This paper restates the results on fuzzy relation equa- tions with sup-inf composition from the viewpoint of decomposition, presents a way to describe the solution set of fuzzy relation equa- tions, and shows a necessary and sufficient condition, which partly answers the open problem for existence of minimal solutions over complete Brouwerian lattices. Keywords— Complete Brouwerian lattice, fuzzy relation equa- tion, minimal solution, solution set, sup-inf composition.
['Xue-ping Wang', 'Feng Sun']
Resolution of fuzzy relation equations with sup-inf composition over complete Brouwerian lattices—a review ∗