Approximation-oriented Fuzzy Rough Set Approaches

Abstract

In this paper we focus on generalizations of the classical rough set approach to fuzzy environments. There are two aspects of rough set approaches: classification and approximation. In the classification aspect, by rough set approaches we can classify objects into positive and negative examples of a class. On the other hand, in the approximation aspect, by rough set approaches we obtain the lower and upper approximations of a class. The former model works better in the attribute reduction while the latter model works better in the rule induction. In the setting of the classical rough set approach, the lower approximation is nothing but the set of positive examples and the upper approximation is the complementary set of negative examples. However, these equalities do not always hold in the generalized settings. Most of fuzzy rough set models proposed earlier are defined in the classification aspect. The approaches based on those models do not always work well in approximating fuzzy subsets. In this paper we define the fuzzy rough set models in the approximation aspect. We investigate their fundamental properties and demonstrate the advantages of fuzzy set approximation. Finally we consider attribute reduction based on the proposed fuzzy rough set models.