Incremental method of updating approximations in DRSA under variations of multiple objects

Dominance-based rough sets approach (DRSA) uses dominance relations to substitute equivalence relations in conventional rough set models so that it can handle preference-ordered information. Up to date, DRSA has been widely used in multi-criteria decision-making problems. In these real-life problems, however, since the collected data are evolving from time to time, there are often some variations of the attribute sets or object sets. In the dynamic information systems, the frequent update of the lower and upper approximations of DRSA is an necessary step for further updating attribute reducts and decision rules which are important for knowledge discovery and decision-making. Incrementally updating approximations is a type of effective methods to reduce the computational load when any variation occurs. Most of current studies on incremental methods only consider conventional rough set models and the situation when a single object varies in an information system. In this paper, we focus on the variations of object sets and discuss incremental methods of updating approximations of DRSA when multiple objects changed. The updating principles in different dynamic situations are given with detail proofs and the corresponding incremental algorithms are also developed. The experimental evaluations on 12 UCI data sets show that our proposed incremental approaches effectively reduce the computational time in comparison with the non-incremental approach as well as a typical incremental method in the literature.