Towards a Conflicting Part of a Belief Function

0430480 - ÚI 2015 RIV CH eng C - Conference Paper (international conference)
Daniel, Milan
Towards a Conflicting Part of a Belief Function.
Information Processing and Management of Uncertainty in Knowledge-Based Systems. Vol. 3. Cham: Springer, 2014 - (Laurent, A.; Strauss, O.; Bouchon-Meunier, B.; Yager, R.), s. 212-222. Communications in Computer and Information Science, 444. ISBN 978-3-319-08851-8. ISSN 1865-0929.
[IPMU 2014 /15./. Montpellier (FR), 15.07.2014-19.07.2014]
R&D Projects: GA ČR GAP202/10/1826
Institutional support: RVO:67985807
Keywords : belief function * Dempster-Shafer theory * Dempster’s semigroup * conflict between belief functions * uncertainty * non-conflicting part of belief function * conflicting part of belief function
Subject RIV: BA - General Mathematics

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.
Permanent Link: http://hdl.handle.net/11104/0235402