On attributes reduction with fuzzy rough sets

Fuzzy rough set is the generalization of Pawlak rough set to deal with both of fuzziness and vagueness in data. The existing research on fuzzy rough sets mainly concentrates on the construction of approximation operators. Less effort has been put on the attributes reduction of fuzzy rough sets. This paper mainly focuses on the attributes reduction of fuzzy rough sets. After analyzing the previous work of reduction of fuzzy rough sets, formal concepts of attributes reduction of fuzzy rough sets are introduced and the structure of reduction is studied completely. An algorithm based on discernibility matrix to compute all the attributes reductions is developed. These concepts have been demonstrated by an example.