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Prejudice in uncertain information merging: Pushing the fusion paradigm of evidence theory further

机译:不确定信息合并的偏见:进一步推动证据理论的融合范式

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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. (C) 2020 Elsevier Inc. All rights reserved.
机译:在1976年的书中,G. Shafer重新解释Dempster作为信仰程度的概率。他研究了来自不同来源的独立基本部分可靠的证据的融合,表明并非所有信仰功能都可以被视为简单支持功能的组合,代表这些证据使用Dempster规则。它只产生一种特殊的信仰函数,称为可分离。 1995年,PH通过结合两个可分离的信仰函数来观看信仰功能,其中一个模型从来源报告的结果,以及另一个通过缩回操作表示怀疑。我们提出了在接收者的偏见方面对后一种信仰功能的新解释,并考虑收回作为一种特殊的信仰变革。其作用是削弱一些焦点集合的支持,可能源于融合来电信息。它提供了一种替代广泛的非教条信念函数,作为合并证据和偏见的理论,这部分地根据支持功能和拟合符合换句者方法。缩回与贴现,修订和来自相互冲突证据的对称组合不同。该方法依赖于正则真实的所谓的差分功能,从充分信心充分利用。我们还讨论依赖于差异函数的信息排序和组合规则。最后,我们研究了辅音案中的基于差异的排序和组合,并表明了达到似然函数协议的可能性理论的新分支。 (c)2020 Elsevier Inc.保留所有权利。

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