Toward an Axiomatic Definition of Conflict Between Belief Functions

Destercke, Sébastien; Bürger, Thomas

doi:10.1109/tsmcb.2012.2212703

Cited by 76 publications

(97 citation statements)

References 32 publications

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“…Following this line, I participated to Destercke's work to define an adapted measure of conflict in an axiomatic way. As a result, we established in [18], that for an imprecise statistics view, Dempster's conflict was indeed the good way to estimate conflict, while for a singular view, a simple plausibility based definition was perfectly sensible. More precisely, in the case of independent sources, we proposed the following measure of conflict, based on the products of contour functions:…”

Section: Conflict Measurementmentioning

confidence: 88%

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Geometric views on conflicting mass functions: From distances to angles

Bürger

2016

International Journal of Approximate Reasoning

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Recently, several works have focused on the study of conflict among belief functions with a geometric approach, trying to elaborate on the intuition that distant belief functions are more conflicting than neighboring ones. In this article, I discuss the extent to which the mathematical properties of a metric are compliant with what can be expected from a conflict measure. As this highlights some inconsistencies, numerous other geometric or algebraic objects are investigated for their potential to give a mathematical formulation to the measurement of conflict: divergences, pseudo-sine functions, kernels and semi-pseudometrics. Finally, only semi-pseudo-metrics (an intermediate object the nature of which relates to both distances and angles) seem to fit. This is practically confirmed by the fact that the outer plausibility conflict is indeed a semi-pseudo-metric.

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Section: Conflict Measurementmentioning

confidence: 88%

“…Third, it is proven that all the properties of semi-pseudo-metrics are desirable. Fourth, the outer plausibility conflict from [18] is demonstrated to be a semi-pseudo-metric.…”

Section: Introductionmentioning

confidence: 96%

Geometric views on conflicting mass functions: From distances to angles

Bürger

2016

International Journal of Approximate Reasoning

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“…The idea behind refinement is that one may be interested in reasoning at different scales, starting with a coarse one and then transferring our beliefs on a finer one using mapping r. As shows the next example, the operators introduced in this article are not immune to such an operation, for the main reason that distances are in general not invariant with respect to refinements (for a discussion about this, see [8]). Although informative partial orders are preserved after refinement, the sets of more informative functions S f (m i ) are different.…”

Section: Properties Of New Conjunctive Operatorsmentioning

confidence: 99%

Idempotent conjunctive and disjunctive combination of belief functions by distance minimization

Klein

Destercke

Colot

2018

International Journal of Approximate Reasoning

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Idempotence is a desirable property when cautiousness is wanted in an information fusion process, since in this case combining identical information should not lead to the reinforcement of some hypothesis. Idempotent operators also guarantee that identical information items are not counted twice in the fusion process, a very important property in decentralized applications where the information origin cannot always be tracked (ad-hoc wireless networks are typical examples). In the theory of belief functions, a sound way to combine conjunctively multiple information items is to design a combination rule that selects the least informative element among a subset of belief functions more informative than each of the combined ones. In contrast, disjunctive rules can be retrieved by selecting the most informative element among a subset of belief functions less informative than each of the combined ones. One interest of such approaches is that they provide idempotent rules by construction.The notions of less and more informative are often formalized through partial orderings extending usual set-inclusion, yet the only two informative partial orders that provide a straightforward idempotent rule leading to a unique result are those based on the conjunctive and disjunctive weight functions. In this article, we show that other partial orders can achieve a similar goal when the problem is slightly relaxed into a distance optimization one. Building upon previous work, this paper investigates the use of distances compatible with informative partial orders to determine a unique solution to the combination problem. The obtained operators are conjunctive/disjunctive, idempotent and commutative, but lack associativity. They are, however, quasi-associative allowing sequential combinations at no extra complexity. Some experiments demonstrate interesting discrepancies as compared to existing approaches, notably with the aforementioned rules relying on weight functions.

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“…They introduced the correction corresponding to a possible loss of the person's synchronization with the day versus night synchronizers to avoid false alarms. The problem of measuring the conflict between two bodies of evidence is been represented by belief functions in [10]. The system proposes to study the notion of conflict from different aspect.…”

Section: Related Workmentioning

confidence: 99%

An Enhanced Approach for a Multiagent Distributed Context Using Tree Topology and Transferable Belief Model

Rajpoot¹,

Mathur²,

Shrivastava³

2017

IJARCSSE

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This paper makes continuation to add transferable belief model to a Multiagent distributed context using tree topology. Agents act as a node and gather data independently using graph with cycles. The cyclic structure improves better communication among mobile unit. Dynamic scenario is been considered where agents gather data that changes over time. A cyclic graph algorithm has been proposed to merge to basic belief assignment based on transferable belief model. The major utilization of transferable belief model is in sensor networks.

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Toward an Axiomatic Definition of Conflict Between Belief Functions

Cited by 76 publications

References 32 publications

Geometric views on conflicting mass functions: From distances to angles

Geometric views on conflicting mass functions: From distances to angles

Idempotent conjunctive and disjunctive combination of belief functions by distance minimization

An Enhanced Approach for a Multiagent Distributed Context Using Tree Topology and Transferable Belief Model

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