Factorization of belief functions
Helmut Thoma · 1990
New methods for storing a multivariate belief function efficiently are proposed. They are based on factorizations and decompositions of both the belief function and its individual focal elements. Computations, such as combination and marginalization, can be done locally, without first reconstructing the belief function from its storage components. A convenient notation for describing and dealing with factorizations is developed based on simplified hypergraphs. We then study how factorization properties change as a belief function undergoes projection or is combined with other belief functions, and how we can combine factorization information. These questions are studied initially for Boolean belief functions (sets), and later for arbitrary belief functions. Finally it is shown that the commonality, one of the four representations of a belief function, can be interpreted as Fourier transform of the basic probability assignment. In analogy to the fast Fourier transformation a fast algorithm for the Moebius transformation is developed, which links the different belief function representations.