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.
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Klein, J., Loudahi, M., Vannobel, JM., Colot, O. (2014). α-Junctions of Categorical Mass Functions. In: Cuzzolin, F. (eds) Belief Functions: Theory and Applications. BELIEF 2014. Lecture Notes in Computer Science(), vol 8764. Springer, Cham. https://doi.org/10.1007/978-3-319-11191-9_1
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DOI: https://doi.org/10.1007/978-3-319-11191-9_1
Publisher Name: Springer, Cham
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