In this paper, we introduce the notions of L-fuzzy topogenous orders, L-fuzzy topology, L-interior operators and L-closure operators in complete residuated lattices. Moreover, we investigate the relations among L-fuzzy topogenous orders, L-interior operators and L-closure operators. We show that there is a Galois correspondence between the category of separated L-fuzzy interior (resp. closure) spaces and that of separated L-fuzzy topogenous (resp. cotopogenous) spaces.
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