Uncertainty measurement for a covering information system

A covering information system as the generalization of an information system is an important model in the field of artificial intelligence. Uncertainty measurement is a critical evaluating tool. This paper investigates uncertainty measurement for a covering information system. The concept of information structures in a covering information system is first described by using set vectors. Then, dependence between information structures in a covering information system is introduced. Next, the axiom definition of granularity measure of uncertainty for covering information systems is proposed by means of its information structures, and based on this axiom definition, information granulation and rough entropy in a covering information system are proposed. Moreover, information entropy and information amount in a covering information system are also considered. Finally, we conduct a numerical experiment on the congressional voting records data set that comes from UCI Repository of machine learning databases, and based on this numerical experiment, effectiveness analysis from the angle of statistics is given to evaluate the performance of uncertainty measurement for a covering information system. These results will be helpful for understanding the essence of uncertainty in a covering information system.