Approximations and uncertainty measures in incomplete information systems

There are mainly two methodologies dealing with uncertainty measurement issue in rough set theory: pure rough set approach and information theory approach. Pure rough set approach is based on the concepts of accuracy, roughness and approximation accuracy proposed by Pawlak. Information theory approach is based on Shannon’s entropy or its variants. Several authors have extended the information theory approach into incomplete information systems. However, there are few studies on extending the pure rough set approach to incomplete information systems. This paper focuses on constructing uncertainty measures in incomplete information systems by pure rough set approach. Three types of definitions of lower and upper approximations and corresponding uncertainty measurement concepts including accuracy, roughness and approximation accuracy are investigated. Theoretical analysis indicates that two of the three types can be used to evaluate the uncertainty in incomplete information systems. Experiments on incomplete real-life data sets have been conducted to test the two selected types (the first type and the third type) of uncertainty measures. Results show that the two types of uncertainty measures are effective.