Interval-valued belief entropies for Dempster-Shafer structures

Abstract

In practical application problems, the uncertainty of an unknown object is often very difficult to accurately determine, so Yager proposed the interval-valued entropies for Dempster-Shafer structures, which is based on Dempster-Shafer structures and classic Shannon entropy and is an interval entropy model. Based on Dempster-Shafer structures and classic Shannon entropy, the interval uncertainty of an unknown object is determined, which provides reference for theoretical research and provides help for industrial applications. Although the interval-valued entropies for Dempster-Shafer structures can solve the uncertainty interval of an object very efficiently, its application scope is only a traditional probability space. How to extend it to the evidential environment is still an open issue. This paper proposes interval-valued belief entropies for Dempster-Shafer structures, which is an extension of the interval-valued entropies for Dempster-Shafer structures. When the belief entropy degenerates to the classic Shannon entropy, the interval-valued belief entropies for Dempster-Shafer structures will degenerate into the interval-valued entropies for Dempster-Shafer structures. Numerical examples are applied to verify the validity of the interval-valued belief entropies for Dempster-Shafer structures. The experimental results demonstrate that the proposed entropy can obtain the interval uncertainty value of a given uncertain object successfully and make decision effectively.

Keywords: Belief entropy; Dempster–Shafer structures; Interval-valued entropies; Shannon entropy; Uncertainty.