. We prove that t-filters and I-filters coincide in residuated lattices. The conditions under which an EIMTL-filter is a t-filter, and under which a residuated lattice has a proper associative filter are established. We also study the existence of a proper EIMTL-filter and prove that every maximal filter is an EIMTL-filter, and hence all residuated lattices have proper EIMTL-filters.

Keywords: Residuated lattice, EIMTL-filter, associative filter, t-filter

DOI: 10.3233/IFS-151774

Journal: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 1, pp. 493-500, 2016