Transitive solutions of relational equations on finite sets and linear lattices

Abstract

The set of solutions of relational equations over a finite referential space and with values from a linear lattice is considered. We determine in this set the greatest max-min transitive solution and the related minimal ones. Further, we investigate for the determination of particular max-min transitive solutions, namely those having Schein rank equal to 1. Related properties of convergence of fuzzy systems represented by the involved relations are also given.Key wordsFinite matrix equationmax-min transitive matrixSchein rank of a matrix