Abstract
Belief functions usually contain some internal conflict. Based on Hájek-Valdés algebraic analysis of belief functions, a unique decomposition of a belief function into its conflicting and non-conflicting part was introduced at ISIPTA’11 symposium for belief functions defined on a two-element frame of discernment.
This contribution studies the conditions under which such a decomposition exists for belief functions defined on a three-element frame. A generalisation of important Hájek-Valdés homomorphism f of semigroup of belief functions onto its subsemigroup of indecisive belief functions is found and presented. A class of quasi-Bayesian belief functions, for which the decomposition into conflicting and non-conflicting parts exists is specified. A series of other steps towards a conflicting part of a belief function are presented. Several open problems from algebra of belief functions which are related to the investigated topic and are necessary for general solution of the issue of decomposition are formulated.
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Daniel, M. (2014). Towards a Conflicting Part of a Belief Function. In: Laurent, A., Strauss, O., Bouchon-Meunier, B., Yager, R.R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2014. Communications in Computer and Information Science, vol 444. Springer, Cham. https://doi.org/10.1007/978-3-319-08852-5_22
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DOI: https://doi.org/10.1007/978-3-319-08852-5_22
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