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Podmiňování domnění v DSmT
Daniel, Milan
Basic notions from both Dempster-Shafer theory and DSmT (Dezert-Smarandache theory) are briefly reminded, followed by a recapitulation of the existing results on DSm conditioning. Analogically to the analysis of belief conditioning in the classical case, the existing DSm belief conditioning rules (BCRs) are analysed and the new generalized plain BCR is defined, a general formula for DSm BCRs is presented, and the general DSm BCR is defined. Further, the negative conditioning in the lattice based DSm approach is introduced, the negative plain and negative Dempster's BCRs are defined and first results of these new rules are presented. Finally a wide area of open problems of negative DSm belief conditioning and its relation to positive conditioning is sketched.
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Podmiňovací pravidla pro klasické domněnkové funkce
Daniel, Milan
The classic belief conditioning rules (BCRs) and DSm BCRs applied to classic belief functions are briefly recalled in the contribution. A general idea of belief conditioning by a given evidence is analysed and a new plain BCR is presented. This rule is compared with both the classic and the DSm BCRs. Finally, general formulas for described BCRs and a new general BCR are presented and defined.
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Transformations of Belief Functions to Probabilities
Daniel, Milan
Alternative approaches to widely known pignistic transformation of belief functios are presented and analyzed. Pignistic, cautions, proportional and disjunctive probabilistic transformations are examined from the point of view of their interpretation, of decision making and from the point of view of their communication with rules (operators) for belief function combination.
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Composition and Decomposition of Belief Functions
Daniel, Milan
MinC combination of belief functions - an instance of combination per elements is recalled in order to find its computational simplification. Unique decomposition/composition of n-dimensional belief functions to/from a system of 2-dimensional belief functions is introduced. Decomposition of generalized n-dimensional belief function and an attempt to their composition is presented as well. New demands for an operation of combination of belief functions are stated.
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