RFRR: Robust Fuzzy Rough Reduction

This paper proposes a robust method of dimension reduction using fuzzy rough sets, in which the reduction results can reflect the reducts obtained on all of the possible parameters. Here, the reducts being obtained on all of the possible parameters mean that all of the reducts are obtained on different degrees of robustness to handle noise. This method is completely different from the existing methods of fuzzy rough reduction. The differences are shown in three aspects: the concept, the tool, and the algorithm. First, the key concept of attribute reduction is redefined in a new way. That is, the robust fuzzy rough reduct, which is shortened to a robust reduct, is proposed to reflect the classical reducts obtained on all of the possible parameters. The new “robust reduct” is not a crisp subset of condition attributes; rather, it is a fuzzy subset, whose most interesting property is that any cut set of the robust reduct is a classical reduct on a certain parameter. Second, the tool used to measure the discernibility power is different from the existing discernibility measures. In this paper, the robustness of each attribute to handle misclassification and perturbation is considered. By considering both the robustness and the discernibility, a robust fuzzy discernibility matrix is designed. Finally, the algorithms used to find the robust reducts are designed based upon the robust fuzzy discernibility matrix, which is completely different from the existing algorithms used to find the classical reducts.