A Comparison of Methods for Transforming Belief Function Models to Probability Models

Cobb, Barry R.; Shenoy, Prakash P.

doi:10.1007/978-3-540-45062-7_21

Cited by 43 publications

(38 citation statements)

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“…T P (bel * )(R(X)) = P * (R(X)) = P (X) = T P (bel)(X), for any permutation R of elements of Ω and BF bel * given by m * (R(X)) = m(X). [3] follow the assumption (iv-c) of ⊕-consistency. The addition of an assumption of the ulb-consistency does not justify any unique probabilistic transformation.…”

Section: Definition 4 a Function Pt From The Set Of All Belief Functimentioning

confidence: 94%

“…Besides the new original results, Baroni & Vicigs's results from [2] and Cobb & Shenoy's results [3], the present study includes also Sudano's transformations [36,37] and Smets' new results [34,35].…”

Section: Introductionmentioning

confidence: 95%

“…The (normalized) plausibility probabilistic transformation Pl T, see e.g. [2] or [3], is defined as a normalized plausibility of singletons 8 . Hence we have…”

Section: Plausibility or Cautious Probabilistic Transformationmentioning

confidence: 99%

“…7 The special case of a convex combination of bbas for α = 1 2 was mentioned as averaging of bbas in [13]. 8 Despite of the fact that, Cobb and Shenoy introduce it as a new method [3] in 2003, and Sudano also introduces it as P rN P l in 2003, it was known already in 1991 [1]. 9 This name does not correspond to Smets' wish of using the name of the pignistic transformation, besides it does not satisfy all assumptions required from Smets' pignistic transformation, either the original [31,33] or the recent ones [34,35].…”

Section: Voorbraak's Bayesian Transformation (Vbt)mentioning

confidence: 99%

“…In the last years several papers on alternative probabilistic transformations have been published [2,3,12,13,36,37], and a new justification of pignistic transformation has appeared [34,35].…”

Section: Introductionmentioning

confidence: 99%

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Probabilistic Transformations of Belief Functions

Daniel

2005

Lecture Notes in Computer Science

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Section: Definition 4 a Function Pt From The Set Of All Belief Functimentioning

confidence: 94%

Section: Introductionmentioning

confidence: 95%

“…The (normalized) plausibility probabilistic transformation Pl T, see e.g. [2] or [3], is defined as a normalized plausibility of singletons 8 . Hence we have…”

Section: Plausibility or Cautious Probabilistic Transformationmentioning

confidence: 99%

Section: Voorbraak's Bayesian Transformation (Vbt)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Probabilistic Transformations of Belief Functions

Daniel

2005

Lecture Notes in Computer Science

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On transformations of belief functions to probabilities

Daniel

2006

Int. J. Intell. Syst.

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Alternative approaches to the widely known pignistic transformation of belief functions are presented and analyzed. Pignistic, cautious, 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 commutation with rules~operators! for belief function combination. A relation to the plausibility probabilistic transformation is added.

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Classification of Incomplete Data Using Autoencoder and Evidential Reasoning

Choudhury

Pal

2019

IFIP Advances in Information and Communication Technology

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To classify data with missing values, we propose a method exploiting autoencoders and evidence theory. We augment the complete data by deleting each feature once and imputing it using the nearest neighbor to a set of predefined points generated using a new scheme. We train an autoencoder with the complete data set to get a latent space representation of the input. The network is retrained with the augmented data to get a better latent space representation. Now for each class, we train a support vector machine (SVM) with a one-vs-all strategy using the latent space representation of the complete data set. For an r-class problem, the output of each of the r SVMs is used to define a Basic Probability Assignment (BPA). The BPAs are combined using Dempster's rule of combination to make the final decision. Now to classify any test instance with missing values, we make an initial guess of the missing values using the nearest neighbor rule. We take the latent space representation of that imputed instance and pass it through each trained SVM. As done earlier, using each SVM output, we generate a BPA and the r BPAs are aggregated to get a composite BPA. The class label of the test point is then determined using the Pignistic probabilities. We have compared the proposed method with four state-of-the-art techniques using three experiments with artificial and real datasets. The proposed method is found to perform better.

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A Comparison of Methods for Transforming Belief Function Models to Probability Models

Cited by 43 publications

References 10 publications

Probabilistic Transformations of Belief Functions

Probabilistic Transformations of Belief Functions

On transformations of belief functions to probabilities

Classification of Incomplete Data Using Autoencoder and Evidential Reasoning

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