Second-Order Rough Approximations in Multi-criteria Classification with Imprecise Evaluations and Assignments

Abstract

The rough approximations are considered in the context of multi-criteria classification problem where evaluations of objects on particular criteria and their assignments to decision classes are imprecise and given in the form of intervals of possible values. Within Dominance-based Rough Set Approach (DRSA), the lower and upper approximations reflect the inconsistencies with respect to dominance principle. In the considered case, also the interval assignments have to be taken into account. This requires a new formulation of the dominance principle. A possible solution to the problem consists in introducing the second-order rough approximations. The methodology based on these approximations preserves well-known properties of rough approximations, such as rough inclusion, complementarity, identity of boundaries and monotonicity.