Lattices of (generalized) fuzzy 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: (Generalized) fuzzy filters in logical algebras were extensively researched. In this paper, associated with the notion of tip-extended pair of fuzzy sets, it is proved, respectively, that the sets of all fuzzy filters and all generalized fuzzy filters form bounded distributive lattices.

Keywords: Residuated lattice, bounded distributive lattice, fuzzy filter, generalized fuzzy filter

DOI: 10.3233/IFS-141191

Journal: Journal of Intelligent & Fuzzy Systems, vol. 27, no. 5, pp. 2281-2287, 2014