Rough set classification based on quantum logic

By combining the advantages of quantum computing and soft computing, the paper shows that rough sets can be used with quantum logic for classification and recognition systems. We suggest the new definition of rough set theory as quantum logic theory. Rough approximations are essential elements in rough set theory, the quantum rough set model for set-valued data directly construct set approximation based on a kind of quantum similarity relation which is presented here. Theoretical analyses demonstrate that the new model for quantum rough sets has new type of decision rule with less redundancy which can be used to give accurate classification using principles of quantum superposition and non-linear quantum relations. To our knowledge, this is the first attempt aiming to define rough sets in representation of a quantum rather than logic or sets. The experiments on data-sets have demonstrated that the proposed model is more accuracy than the traditional rough sets in terms of finding optimal classifications.