We revisit Zadeh's notion of “evidence of the second kind” and show that it provides the foundation for a general theory of epistemic random fuzzy sets, which generalizes both the Dempster-Shafer theory of belief functions and possibility theory. In this perspective, Dempster-Shafer theory deals with belief functions generated by random sets, while possibility theory deals with belief functions induced by fuzzy sets. The more general theory allows us to represent and combine evidence that is both uncertain and fuzzy. We demonstrate the application of this formalism to statistical inference, and show that it makes it possible to reconcile the possibilistic interpretation of likelihood with Bayesian inference.

我们重新审视 Zadeh 的“第二类证据”概念，并表明它为认知随机模糊集的一般理论提供了基础，该理论概括了信念函数的 Dempster-Shafer 理论和可能性理论。从这个角度来看，Dempster-Shafer 理论处理由随机集产生的置信函数，而可能性理论处理由模糊集引起的置信函数。更一般的理论使我们能够表示和组合既不确定又模糊的证据。我们展示了这种形式主义在统计推断中的应用，并表明它可以将可能性的可能性解释与贝叶斯推断相协调。