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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.

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L -fuzzy approximating spaces

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