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On Three Conditioning Rules in Evidence Theory
Vejnarová, Jiřina
In evidence theory various rules were proposed to define conditional beliefs and/or plausibilities (or basic assignments). However, there exist no generally accepted criteria along which these rules can be compared. In this paper we concentrate to three of them (Dempster's conditioning rule, focusing and the approach based on lower and upper envelopes of sets of conditional probabilities) to study their mutual relationship. A new conditional rule for variables is presented afterwards and its correctness is proven.
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Morphisms of Dempster's Semigroup: A Revision and Interpretation
Daniel, Milan
Analyzing three new approaches to interpretation, definition, and measurement of conflicts of belief Functions (BFs), we previously observed a possibility of expression of a BF Bel as Dempster's sum of non-conflicting BF Bel0 with the same plausibility decisional support as the original BF Bel has and of indecisive BF BelS which does not prefer any of the elements of frame of discernment. Based on this observation, the theory of homomorphisms of Dempster's semigroup (the algebra of non-extremal BFs on 2-element frame of discernment with Dempster's rule as its binary operation) is updated in the present contribution. New homomorphisms are introduced; their interpretation and relation to the original ones are presented.
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A Note on Factorization of Belief Functions
Jiroušek, Radim ; Shenoy, P. P.
The paper compares two main types of factorization of belief functions (one based on the Dempster´s rule of combination, the other based on the operator of composition) and shows that both the approaches are equivalent to each other in case of unconditional factorization and shows what are the differences when overlapping factorization is studied.
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Conditioning and Flexibility in Compositional Models
Kratochvíl, Václav
Reasoning by cases or assumptions is a common form of human reasoning. In case of probability reasoning, this is modeled by conditioning of a multidimensional probability distribution. Compositional models are defined as a multidimensional distributions assembled from a (so called generating) sequence of lowdimensional probability distributions, with the help of operators of composition. In this case, the conditioning process can be viewed as a transformation of one generating sequence into another one. It appears that the conditioning process is simple when conditioning variable appears in the argument of the first distribution of the corresponding generating sequence. That is why we introduce the so called flexible sequences. Flexible sequences are those, which can be reordered in many ways that each variable can appears among arguments of the first distribution. In this paper, we study the problem of flexibility in light of the very recent solution of the equivalence problem.
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