Abstract: In this paper, we study the relationships between L -fuzzy interior spaces, L -fuzzy quasi-uniform spaces andL -fuzzy topological spaces. Also, we introduce the concept of L - fuzzy preinterior spaces and the notions of their continuities are investigated. Finally, we give their examples.
Abstract: In this paper, we investigated the properties of two L -fuzzy interior operators and two L -fuzzy topologies induced by L -quasi-uniformity in complete residuated lattices. We study the relations among L -fuzzy quasi-uniformities, L -fuzzy interior operators and L -fuzzy topologies. We give their examples.
Abstract: In this paper, we introduce the notions of L -fuzzy semi-topogenous order, L -fuzzy topogenous (cotopogenuous) space, L -fuzzy topology (cotopology), L -fuzzy quasi-uniform space and the L -fuzzy quasi-proximity space. We study some relationships between previous spaces. The notions of their continuities are investigated.
Abstract: In this paper, we introduce the notions of L-fuzzy topoenous orders and investigate some of properties. We investigate the relationships among L-fuzzy topoenous orders, L-fuzzy topologies and L-fuzzy interior operators.
Abstract: In this paper, we investigate the relations between the L -fuzzy pre-proximities, L -fuzzy interior operators and L -fuzzy topological spaces in complete residuated lattices. In addition, degrees of L -fuzzy continuity, L -fuzzy proximity and L -fuzzy interior mappings are proposed and their connections are studied. Also, we show that there is a Galois correspondence between the category of separated L -fuzzy interior spaces and that of separated L -fuzzy pre-proximity spaces. Finally, we give their examples.