Uncertainty Measurement Based on In-sim-dominance Relation

In-sim-dominance relation is proposed to deal with hybrid information system in which the objects are described by a finite set of qualitative and quantitative attributes. Accuracy and roughness are two main tools to deal with uncertainty measurement issue in Pawlak rough set theory. However, there are few studies on uncertainty measurement based on the in-sim-dominance relation. In this paper, traditional accuracy and roughness measurements are extended to deal with hybrid information system, approximation accuracy and approximation roughness based on the in-sim-dominance relation are also defined. In particular, a concept called hybrid entropy is first introduced to measure the uncertainty of a hybrid information system. Then entropy-based roughness and approximation roughness of hybrid information system are proposed. Experiments are conducted on standard UCI data sets to test the proposed methodologies, and the results demonstrate that the entropy-based approximation roughness is effective and suitable for measuring the uncertainty of hybrid information system.