## Classic Works of the Dempster-Shafer Theory of Belief FunctionsRonald R. Yager, Liping Liu This is a collection of classic research papers on the Dempster-Shafer theory of belief functions. The book is the authoritative reference in the field of evidential reasoning and an important archival reference in a wide range of areas including uncertainty reasoning in artificial intelligence and decision making in economics, engineering, and management. The book includes a foreword reflecting the development of the theory in the last forty years. |

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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 |

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798 | |

### Other editions - View all

Classic Works of the Dempster-Shafer Theory of Belief Functions Ronald R. Yager,Liping Liu Limited preview - 2008 |

Classic Works of the Dempster-Shafer Theory of Belief Functions Ronald R. Yager,Liping Liu No preview available - 2010 |

### Common terms and phrases

applied argument Artiﬁcial Intelligence audit objective audit risk basic probability assignment Bayesian inference Bel(A Bel1 Bel2 belief function belief function Bel belief-function Bernoulli betting bodies of evidence classiﬁers computation conditional probabilities conﬂict Conjectandi corresponding decision deﬁned deﬁnition degrees of belief Dempster-Shafer Dempster-Shafer theory Dempster’s rule denote diﬀerent eﬀect epistemic probability evidential example ﬁducial ﬁnancial statement ﬁnd ﬁnite ﬁrst focal elements formula frame of discernment fuzzy set given Glenn Shafer hyperedges hypertree hypotheses independent inference interpretation intersection items of evidence logic lower probabilities m-values mapping mycin nodes normalization observations obtained parameter plausibility functions possible probability distribution probability judgments probability measure problem proposition random represented result rule of combination sample Sect simple support function speciﬁc statistical subset Suppose theorem theory of belief Theory of Evidence tion transferable belief model uncertainty upper and lower vacuous values