Minimal Solutions of Fuzzy Relation Equations with General Operators on the Unit Interval

Abstract

Fuzzy relation equations arise as a mechanism to solve problems in several frameworks, such as in fuzzy logic. Moreover, the solvability of these equations has been related to fuzzy property-oriented concept lattices. This paper studies a procedure to obtain the minimal solutions of fuzzy relation equations R {ring operator} X = T, with an isotone binary operation associated with a (left or right) residuated implication on the unit interval. From this study several results, based on the covering problem, are introduced generalizing other ones given in the literature. © Springer International Publishing Switzerland 2014.