Resolutions Of Fuzzy Relational Equations In Generalized Residuated Lattices

This paper considers the resolutions of fuzzy relational equations in general-ized residuated lattices. First, we give the properties of solutions and necessary and sufcientconditions under which fuzzy relational equations with inf-â†'composition and fuzzy relation-al equations with inf-composition have solutions, respectively, over generalized residuatedlattices. Then a kind of special solutions and a subset of the solution set for the respectiveequations are given. Secondly, we investigate a single fuzzy relational equation with inf-â†'composition and a single fuzzy relational equation with inf-composition, respectively, ingeneralized residuated lattices. A sufcient condition for existence of maximal solutions, allmaximal solutions are formulated, and the complete solution set of the respective equationsare described. Finally, we consider resolution of a single fuzzy relational equation with inf-â†'in a residuated lattice, a sufcient condition for existence of maximal solutions, all maximalsolutions are characterized, and the complete solution set of the equation are described.