An entropy-based uncertainty measurement approach in neighborhood systems

Uncertainty measures can provide us with principled methodologies to analyze uncertain data and unveil the substantive characteristics of the data sets. Accuracy and roughness proposed by Pawlak are two main tools to deal with uncertainty measurement issue in rough set theory. Many uncertainty measure methodologies for discrete-valued information systems or discrete-valued decision systems have been developed. However, there are only limited on the uncertainty measurement for neighborhood systems. In this paper, we address the issues of uncertainty of a neighborhood system and extend the traditional accuracy and roughness measures to deal with neighborhood systems. In particular, a concept called neighborhood entropy is first introduced to evaluate the uncertainty of a neighborhood information system. Consequently, the entropy-based roughness and approximation roughness measures of neighborhood system are presented. Theoretical analysis indicates that entropy-based measures can be used to evaluate the uncertainty in neighborhood systems. Experiments are conducted on artificial data sets and standard UCI data sets to test our proposed methodologies. Results demonstrate that the entropy-based measures are effective and valid for evaluating the uncertainty of neighborhood systems.