Reduction algorithms for hybrid data based on fuzzy rough set approaches

Classical rough set theory is a powerful tool for nominal data. It has been generalized to fuzzy case with fuzzy indiscernibility relation, which is much general for real-world application. We introduce and extend Yager´s entropy measure and the definition of conditional entropy is interpreted as the increment of discernibility power by introducing an unseen attribute which is used as a significance measure of the attribute in rough set theory framework. We give novel definitions of independence, reduct, and relative reduct based on the entropy measure in fuzzy rough set model. Then two greedy algorithms are proposed for computing reduct and relative reduct, respectively. Two illustrative examples show the proposed approaches are efficient.