  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.
