Uncertainty measurement for probabilistic set-valued data: Gaussian kernel method

Abstract

The uncertainty of information plays an important role in practical applications. Uncertainty measurement (UM) can help us in disclosing the substantive characteristics of information. Probabilistic set-valued data is an important class of data in machine learning. UM for probabilistic set-valued data is worth studying. This paper measures the uncertainty of a probability set-valued information system (PSVIS) by means of its information structures based on Gaussian kernel method. According to Bhattacharyya distance, the distance between objects in each subsystem of a PSVIS is first built. Then, the fuzzy Tcos-equivalence relations in a PSVIS by using Gaussian kernel method are obtained. Next, information structures in a PSVIS are defined. Moreover, dependence between information structures is investigated by using the inclusion degree. As an application for the information structures, UM in a PSVIS is investigated. Finally, to evaluate the performance of the investigated measures, effectiveness analysis is performed from dispersion analysis, correlation analysis, and analysis of variance and post-hoc test.