An Information Quantity-Based Uncertainty Measure to Incomplete Numerical Systems

Abstract

The uncertainty measure plays an important role in the analysis of data. At present, many uncertain measures for incomplete information systems or incomplete decision systems have been developed. However, these measures are mainly aimed at discrete valued information systems, but they are not suitable for real valued data sets. In this paper, we mainly study the uncertainty measurement method of incomplete numerical information systems. By introducing neighborhood tolerant rough sets model, each concept has a neighborhood tolerant subset called neighborhood tolerance granule. Neighborhood tolerance information quantity uncertainty measure is proposed. We then prove that it satisfies non-negativity and monotonicity, giving maximum and minimum values. On this basis, the concept of neighborhood-tolerance joint quantity and neighborhood-tolerance condition quantity is proposed, and the relation between them and neighborhood tolerance information is discussed. Theoretical analysis and experimental results show that, in incomplete numerical information systems, the uncertainty measures we propose are performed better than the neighborhood-tolerance approximation accuracy measure in some case.