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Kompozicionální modely domněnkvých funkcí
Jiroušek, Radim ; Vejnarová, Jiřina ; Daniel, Milan
After it has been successfully done in probability and possibility theories, the paper is the first attempt to introduce the operator of composition also for belief functions. We prove that the proposed definition preserves all the necessary properties of the operator enabling us to define compositional models as an efficient tool for multidimensional models representation.
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Několik poznámek a otázek k Josangově uhlazenému zhrubění.
Daniel, Milan
Definitions of two different ways of coarsening of basic belief assignments to opinions - simple coarsening and smooth coarsening – are recalled in this contribution. A relation of results of combination of smooth opinions using the consensus operator to belief functions on an original $n$-element frame of discernment is examined. A question of an interpretation of smoothly coarsened opinions is discussed.
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Co je to Hybridní DSm Pravidlo pro kombinování domněnkových funkcí?
Daniel, Milan
This contribution is dealing with DSm theory of belief functions. Two different versions of hybrid DSm combination rule are presented. Inconsistencies of the newer version are observed and its corrections are suggested. New DSmH rules, which produce more specified results are suggested, and a schema, which covers a large family of combination rules derived from the generalized conjunctive combination rule, is presented.
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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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