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

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.
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Submitted on : Tuesday, January 26, 2021 - 4:50:08 PM
Last modification on : Monday, July 4, 2022 - 9:59:17 AM
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Didier Dubois, Francis Faux, Henri Prade. Prejudice in uncertain information merging: Pushing the fusion paradigm of evidence theory further. International Journal of Approximate Reasoning, Elsevier, 2020, 121, pp.1-22. ⟨10.1016/j.ijar.2020.02.012⟩. ⟨hal-03121921⟩



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