Abstract In his 1976 book, G. Shafer reinterprets Dempster lower probabilities as degrees of belief. He studies the fusion of independent elementary partially reliable pieces of evidence coming from different sources, showing that not all belief functions can be seen as the combination of simple support functions, representing such pieces of evidence, using Dempster rule. It only yields a special kind of belief functions called separable. In 1995, Ph. Smets has indicated that any non-dogmatic belief function can be seen as the combination of so-called generalized simple support functions, whose masses may lie outside the unit interval. It comes down to viewing a belief function as the result of combining two separable belief functions, one of which models reports from sources, and the other one expresses doubt, via a retraction operation. We propose a new interpretation of the latter belief function in terms of prejudice of the receiver, and consider retraction as a special kind of belief change. Its role is to weaken the support of some focal sets of a belief function, possibly stemming from the fusion of the incoming information. It provides an alternative extensive account of non-dogmatic belief functions as a theory of merging pieces of evidence and prejudices, which partially differs from Shafer approach's based on support functions and coarsenings. Retraction differs from discounting, revision, and from the symmetric combination of conflicting evidence. The approach relies on a so-called diffidence function on the positive reals ranging from full confidence to full diffidence. We also discuss information orderings and combination rules that rely on diffidence functions. Finally, we study the diffidence-based ordering and combination in the consonant case, and show that the diffidence view suggests a new branch of possibility theory, in agreement with likelihood functions.

中文翻译：

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不确定信息融合中的偏见：进一步推动证据理论的融合范式

摘要在他 1976 年的书中，G. Shafer 将 Dempster 低概率重新解释为置信度。他研究了来自不同来源的独立基本部分可靠证据的融合，表明并非所有的信念函数都可以被视为简单支持函数的组合，使用登普斯特规则表示这些证据。它只产生一种特殊的信念函数，称为可分离的。1995 年，Ph. Smets 指出，任何非教条的信念函数都可以看作是所谓广义简单支持函数的组合，其质量可能位于单位区间之外。归结为将信念函数视为结合两个可分离的信念函数的结果，其中一个模型从来源报告，另一个表示怀疑，通过收回操作。我们从接收者的偏见角度对后者的信念函数提出了新的解释，并将收回视为一种特殊的信念变化。它的作用是削弱一些信念函数的焦点集的支持，这可能源于传入信息的融合。它提供了对非教条信念函数的另一种广泛解释，作为合并证据和偏见的理论，这部分不同于基于支持函数和粗化的谢弗方法。撤回不同于打折、修订和冲突证据的对称组合。该方法依赖于从完全置信到完全置信的正实数上的所谓差分函数。我们还讨论了依赖于差异函数的信息排序和组合规则。