Probability approach for interval-valued ordered decision systems in dominance-based fuzzy rough set theory.

Interval-valued data exist in many practical situations, due to various factors such as random error, incompletion or inaccuracy. In rough set theory, interval-valued decision systems can be viewed as generalized models of single-valued decision systems. In this paper, from the viewpoint of interval variable, we propose a new dominance relation based on probability distribution. Consequently, dominance-based rough set model for interval-valued ordered decision systems is constructed with the proposed dominance relation. Moreover, the proposed model examines attribute reduction in interval-valued ordered decision systems.