In this paper, we propose two new definitions of local differential privacy for belief functions. One is based on Shafer's semantics of randomly coded messages and the other from the perspective of imprecise probabilities. We show that such basic properties as composition and post-processing also hold for our new definitions. Moreover, we provide a hypothesis testing framework for these definitions and study the effect of "don't know" in the trade-off between privacy and utility in discrete distribution estimation.

翻译：在本文中,我们为信仰功能的地方差异隐私提出了两个新的定义。一个基于Safer随机编码信息语义的语义,另一个基于不精确概率的视角。我们表明组成和后处理等基本特性也为我们的新定义提供了依据。此外,我们为这些定义提供了一个假设测试框架,并研究了“不知道”在隐私和独立分配估计的实用性之间取舍“不知道”的影响。