Entropy measures and granularity measures for set-valued information systems

Set-valued information systems are generalized models of single-valued information systems. In this paper, we propose two new relations for set-valued information systems. Based on these two relations, the concepts of knowledge information entropy, knowledge rough entropy, knowledge granulation and knowledge granularity measure are defined in set-valued information systems, and some properties are investigated. Moreover, relationship between knowledge information entropy and knowledge granulation, knowledge rough entropy and knowledge granularity measure are studied. It is also shown that knowledge information entropy and knowledge granularity measure can be used to evaluate the certainty degree of knowledge in set-valued information systems, and knowledge rough entropy and knowledge granulation can be used to evaluate the uncertainty degree of knowledge in set-valued information systems. These results may supply a further understanding the essence of uncertainty and granularity in set-valued information systems.