Abstract
Uncertainty measures are important for knowledge discovery and data mining. Rough set theory (RST) is an important tool for measuring and processing uncertain information. Although many RST-based methods for measuring system uncertainty have been investigated, the existing measures cannot adequately characterise the imprecision of a rough set. Moreover, these methods are suitable only for complete information systems, and it is difficult to generalise methods for complete information systems to incomplete information systems. To overcome these shortcomings, we present new uncertainty measures, integrated accuracy and integrated roughness, that are based on general binary relations, and we study important properties of these measures. A theoretical analysis and examples show that the proposed integrated measures are more precise than existing uncertainty measures, they are suitable for both complete and incomplete information systems, and they are logically consistent. Therefore, integrated accuracy and integrated roughness overcome the limitations of existing measures. This research not only develops the theory of uncertainty, it also expands the application domain of uncertainty measures and provides a theoretical basis for knowledge acquisition in information systems based on general binary relations.
Highlights
Uncertainty is an important topic in research on artificial intelligence (Li and Du 2005)
Limitations of existing uncertainty measures In classical Rough set theory (RST), there are two main causes of uncertainty: the information granularity derived from the binary relation in the universe, which is knowledge uncertainty, and the boundary of the rough set in the given approximation space, which is set uncertainty (Pawlak 1991)
The extension of RST to incomplete information systems is important for making RST practical
Summary
Uncertainty is an important topic in research on artificial intelligence (Li and Du 2005). The accuracy measure reflects only the size of the boundary region but not the size of the information granularities formed by the attribute sets, which limits the applicability of classical rough sets (Pawlak 1991) To solve this problem, researchers have proposed a number of integrated uncertainty measures based on certain binary relations (Teng et al 2016; Wang et al 2008a; Liang et al 2009) that consider both the knowledge uncertainty and the set uncertainty. Limitations of existing uncertainty measures In classical RST, there are two main causes of uncertainty: the information granularity derived from the binary relation in the universe, which is knowledge uncertainty, and the boundary of the rough set in the given approximation space, which is set uncertainty (Pawlak 1991).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
