Classic Works of the Dempster-Shafer Theory of Belief Functions (Google eBook)

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Ronald R. Yager, Liping Liu
Springer Science & Business Media, Feb 22, 2008 - Business & Economics - 806 pages
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This volume is a welcome addition to the literature on the Dempster-Shafer theory. It mayhelp turn the theory, which now enjoys a lively but fragmented existence, into a more coherent and better understood set of tools for pro- bilistic thinking in science and technology. Thevolume’stitlesuggeststhatthetheoryhadaclassicalperiodextending from the 1960s through the 1980s. In its ?rst two decades, it consisted of theoretical writings by the two of us: Dempster’s work on upper and lower probabilities in the 1960s and Shafer’s work on belief functions in the 1970s. Then interestinapplications suddenly ?owered.After Je?Barnettintroduced thename“Dempster-Shafer”in1981[1],thetheoryquicklyacquiredtextbook statusinarti?cialintelligence.Bytheendoftheclassicalperiod,around1990, the theory had acquired powerful computational tools, remarkably diverse applications, and the attention of many researchers interested in variations and generalizations. By many measures, the theory continues to ?ourish in the 21st century. Internet searches for “Dempster-Shafer” produce ever more hits. The theory is used in many branches of technology,only a few of which are representedin thisvolume.Articlesonthetheoryanditsapplicationsappearinaremarkable number of journals and recurring conferences. Books on the theory continue to appear. In other important respects, however, the theory has not been moving forward.Westillhearquestionsthatwereaskedinthe1980s:Howdowetellif bodiesofevidenceareindependent?Whatdowedoiftheyaredependent?We still encounter confusion and disagreement about how to interpret the theory. And we still ?nd little acceptance of the theory in mathematical statistics, where it ?rst began 40 years ago. We have come to believe that three things are needed to move the theory forward.
  

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Contents

Classic Works of the DempsterShafer Theory of Belief Functions An Introduction
1
New Methods for Reasoning Towards Posterior Distributions Based on Sample Data
35
Upper and Lower Probabilities Induced by a Multivalued Mapping
57
A Generalization of Bayesian Inference
73
On Random Sets and Belief Functions
105
NonAdditive Probabilities in the Work of Bernoulli and Lambert
117
Allocations of Probability
182
Computational Methods for A Mathematical Theory of Evidence
197
Some Characterizations of Lower Probabilities and Other Monotone Capacities through the use of Möbius Inversion
477
Axioms for Probability and BeliefFunction Propagation
499
Generalizing the DempsterShafer Theory to Fuzzy Sets
529
Bayesian Updating and Belief Functions
555
BeliefFunction Formulas for Audit Risk
577
Decision Making Under DempsterShafer Uncertainties
619
Belief Functions The Disjunctive Rule of Combination and the Generalized Bayesian Theorem
633
Representation of Evidence by Hints
665

Constructive Probability
217
Belief Functions and Parametric Models
265
Entropy and Specificity in a Mathematical Theory of Evidence
291
A Method for Managing Evidential Reasoning in a Hierarchical Hypothesis Space
310
Languages and Designs for Probability Judgment
345
A SetTheoretic View of Belief Functions
375
Weights of Evidence and Internal Conflict for Support Functions
411
A Framework for EvidentialReasoning Systems
418
Epistemic Logics Probability and the Calculus of Evidence
435
Implementing Dempsters Rule for Hierarchical Evidence
449
Combining the Results of Several Neural Network Classifiers
682
The Transferable Belief Model
693
A kNearest Neighbor Classification Rule Based on DempsterShafer Theory
737
Logicist Statistics II Inference
761
About Editors
786
About Authors
788
Author Index
797
Subject Index
798
Copyright

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