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Abstract
In this paper, the concepts of derived sets and derived operators are generalized to $(L, M)$-fuzzy topological spaces and their characterizations are given. What is more, it is shown that the category of stratified $(L, M)$-fuzzy topological spaces, the category of stratified $(L, M)$-fuzzy closure spaces and the category of stratified $(L, M)$-fuzzy quasi-neighborhood spaces are all isomorphic to the category of stratified $(L, M)$-fuzzy derived spaces.
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