Entropies of fuzzy indiscernibility relation and its operations

Yager's entropy was proposed to compute the information of fuzzy indiscernibility relation. In this paper we present a novel interpretation of Yager's entropy in discernibility power of a relation point of view. Then some basic definitions in Shannon's information theory are generalized based on Yager's entropy. We introduce joint entropy, conditional entropy, mutual information and relative entropy to compute the information changes for fuzzy indiscerniblity relation operations. Conditional entropy and relative conditional entropy are proposed to measure the information increment, which is interpreted as the significance of an attribute in fuzzy rough set model. As an application, we redefine independency of an attribute set, reduct, relative reduct in fuzzy rough set model based on Yager's entropy. Some experimental results show the proposed approach is suitable for fuzzy and numeric data reduction.