Tolerance Dominance Relation in Incomplete Ordered Decision Systems

To deal with inconsistencies coming from consideration of criteria, that is, attributes with preference‐ordered domains (scales), such as product quality, market share, and debt ratio, the dominance‐based rough set approach has been proposed. However, it is not much useful for analyzing incomplete information. In this paper, we attempt to present research focusing on incomplete ordered decision systems where all attributes are considered as criteria and some objects’ criterion values are unknown. Under the assumption that all unknown values are the “do not care” semantics, the concept of tolerance dominance relation is introduced. Then, the rough approximations induced by it are obtained. And their properties are investigated. Especially, the important properties of rough approximations, such as rough inclusion, complementarity, identity, and monotonicity, are preserved well‐known in the presented methodology. Moreover, an example is employed to illustrate these results. We expand the potential applications of dominance‐based rough set approach.