An Uncertainty Measure for Incomplete Decision Tables and Its Applications

Uncertainty measures can supply new viewpoints for analyzing data. They can help us in disclosing the substantive characteristics of data. The uncertainty measurement issue is also a key topic in the rough-set theory. Although there are some measures to evaluate the uncertainty for complete decision systems (also called decision tables), they cannot be trivially transplanted into incomplete decision systems. There are relatively few studies on uncertainty measurement in incomplete decision systems. In this paper, we propose a new form of conditional entropy, which can be used to measure the uncertainty in incomplete decision systems. Some important properties of the conditional entropy are obtained. In particular, two validity theorems guarantee that the proposed conditional entropy can be used as a reasonable uncertainty measure for incomplete decision systems. Experiments on some real-life data sets are conducted to test and verify the validity of the proposed measure. Applications of the proposed uncertainty measure in ranking attributes and feature selection are also studied with experiments.