Information Entropy-Based Attribute Reduction for Incomplete Set-Valued Data

Abstract

This paper investigates attribute reduction for incomplete set-valued data based on information entropy. The similarity degree between information values on a conditional attribute of an incomplete set-valued decision information system (ISVDIS) is first proposed. Then, the tolerance relation on the object set with respect to a conditional attribute subset in an ISVDIS is obtained. Next, $\lambda $ -reduction in an ISVDIS is presented. What’s more, connections between the proposed attribute reduction and uncertainty measurement are exhibited. Furthermore, an attribute reduction algorithm based on $\lambda $ -information entropy in an ISVDIS is provided. Finally, experiments to evaluate the performance of the proposed algorithm are carried out, and Friedman test and Nemenyi test in statistics are conducted. The experimental results indicate that the proposed algorithm is more effective for an ISVDIS than some existing algorithms.

Keywords

• Rough set theory
• ISVDIS
• similarity degree
• λ-reduction%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">λ</italic>-reduction
• λ-information entropy%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">λ</italic>-information entropy
• attribute reduction algorithm