Fuzzy complementary entropy using hybrid-kernel function and its unsupervised attribute reduction

Abstract

Fuzzy rough set theory has been proved to be an effective tool to deal with uncertainty data. Some different forms of fuzzy uncertainty measures have been introduced in fuzzy rough set theory, such as fuzzy information entropy, fuzzy conditional entropy, and fuzzy mutual information. However, as far as we know, most of the above fuzzy conditional entropy and fuzzy mutual information are non-monotonic, which may lead to a non-convergent learning algorithm. For this reason, this paper proposes a novel fuzzy complementary entropy based on the hybrid-kernel function. Then, based on the proposed fuzzy complementary entropy, some corresponding uncertainty measures are also proposed. Furthermore, fuzzy complementary conditional entropy and fuzzy complementary mutual information are proved to change monotonously with attributes. Finally, based on the proposed uncertainty measures, three kinds of evaluation criteria for unsupervised hybrid attribute reduction are defined and a generalized attribute reduction algorithm is designed. The experimental results show that the proposed method is an effective scheme for reducing hybrid attributes.