We consider credibility measures introduced by Liu and Liu and the corresponding credibility expectations, obtained through the Choquet integral. In analogy with de Finetti’s approach to probability, we show that also for credibility measures and expectations, a subjective interpretation can be given through suitable notions of coherence. In detail, coherence can be expressed equivalently in terms of consistency, through a fair betting scheme and through a penalty criterion. Such notions of coherence rest upon the concepts of partially resolving uncertainty due to Jaffray, the notion of consonance due to Shafer and the notion of pessimism-optimism indifference introduced in this paper.

我们考虑 Liu 和 Liu 引入的可信度度量以及通过 Choquet 积分获得的相应可信度期望。与 de Finetti 的概率方法类似，我们表明，对于可信度度量和期望，也可以通过适当的连贯性概念给出主观解释。具体而言，一致性可以通过公平投注方案和惩罚标准等价地表示为一致性。这种一致性的概念基于 Jaffray 的部分解决不确定性的概念、Shafer 的协调概念以及本文引入的悲观主义-乐观主义冷漠的概念。