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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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Associativity in Combination of Belief Functions
Daniel, Milan
The nature of a contradiction (conflict) between two belief functions is investigated. Alternative ways of distribution of the contradiction among nonempty subsets of frame of discernment are studied. A new approach to understanding of the contradiction is used and an original notion of a potential contradiction is introduced. A new way of an associative combination of generalized belief functions is presented. A way of its proportionalization is suggested as well.
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