Nodal filters in Residuated Lattices

Article type: Research Article

Authors: Bakhshi, Mahmood^*

Affiliations: Department of Mathematics, University of Bojnord, Bojnord, Iran

Correspondence: [*] Corresponding author. Mahmood Bakhshi, Department of Mathematics, University of Bojnord, P. O. Box 1339, Bojnord, Iran. Tel.: +98 58 2284610; Fax: +98 58 22410700; E-mail: [email protected].

Abstract: In this paper, we introduce the notion of a nodal filter in residuated lattices. We give several characterizations of these filters and also some relationships between these filters and other types of filters are obtained, as well. Finally, we prove that the class of all nodal filters of a residuated lattice forms a Heyting algebra.

Keywords: Algebras of logics, residuated lattice, node, nodal filter, Heyting algebra

DOI: 10.3233/IFS-151804

Journal: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 5, pp. 2555-2562, 2016