Optimal-Neighborhood Statistics Rough Set Approach with Multiple Attributes and Criteria

This paper focuses on the sorting problems with multiple types of attributes. About the attributes, in which are divided into qualitative attributes, quantitative attributes, qualitative criteria and quantitative criteria. Granules of knowledge are defined by applying four types of relations simultaneously: indiscernibility relation defined on qualitative attributes, similarity relation defined on quantitative attributes, dominance relation defined on qualitative criteria and quasi-partial order relation defined on quantitative criteria. To guarantee the tolerance of the system, the threshold is adjusted, resulting in a N-neighborhood system comes into being. The consistency measure which possess properties of monotonicity is regarded as the Likelihood Function, so the optimal threshold is obtained by Maximum Likelihood Estimation, as a result, N-neighborhood system is converted into optimal 1-neighborhood system. Therefore, we proposed the Optimal-Neighborhood Statistics Rough Set Approach with Multiple Attributes and Criteria.