International Conference on Belief Functions

BELIEF 2014: Belief Functions: Theory and Applications pp 1-10 | Cite as

α-Junctions of Categorical Mass Functions

  • John Klein
  • Mehena Loudahi
  • Jean-Marc Vannobel
  • Olivier Colot
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8764)

Abstract

The set of α-junctions is the set of linear associative and commutative combination operators for belief functions. Consequently, the properties of α-junctive rules make them particularly attractive on a theoretic point of view. However, they are rarely used in practice except for the α = 1 case which corresponds to the widely used and well understood conjunctive and disjunctive rules. The lack of success of α-junctions when α < 1 is mainly explained by two reasons. First, they require a greater computation load due to a more complex mathematical definition. Second, the mass function obtained after combination is hard to interpret and sometimes counter-intuitive. Pichon and Denœux [4] brought a significant contribution to circumvent both of these two limitations. In this article, it is intended to pursue these efforts toward a better understanding of α-junctions. To that end, this study is focused on the behavior of α-junctions when categorical mass functions are used as entries of an α-junctive combination rule. It is shown that there exists a conjunctive and a disjunctive canonical decomposition of the mass function obtained after combination.

Keywords

evidence theory Dempster-Shafer theory combination rules α-junctions categorical mass functions 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • John Klein
    • 1
  • Mehena Loudahi
    • 1
  • Jean-Marc Vannobel
    • 1
  • Olivier Colot
    • 1
  1. 1.Lille1 University, LAGIS UMR CNRS 8219Villeneuve d’AscqFrance

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