Criteria Reduction of Set-valued Ordered Decision System Based on Approximation Quality

The purpose of this paper is to further investigate criteria reduction in the set-valued ordered decision system, in which some objects may have more than one value for an attribute with preference-ordered domains. By considering the uncertainty of criteria values in such information system, we define a similarity dominance relation and give the dominance-based rough approximation of the upward and downward unions. To obtain criteria reduction from the inconsistent set-valued ordered decision system, the upward and downward approximation quality is proposed. Two types of criteria reduction are then formed for preserving the approximation quality. Furthermore, by the significance of the criterion, an algorithm is designed to compute a smallest reduction of a given set-valued ordered decision system. And finally, a numerical example is employed to substantiate the conceptual arguments.