Abstract
In this work, we have proposed a new relationship among rough set, soft set and quantales with the help of soft compatible relation. This typical relationship is used to approximate the fuzzy substructures in quantales in association with soft compatible relations by using aftersets and foresets. This type of approximation is extended notation of rough quantales, rough fuzzy subquantales and soft subquantales. We have corroborated this work by considering some test examples containing soft compatible relations over quantales. Moreover, by using soft compatible relations, we will describe the relationship between upper (lower) generalized rough fuzzy soft substructures of quantale and the upper (lower) approximations of their homomorphic images with the help of weak quantale homomorphism. The comparison of this type approximations and their results affirms the superiority of our new approximation method over current methods on the topic.
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