Dominance-based fuzzy rough set approach for incomplete interval-valued data

Interval-valued information systems are general models of single-valued information systems. Interval-values appear to a way to describe the uncertainty that affects the observed objects. However, there are relatively few studies on incomplete interval-valued data. The aim of this paper is to present a dominance-based fuzzy rough set approach to incomplete interval-valued information systems. A fuzzy dominance relation which aims to describe the degree of dominance in terms of pairs of objects is proposed. Based on the proposed relation, we extend the definitions of fuzzy approximation operators and investigate the uncertainty measurement issue. A new form of fuzzy conditional entropy to measure attribute importance is presented. Meanwhile, a corresponding heuristic attribute reduction algorithm is constructed for incomplete interval-valued decision systems. Experiments show that the presented fuzzy conditional entropy and the proposed algorithm are effective.