Interval-valued belief entropies for Dempster–Shafer structures

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.