An algorithmic approach to combining belief functions

Tonn, Bruce

doi:10.1002/(sici)1098-111x(199607)11:7<463::aid-int3>3.0.co;2-k

Cited by 3 publications

(3 citation statements)

References 3 publications

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“…In [41], Josang develops a consensus operator described on binary frames, see also [42]. For other proposals, see [4,117,108,83,57,56,54,43,10,107]. Many proposed solutions are purely ad hoc.…”

Section: A31 Normalized Beliefs On Boolean Algebrasmentioning

confidence: 99%

Analyzing the combination of conflicting belief functions

2007

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We consider uncertain data which uncertainty is represented by belief functions and that must be combined. The result of the combination of the belief functions can be partially conflictual. Initially Shafer proposed Dempster's rule of combination where the conflict is reallocated proportionally among the other masses. Then Zadeh presented an example where Dempster's rule of combination produces unsatisfactory results. Several solutions were proposed: the TBM solution where masses are not renormalized and conflict is stored in the mass given to the empty set, Yager's solution where the conflict is transferred to the universe and Dubois and Prade's solution where the masses resulting from pairs of conflictual focal elements are transferred to the union of these subsets. Many other suggestions have then been made, creating a 'jungle' of combination rules. We discuss the nature of the combinations (conjunctive versus disjunctive, revision versus updating, static versus dynamic data fusion), argue about the need for a normalization, examine the possible origins of the conflicts, determine if a combination is justified and analyze many of the proposed solutions.

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Section: A31 Normalized Beliefs On Boolean Algebrasmentioning

confidence: 99%

Analyzing the combination of conflicting belief functions

2007

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“…Consensus algorithms exist if one needs to find a consensus among imprecise probabilities provided by a group of experts in a Delphi exercise, for example [13]. Combination of pieces of evidence [11], and conditionalization and up-dating [14] of existing imprecise probabilities are additional topics related to manipulating imprecise probabilities.…”

Section: Resultsmentioning

confidence: 99%

Imprecise probabilities and scenarios

Tonn

2005

Futures

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“…This combination method has several deficiencies. (25,48,49) Tonn (47) presents an alternative method for combining basic probability assignments. Using this method, the combination of the pieces of evidence presented in Table II yields a lower probability of extinction of .22 and a lower probability of survival of .14 over the next 1,000 years, with a substantial amount of uncertainty remaining in the analysis (as allocated to both extinction and survival).…”

Section: Evidential Reasoningmentioning

confidence: 99%

Evaluating Methods for Estimating Existential Risks

Tonn

Stiefel

2013

Risk Analysis

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Researchers and commissions contend that the risk of human extinction is high, but none of these estimates have been based upon a rigorous methodology suitable for estimating existential risks. This article evaluates several methods that could be used to estimate the probability of human extinction. Traditional methods evaluated include: simple elicitation; whole evidence Bayesian; evidential reasoning using imprecise probabilities; and Bayesian networks. Three innovative methods are also considered: influence modeling based on environmental scans; simple elicitation using extinction scenarios as anchors; and computationally intensive possible-worlds modeling. Evaluation criteria include: level of effort required by the probability assessors; level of effort needed to implement the method; ability of each method to model the human extinction event; ability to incorporate scientific estimates of contributory events; transparency of the inputs and outputs; acceptability to the academic community (e.g., with respect to intellectual soundness, familiarity, verisimilitude); credibility and utility of the outputs of the method to the policy community; difficulty of communicating the method's processes and outputs to nonexperts; and accuracy in other contexts. The article concludes by recommending that researchers assess the risks of human extinction by combining these methods.

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An algorithmic approach to combining belief functions

Cited by 3 publications

References 3 publications

Analyzing the combination of conflicting belief functions

Analyzing the combination of conflicting belief functions

Imprecise probabilities and scenarios

Evaluating Methods for Estimating Existential Risks

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