Affiliations: [a] School of Mathematics and Statistics, Hunan University of Technology and Business, Changsha, Hunan, P.R.China | [b] Key Laboratory of Complex System Optimization and Big Data Processing in Department of Guangxi Education, Yulin Normal University, Yulin, P.R.China
Correspondence:
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Corresponding author. Pei Wang, Key Laboratory of Complex System Optimization and Big Data Processing in Department of Guangxi Education, Yulin Normal University, Yulin, Guangxi 537000, P.R.China. E-mail: [email protected].
Abstract: Rough set theory (for short, RST) are widely applied to artificial intelligence. Fuzzy rough sets (for short, FRSs) are the results of approximation of fuzzy sets on a fuzzy approximation space. In this paper, L-fuzzy is briefly denoted by LF. We study a topological problem of FRSs based on residuated lattices, i.e., suppose that L is a complete residuated lattice, then when may the given LF-topology be consistent with the LF-topology induced by some preorder LF-relation? In order to answer this problem, the notion of LF-approximating spaces is introduced. Moreover, determinant conditions for LF-topological spaces to be LF-approximating spaces are given.
