Rough substructures based on overlaps of successor in Quantales under serial fuzzy relations

In this research article, a new connection between serial fuzzy relations and an extended version of rough sets in algebraic structure quantale is established. The notion consists successor class overlap the element quantale. Thus approximation space based on via overlaps quantales, are introduced. main purpose study to provide basic structures fuzzy-relations. way, acquires certain appealing properties. Compatible being applied introduce notions multiplicative set, m-system further substructures quantales. Following that, various described terms under relations, leading development some key theorems. Moreover, several results including homomorphism their homomorphic images provided. It concluded that significantly easy superior types approximations structures. Furthermore, different examples given show effectiveness developed approach comparative investigated with existing methods expressed broadly which more effective than approaches.