Minimal join decompositions and their applications to fuzzy relation equations over complete Brouwerian lattices

This paper deals with the existence of minimal solutions of fuzzy relation equations over complete Brouwerian lattices from the viewpoint of join decompositions. First, the concept of a minimal join decomposition is introduced. Then the existence conditions and properties of such decomposition are discussed. As their applications, the conditions for the existence of minimal solutions of fuzzy relation equations over complete Brouwerian lattices and complete lattices are given, respectively.