Abstract
Commutative monoids of belief states have been defined by imposing one or more of the usual axioms and assigning a combination rule. Familiar operations such as normalization and the Voorbraak map are surjective homomorphisms. The latter map takes values in a monoid of Bayesian states. The pignistic map is not a monoid homomorphism. This can impact robust decision making for frames of cardinality at least 3. We adapt the concept of measure zero reflecting functions between probability spaces to define a category P0 R having belief states as objects and plausibility zero reflecting functions as morphisms. This definition encapsulates a generalization of the notion of absolute continuity to the context of belief spaces. We show that the Voorbraak map induces a functor valued in P0 R that is right adjoint to the embedding of Bayesian states.
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Wojtowicz, R.L. (2008). On Transformations between Belief Spaces. In: Dubois, D., Lubiano, M.A., Prade, H., Gil, M.Á., Grzegorzewski, P., Hryniewicz, O. (eds) Soft Methods for Handling Variability and Imprecision. Advances in Soft Computing, vol 48. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85027-4_38
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DOI: https://doi.org/10.1007/978-3-540-85027-4_38
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85026-7
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