Formulations of Empirical Risk Minimization on Variable-Precision Dominance-based Rough Set Approach

Abstract

For modeling of preference relations, dominance-based rough set approach (DRSA) was proposed. In the framework of DRSA, classification involving a preference order is considered, and data are expressed by criteria. The inconsistency between the classification and criteria is modeled by approximations of rough set theory. Variable-precision DRSA (VP-DRSA) is an extension of DRSA, in which a certain degree of the inconsistency is tolerated. The lower approximations of VP-DRSA can be interpreted by empirical risk minimization. In this paper, we study formulations of the empirical risk minimization related to VP-DRSA. We propose a new formulation using a nonlinear discriminant function.