Information Entropy and Mutual Information-based Uncertainty Measures in Rough Set Theory

As an extension of the classical set theory, rough set theory plays a crucial role in uncertainty measurement. In this paper, concepts of information entropy and mutual information-based uncertainty measures are presented in both complete and incomplete information/decision systems. Then, some important properties of these measures are investigated, relationships among them are established, and comparison analyses with several representative uncertainty measures are illustrated as well. Theoretical analysis indicates that these proposed uncertainty measures can be used to evaluate the uncertainty ability of different knowledge in complete/incomplete decision systems, and then these results can be helpful for understanding the essence of knowledge content and uncertainty measures in incomplete information/decision systems. Thus, these results have a wide variety of applications in rule evaluation and knowledge discovery in rough set theory.