Document Type: Research Paper


1 College of Science, North China University of Technology, Beijing, P. R. China and School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P. R. China

2 School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P. R. China and Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing, P. R. China


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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