Quantale-valued quasi-neighborhood systems: fundamentals and application to L-quasi-topologies, L-quasi-uniformities, and rough approximation operators

In accordance with Rodabaugh’s approach to L -quasi-topology, the aim of this paper is to use the concept of semi-quantales as a theoretical basis to construct and study the notion of quantale-valued quasi-neighborhood systems as a generalized form of the resent Höhle–S̆ostak’s L -neighborhood systems. Some properties of such notion and relationships with L -quasi-topologies, L -quasi-fuzzy topologies, L -quasi-uniform structures and L -fuzzy rough approximation operators are established.