In the standard literature on evidence, a customary assumption provides for the existence of a single likelihood function associated to each agent's hypothesis. In this paper the authors start from the consideration that in many practical situations this assumption raises some issues when using evidence for making decisions. Therefore, they supply a new general framework which allows the reader to deal with the case of uncertain likelihood functions. The authors' approach is consistent with Shafer's approach to handling evidence. Many examples and the deferring of technical proofs to an appendix make the reading easier.