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Alternative Formulations of the Theory of Evidence Based on Basic Plausibility and Commonality Assignments

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Part of the Lecture Notes in Computer Science book series (LNAI,volume 5351)

Abstract

In this paper we introduce indeed two alternative formulations of the theory of evidence by proving that both plausibility and commonality functions share the same combinatorial structure of sum function of belief functions, and computing their Moebius inverses called basic plausibility and commonality assignments. The equivalence of the associated formulations of the ToE is mirrored by the geometric congruence of the related simplices. Applications to the probabilistic approximation problem are briefly presented.

Keywords

  • Alternative Formulation
  • Belief Function
  • Commonality Function
  • Commonality Space
  • Binary Case

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Cuzzolin, F. (2008). Alternative Formulations of the Theory of Evidence Based on Basic Plausibility and Commonality Assignments. In: Ho, TB., Zhou, ZH. (eds) PRICAI 2008: Trends in Artificial Intelligence. PRICAI 2008. Lecture Notes in Computer Science(), vol 5351. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89197-0_12

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  • DOI: https://doi.org/10.1007/978-3-540-89197-0_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89196-3

  • Online ISBN: 978-3-540-89197-0

  • eBook Packages: Computer ScienceComputer Science (R0)