Fuzzy set inequations and equations with a meet-continuous codomain lattice

Article type: Research Article

Authors: Stepanović, Vanja^{; *}

Affiliations: University of Belgrade, Faculty of Agriculture, Zemun, Belgrade

Correspondence: [*] Corresponding author. Vanja Stepanović, University of Belgrade, Faculty of Agriculture, Zemun, Belgrade. E-mail: vanja@agrif.bg.ac.rs.

Abstract: Some fuzzy set and fuzzy relational inequations and equations are considered in the framework of a meet-continuous codomain lattice. The existence of maximal solutions to some fuzzy set inequations is proven. An algorithm is given for calculating the closure of a fuzzy set (relation) under the composition with a given fuzzy relation. Another algorithm for finding the transitive closure is proven to work in this framework.

Keywords: meet-continuous lattice, fuzzy set (relational) inequation (equation), transitive closure

DOI: 10.3233/JIFS-171098

Journal: Journal of Intelligent & Fuzzy Systems, vol. 34, no. 6, pp. 4009-4021, 2018