Extension of Rough Set Based on Positive Transitive Relation
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The application of rough set theory in incomplete information systems is one of the key problems in practice since the missing values always occur in knowledge acquisition due to the error of data measuring, the limitation of acquiring data or the limitation of comprehension of data, etc. An incomplete information system is mainly processed by compressing the indiscernibility relation. The existing rough set extension models based on tolerance or symmetric similarity relation typically discards one relation among the reflexive, symmetric and transitive relations, especially the transitive relation. In order to overcome the limitations of the existing rough set extension models, we define a new relation called the positive transitive relation and then propose a new rough set extension model based on the positive transitive relation. The new model inherits the merit of the other extensions of the classical rough set models and avoid their limitations of discarding transitivity or symmetry. In comparison with the existing extension models, the proposed model has a better performance to process the incomplete information systems and substantially reduce the computational complexity, take account of the relation of tolerance and similarity of positive transitivity, and supplement the related theories in accordance with the intuitive classification of incomplete information. Moreover, the proposed extension model can significantly decrease the computational cost in the knowledge reduction. Thus, the positive transitive relation can improve current theoretical analysis of incomplete information systems and the proposed extension model is more suitable for processing incomplete information systems and has a broad application prospect.
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