Knowledge granularity measures for incomplete interval-valued information

Interval-valued information systems are generalized models of single-valued information systems. However, there are few studies on incomplete interval-valued data, which exist in many practical issues. In this paper, we propose a dominance relation for incomplete interval-valued information systems. Based on the dominance relation, the concepts of knowledge information entropy, knowledge rough entropy, knowledge granulation, knowledge granularity measure are introduced into incomplete interval-valued information systems, some important properties are discussed, and the relationships among those concepts are studied. Experimental results show that the proposed measures are helpful for evaluating the discernibility ability of knowledge in incomplete interval-valued information systems.