A new approach of attribute reduction of rough sets based on soft metric

Attribute reduction is considered as an important processing step for pattern recognition, machine learning and data mining. In this paper, we combine soft set and rough set to use them in applications. We generalize rough set model and introduce a soft metric rough set model to deal with the problem of heterogeneous numerical feature subset selection. We construct a soft metric on the family of knowledge structures based on the soft distance between attributes. The proposed model will degrade to the classical one if we specify a zero soft real number. We also provide a systematic study of attribute reduction of rough sets based on soft metric. Based on the constructed metric, we define co-information systems and consistent co-decision systems, and we provide a new method of attribute reductions of each system. Furthermore, we present a judgement theorem and discernibility matrix associated with attribute of each type of system. As an application, we present a case study from Zoo data set to verify our theoretical results.