Foundations for a new theory of plausible and paradoxical reasoning
Information & Security An International JournalPublished 1 January 2002Open access
Jean Dezert
Citations162
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This paper focuses on the development of a new theory of plausible and paradoxical reasoning which can be interpreted as a generalization of the theory of evidence and discusses the justification of the new rule of combination of uncertain and Paradoxical sources of evidences.
Abstract
Foundations for a new theory of plausible and paradoxical reasoning
Keywords
Computer ScienceDecision Sciences
Elements of Information Theory
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183 Citations1995Jürg Kohlas, Paul-André Monney
This chapter discusses the construction of a model of a hint, the role of support, and the structure of support and Plausibility in the general case.
Zenodo (CERN European Organization for Nuclear Research)A Unifying Field In Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability And Statistics
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Transactions of the American Mathematical SocietyOn Dedekind’s problem: the number of isotone Boolean functions. II
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