Attribute reduction in ordered decision tables via evidence theory

Rough set theory and Dempster–Shafer theory of evidence are two distinct but closely related approaches to modeling and manipulating uncertain information. It is quite natural to set up a hybrid model based on these two theories. In this paper, we investigate the problem of attribute reduction for ordered decision tables based on evidence theory. Belief and plausibility functions, which are strongly connected with lower and upper approximation operators in dominance-based rough set approach, are proposed to define relative belief and plausibility reducts of ordered decision tables. Relationships among various types of relative reducts are thoroughly studied in consistent and inconsistent ordered decision tables. A pair of numeric measures, the inner and outer significance measures of a criterion, is presented to search for a relative belief/plausibility reduct, which is meaningful for practical problems. Some real-world tasks taken from the UCI repository are employed to verify the feasibility and effectiveness of the proposed technique.