$\alpha$-junctions of categorical mass functions
Résumé
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.
Domaines
Intelligence artificielle [cs.AI]Origine | Fichiers produits par l'(les) auteur(s) |
---|
Loading...