Book ChapterDOI
The Internal Conflict of a Belief Function
Johan Schubert
- pp 169-177
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TLDR
The conflict in Dempster’s rule of the combination of the base set is defined as the internal conflict of the belief function and this is extended also to non-consonant belief functions.Abstract:
In this paper we define and derive an internal conflict of a belief function We decompose the belief function in question into a set of generalized simple support functions (GSSFs). Removing the single GSSF supporting the empty set we obtain the base of the belief function as the remaining GSSFs. Combining all GSSFs of the base set, we obtain a base belief function by definition. We define the conflict in Dempster’s rule of the combination of the base set as the internal conflict of the belief function. Previously the conflict of Dempster’s rule has been used as a distance measure only between consonant belief functions on a conceptual level modeling the disagreement between two sources. Using the internal conflict of a belief function we are able to extend this also to non-consonant belief functions.read more
Citations
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Journal ArticleDOI
How to preserve the conflict as an alarm in the combination of belief functions
Eric Lefevre,Zied Elouedi +1 more
TL;DR: A formalism preserving the initial role of the conflict as an alarm signal announcing that there is a kind of disagreement between sources is defined, which allows to preserve some conflict, after the fusion by keeping only the part of conflict reflecting the opposition between the belief functions.
Journal ArticleDOI
Toward an Axiomatic Definition of Conflict Between Belief Functions
TL;DR: This paper starts by examining consistency and conflict on sets and extracts from this settings basic properties that measures of consistency and Conflict should have, and extends this basic scheme to belief functions in different ways.
Journal ArticleDOI
Discounted combination of unreliable evidence using degree of disagreement
TL;DR: A new degree of disagreement is proposed through which discounting factors can be generated for discounting combinations of unreliable evidence using distance of evidence and it can be experimentally verified that it describes the disagreements or differences among bodies of evidence well.
Journal ArticleDOI
Geometric views on conflicting mass functions
TL;DR: The extent to which the mathematical properties of a metric are compliant with what can be expected from a conflict measure is discussed, including the possibility of semi-pseudo-metrics in the outer plausibility conflict.
Journal ArticleDOI
New distances between bodies of evidence based on Dempsterian specialization matrices and their consistency with the conjunctive combination rule
TL;DR: It is proved that the L 1 Dempsterian matrix distance succeeds to fulfill all requirements and interesting and unprecedented ties between the conjunctive combination rule and this distance are demonstrated.
References
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Book
A mathematical theory of evidence
TL;DR: This book develops an alternative to the additive set functions and the rule of conditioning of the Bayesian theory: set functions that need only be what Choquet called "monotone of order of infinity." and Dempster's rule for combining such set functions.
Book ChapterDOI
Upper and Lower Probabilities Induced by a Multivalued Mapping
TL;DR: A distinctive feature of the present approach is a rule for conditioning, or more generally, arule for combining sources of information, as discussed in Sects.
Upper and Lower Probabilities Induced by a Multivalued Mapping.
TL;DR: In this paper, a multivalued mapping from a space X to a space S carries a probability measure defined over subsets of X into a system of upper and lower probabilities over S. Some basic properties of such systems are explored in Sects. 1 and 2.
Book ChapterDOI
A generalization of bayesian inference
TL;DR: Procedures of statistical inference are described which generalize Bayesian inference in specific ways Probability is used in such a way that in general only bounds may be placed on the probabilities of given events, and probability systems of this kind are suggested both for sample information and for prior information as discussed by the authors.
A Generalization of Bayesian Inference.
TL;DR: Procedures of statistical inference are described which generalize Bayesian inference in specific ways and some comments are made on the general class of models which produce upper and lower probabilities, and on the specific models which underlie the suggested inference procedures.