Measures of Uncertainty for an Incomplete Set-Valued Information System With the Optimal Selection of Subsystems: Gaussian Kernel Method

A set-valued information system (SVIS) with missing values is known as an incomplete set-valued information system (ISVIS). This article focuses on studying uncertainty measurement for an ISVIS and the optimal selection of subsystems by means of Gaussian kernel. First, the distance between two information values on each attribute in an ISVIS is put forward. Second, the fuzzy $T_{cos}$ -equivalence relation induced by a given subsystem is proposed based on Gaussian kernel. Next, some tools are used to measure the uncertainty of an ISVIS. Moreover, effectiveness analysis is done from a statistical point of view. In the end, the optimal selection of subsystems based on $\delta $ -information granulation and $\delta $ -information amount is given. These results will help us comprehend nature of uncertainty in an ISVIS.