Conclusions
In this paper, we have proposed four measuring tools (i.e., θ-information granulation, θ-information amount, θ-rough entropy and θ-information entropy) to evaluate the uncertainty of a given interval-valued information system by means of its information structure. As an application of information granulation, we have proposed the rough entropy of a rough set in interval-valued information systems. We have presented a numerical experiment on the Face recognition dataset and conducted a statistical effectiveness analysis from three aspects, namely, dispersion analysis, correlation analysis and variance analysis, to demonstrate the feasibility of the proposed measures. The measures proposed in this paper can be applied to data mining from interval data. In the future, we will consider additional applications of the proposed measures.
