A subjective interpretation of Liu-Liu's credibility measures and expectations

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.