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Algebraic Uncertainty Theory
A Unifying Perspective on Reasoning under Uncertainty

dc.contributor.advisorCremers, Armin B.
dc.contributor.authorZimmermann, Jörg
dc.date.accessioned2020-04-18T20:21:32Z
dc.date.available2020-04-18T20:21:32Z
dc.date.issued22.05.2013
dc.identifier.urihttps://hdl.handle.net/20.500.11811/5686
dc.description.abstractThe question of how to represent and process uncertainty is of fundamental importance to the scientific process, but also in everyday life. Currently there exist a lot of different calculi for managing uncertainty, each having its own advantages and disadvantages. Especially, almost all are defining the domain and structure of uncertainty values a priori, e.g., one real number, two real numbers, a finite domain, and so on, but maybe uncertainty is best measured by complex numbers, matrices or still another mathematical structure. This thesis investigates the notion of uncertainty from a foundational point of view, provides an ontology and axiomatic core system for uncertainty and derives and not defines the structure of uncertainty. The main result, the ring theorem, stating that uncertainty values are elements of the [0,1]-interval of a partially ordered ring, is used to derive a general decomposition theorem for uncertainty values, splitting them into a numerical interval and an ``interaction term''. In order to illustrate the unifying power of these results, the relationship to Dempster-Shafer theory is discussed and it is shown that all Dempster-Shafer measures over finite domains can be represented by ring-valued uncertainty measures. Finally, the historical development of approaches to modeling uncertainty which have led to the results of this thesis are reviewed.en
dc.language.isoeng
dc.rightsIn Copyright
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectReasoning under Uncertainty
dc.subjectAxiomatization
dc.subjectAlgebra
dc.subjectRing Theory
dc.subjectDempster-Shafer Theory
dc.subjectCox's Theorem
dc.subject.ddc004 Informatik
dc.titleAlgebraic Uncertainty Theory
dc.title.alternativeA Unifying Perspective on Reasoning under Uncertainty
dc.typeDissertation oder Habilitation
dc.publisher.nameUniversitäts- und Landesbibliothek Bonn
dc.publisher.locationBonn
dc.rights.accessRightsopenAccess
dc.identifier.urnhttps://nbn-resolving.org/urn:nbn:de:hbz:5n-32168
ulbbn.pubtypeErstveröffentlichung
ulbbnediss.affiliation.nameRheinische Friedrich-Wilhelms-Universität Bonn
ulbbnediss.affiliation.locationBonn
ulbbnediss.thesis.levelDissertation
ulbbnediss.dissID3216
ulbbnediss.date.accepted30.08.2012
ulbbnediss.fakultaetMathematisch-Naturwissenschaftliche Fakultät
dc.contributor.coRefereeWrobel, Stefan


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