Abstract We define entropy of belief functions in the Dempster-Shafer (D-S) theory that satisfies a compound distributions property that is analogous to the property that characterizes Shannon's definitions of entropy and conditional entropy for probability mass functions. None of the existing definitions of entropy for belief functions in the D-S theory satisfy this property. We describe some important properties of our definition, and discuss its semantics as a measure of dissonance and not uncertainty. Finally, we compare our definition of entropy with some other definitions that are similar to ours in the sense that these definitions measure dissonance and not uncertainty.

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关于 Dempster-Shafer 信念函数的新可分解熵的性质

摘要 我们在 Dempster-Shafer (DS) 理论中定义了置信函数的熵，该理论满足复合分布特性，该特性类似于表征香农对概率质量函数的熵和条件熵的定义的特性。DS 理论中对置信函数的熵的现有定义没有一个满足这个属性。我们描述了我们定义的一些重要属性，并讨论了其语义作为衡量不协调而非不确定性的指标。最后，我们将我们对熵的定义与其他一些与我们的定义相似的定义进行比较，因为这些定义衡量的是不和谐而不是不确定性。