$\alpha$-junctions of categorical mass functions

John Klein 1 Mehena Loudahi 1 Jean-Marc Vannobel 1 Olivier Colot 1
1 LAGIS-SI
LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal
Abstract : The set of $\alpha$-junctions is the set of linear associative and commutative combination operators for belief functions. Consequently, the properties of $\alpha$-junctive rules make them particularly attractive on a theoretic point of view. However, they are rarely used in practice except for the $\alpha=1$ case which corresponds to the widely used and well understood conjunctive and disjunctive rules. The lack of success of $\alpha$-junctions when $\alpha<1$ 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 Den\oe ux [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 $\alpha$-junctions. To that end, this study is focused on the behavior of $\alpha$-junctions when categorical mass functions are used as entries of an $\alpha$-junctive combination rule. It is shown that there exists a conjunctive and a disjunctive canonical decomposition of the mass function obtained after combination.
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John Klein, Mehena Loudahi, Jean-Marc Vannobel, Olivier Colot. $\alpha$-junctions of categorical mass functions. third international conference on belief functions, Sep 2014, Oxford, United Kingdom. pp.1-10, ⟨10.1007/978-3-319-11191-9_1⟩. ⟨hal-01012048v2⟩

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