Dominance-based rough set approach to incomplete ordered information systems

Dominance-based rough set approach has attracted much attention in practical applications ever since its inception. This theory has greatly promoted the research of multi-criteria decision making problems involving preferential information. This paper mainly deals with approaches to attribute reduction in incomplete ordered information systems in which some attribute values may be lost or absent. By introducing a new kind of dominance relation, named the characteristic-based dominance relation, to incomplete ordered information systems, we expand the potential applications of dominance-based rough set approach. To eliminate information that is not essential, attribute reduction in the sense of reducing attributes is needed. An approach on the basis of the discernibility matrix and the discernibility function to computing all (relative) reducts is investigated in incomplete ordered information systems (consistent incomplete ordered decision tables). To reduce the computational burden, a heuristic algorithm with polynomial time complexity for finding a unique (relative) reduct is designed by using the inner and outer significance measures of each criterion candidate. Moreover, some numerical experiments are employed to verify the feasibility and effectiveness of the proposed algorithms.