Abstract
Most of the research in fuzzy rough sets and fuzzy topological structures have been studied on the basis of fuzzy partially ordered sets. Instead of fuzzy partially ordered sets, the concept of distance functions in complete co-residuated lattices is introduced. Using distance functions, we define Alexandrov pretopology, Alexandrov precotopology and fuzzy interior (fuzzy closure) operators in complete co-residuated lattices, and we investigate their properties. Moreover, we prove that there exist isomorphic categories and Galois correspondence between topological categories.
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