Conditional plausibility entropy of belief functions based on Dempster conditioning

Uncertainty quantification of belief functions is an unsolved issue in belief function theory that is used widely to tackle epistemic uncertainty. This study provides a new definition of conditional entropy of belief functions, called conditional plausibility entropy, in terms of Dempster conditioning and plausibility entropy of mass functions. The proposed conditional plausibility entropy mainly meets two aspects of good properties, one is the semantics of independence property, the other is the compatibility with Shannon's conditional entropy for probability distributions, which are not simultaneously satisfied by existing definitions of conditional entropy of belief functions. The effectiveness of conditional plausibility entropy is validated further through comparison and analysis on the basis of different conditioning methods.