Uncertainty measurement for incomplete interval-valued information systems based on α-weak similarity

Rough set theory is a powerful mathematical tool to deal with uncertainty in data analysis. Interval-valued information systems are generalized models of single-valued information systems. Recently, uncertainty measures for complete interval-valued information systems or complete interval-valued decision systems have been developed. However, there are few studies on uncertainty measurements for incomplete interval-valued information systems. This paper aims to investigate the uncertainty measures in incomplete interval-valued information systems based on an α-weak similarity. Firstly, the maximum and the minimum similarity degrees are defined when interval-values information systems are incomplete based on the similarity relation. The concept of α-weak similarity relation is also defined. Secondly, the rough set model is constructed. Based on this model, accuracy, roughness and approximation accuracy are given to evaluate the uncertainty in incomplete interval-valued information systems. Furthermore, experimental analysis shows the effectiveness of the constructed uncertainty measures for incomplete interval-valued information systems.