Fuzzy preference based rough sets

Preference analysis is an important task in multi-criteria decision making. The rough set theory has been successfully extended to deal with preference analysis by replacing equivalence relations with dominance relations. The existing studies involving preference relations cannot capture the uncertainty presented in numerical and fuzzy criteria. In this paper, we introduce a method to extract fuzzy preference relations from samples characterized by numerical criteria. Fuzzy preference relations are incorporated into a fuzzy rough set model, which leads to a fuzzy preference based rough set model. The measure of attribute dependency of the Pawlak's rough set model is generalized to compute the relevance between criteria and decisions. The definitions of upward dependency, downward dependency and global dependency are introduced. Algorithms for computing attribute dependency and reducts are proposed and experimentally evaluated by using two publicly available data sets.