Belief and plausibility reducts in incomplete information systems with fuzzy decision

In this paper, the concept of incomplete information systems with fuzzy decision is introduced. Lower and upper approximations of fuzzy decision classes with respect to a conditional attribute subset are defined and their properties are presented. The connection between rough set approximations and Dempster-Shafer theory of evidence in incomplete information systems with fuzzy decision is established. The notions of lower approximation reducts, upper approximation reducts, belief reducts and plausibility reducts in incomplete information systems with fuzzy decision are further defined and their relationships are examined.