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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. [ABSTRACT FROM AUTHOR]