Composition of Rough Approximations under the Dominance-Based Relation

In daily life people often make their decisions according to the available information as much as they can collect. Most of the available information contains many indicators that reflect the characteristics of things. These indicator data are ordered. The dominance-based rough set approach is an extension of the classical rough set model and can be used to process ordered information. Computing approximations is a time-consuming and key mission to discover useful knowledge from available information by using rough set theory. The aim of this work is to investigate how to compose approximations of dominance-based rough sets by using some existing intermediate results instead of computing them with beginning from scratch. In the paper, we construct a decomposing and composing mechanism for computing approximations of dominance-based rough sets. Under this mechanism, some matrix operations were defined and employed in composing approximations. A numerical example illustrates the feasibility of composing approximations under dominance-based relation.