L -fuzzy rough approximation operators via three new types of L -fuzzy relations

Considering L being a frame with an order-reversing involution, three new types of L -fuzzy relations are introduced, which are called mediate, Euclidean and adjoint L -fuzzy relations, respectively. By means of these L -fuzzy relations, three types of L -fuzzy rough approximation operators are constructed and their connections with those three L -fuzzy relations are examined, respectively. An axiomatic approach is adopted to deal with L -fuzzy rough approximation operators. It is shown that each type of L -fuzzy rough approximation operators corresponding to mediate, Euclidean and adjoint L -fuzzy relations as well as their compositions can be characterized by single axioms.