Combination of partially non-distinct beliefs: The cautious-adaptive rule

  • Authors:

  • Abdelaziz Kallel;Sylvie Le Hégarat-Mascle

  • Affiliations:

  • CETP/IPSL, 10-12 Avenue de l'Europe, 78140 Vélizy, France;IEF/AXIS, Université de Paris-Sud, 91405 Orsay Cedex, France

  • Venue:
  • International Journal of Approximate Reasoning
  • Year:
  • 2009

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Abstract

The combination rule is critical in an evidence based fusion process. The conjunctive rule is most common eventhough when the cognitive independence - distinctness - assumption is often questionable. A new combination rule is tested here in both discrete and continuous cases, accounting for a partial non-distinctness between evidences. It is based on 'generalized discounting', that we define for separable basic belief assignments (bbas) or basic belief densities (bbds), to be applied to the source correlation derived from the cautious rule. This correlation can be specified in both considered cases of consonant bbas/bbds (as proposed by Dubois et al.) and separable bbas/bbds (as proposed by Denoeux). Then, the so-called 'cautious-adaptive' rule varies between the conjunctive rule and the cautious one, depending on the discounting level. In the Gaussian case with standard deviation @s, the evidence non-distinctness will be parameterized by a factor @r@?[0,1] dividing @s. It leads to the generalized discounting needed in the cautious-adaptive formulation.