Affiliations: [a] School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P.R. China | [b] School of Civil Engineering and Architecture, Yanching Institute of Technology, Hebei, P.R. China | [c] College of Science, North China University of Technology, Beijing, P.R. China
Correspondence:
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Corresponding author. Yu Zhong, College of Science, North China University of Technology, Beijing 100144, P.R. China. E-mail: zhongyu199055@126.com.
Abstract: In this paper, the notions of M-fuzzifying derived sets and M-fuzzifying derived operators are introduced, when M is a fuzzy lattice. Then their characterizations are given. What’s more, it is shown that the category of M-fuzzifying topological spaces, the category of M-fuzzifying closure spaces and the category of M-fuzzifying neighborhood spaces are all isomorphic to the category of M-fuzzifying derived spaces. Besides, we prove that the M-fuzzifying derived operators induced by M-fuzzifying neighborhood systems are equivalent to those in the sense of Ying.
