Conflict, Consistency and Consonance in Belief Functions: Coherence and Integrity of Belief Systems

  • Peter R. Gillett
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 88)


This paper discusses how the belief function formalism gives rise to new concepts of conflict and nonspecificity that are more important than conflict in the case of probability theory; assessing this conflict can be important for the strategic choices of whether to seek additional evidence or to discount or retract existing evidence, and which beliefs to retract; it is important to consider not just the external conflict between beliefs, but the internal conflict within belief functions arising from masses assigned to non-intersecting focal elements. The paper considers six measures of conflict: two that apply only to separable belief functions, and that require the canonical decomposition to be found (based on Shafer’s work), and four based on extension of the entropy concept (by Yager, Höhle, Ramer, Klir and others). Detailed computations of the various measures are exhibited for two illustrative examples. Axioms for conflict in the context of its intended use are given, and it is argued that dissonance may be the conflict measure that fits them most closely. Finally, a method is given for using conflict to decide which of a set of beliefs to retract (or discount).


Support Function Belief Function Internal Conflict Canonical Decomposition Focal Element 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Peter R. Gillett
    • 1
  1. 1.Rutgers: The State University of New JerseyUSA

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