Variable precision dominance based rough set model and reduction algorithm for preference-ordered data

Dominance-based rough set model has proven to be a powerful mathematical tool for preference-ordered information system. We define some measures of roughness of approximation and conclude that the definition of lower and upper approximations is not robust to noise sample in the former approaches, and then an extended model is presented based on majority inclusion. Some measures are introduced to calculate the accuracy and quality of approximation using variable precision dominance rough set methodology. The quality of approximation of partition is used as a measure of the significance of attributes. Based on the measure, the definitions of dependency of attribute set, redundancy of attribute, reduct and core are given. A greedy algorithm is constructed for preference-ordered data reduction.