On Uncertainty Measure Issues in Rough Set Theory

Abstract

Rough set theory is a tool for dealing with uncertainty problems. How to measure the uncertainty of a knowledge is an important issue in the theory. However, the existing uncertainty measures may not accurately reflect the uncertainty degree. This study analyzes the causes of it and explores a reasonable solution to it. Firstly, the existing accuracy models only focuses on some factors related to the target set while neglecting its own important influence on the model. Secondly, since no one gives a clear definition of knowledge uncertainty in approximation space, it is difficult to evaluate the accuracy and rationality of a knowledge uncertainty measure. Thirdly, most uncertain measures of knowledge are constructed based on the structure of knowledge itself, while neglecting other factors in the approximation model. In view of these, we first propose a new accuracy model which fully considers the important role of the target set itself. Second, two definitions of accuracy measure of knowledge are proposed to explain what the uncertainty of a knowledge is. And then, two uncertainty measures of knowledge are proposed and a method for quickly calculating them is designed. At last, an uncertain entropy is constructed for more conveniently calculating of knowledge uncertainty.

Keywords

• Accuracy measure
• approximation accuracy
• approximation quality
• rough sets
• uncertainty measure