This book brings together a collection of classic research papers on the Dempster-Shafer theory of belief functions. By bridging fuzzy logic and probabilistic reasoning, the theory of belief functions has become a primary tool for knowledge representation and uncertainty reasoning in expert systems. This book will serve as 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. From over 120 nominated contributions, the editors selected 30 papers, which are widely regarded as classics and will continue to make impacts on the future development of the field. The contributions are grouped into seven sections, including conceptual foundations, theoretical perspectives, theoretical extensions, alternative interpretations, and applications to artificial intelligence, decision-making, and statistical inferences. The book also includes a foreword by Dempster and Shafer reflecting the development of the theory in the last forty years, and an introduction describing the basic elements of the theory and how each paper contributes to the field.

Inhalt

Classic Works of the Dempster-Shafer Theory of Belief Functions: An Introduction.- New Methods for Reasoning Towards Posterior Distributions Based on Sample Data.- Upper and Lower Probabilities Induced by a Multivalued Mapping.- A Generalization of Bayesian Inference.- On Random Sets and Belief Functions.- Non-Additive Probabilities in the Work of Bernoulli and Lambert.- Allocations of Probability.- Computational Methods for A Mathematical Theory of Evidence.- Constructive Probability.- Belief Functions and Parametric Models.- Entropy and Specificity in a Mathematical Theory of Evidence.- A Method for Managing Evidential Reasoning in a Hierarchical Hypothesis Space.- Languages and Designs for Probability Judgment.- A Set-Theoretic View of Belief Functions.- Weights of Evidence and Internal Conflict for Support Functions.- A Framework for Evidential-Reasoning Systems.- Epistemic Logics, Probability, and the Calculus of Evidence.- Implementing Dempster's Rule for Hierarchical Evidence.- Some Characterizations of Lower Probabilities and Other Monotone Capacities through the use of Möbius Inversion.- Axioms for Probability and Belief-Function Propagation.- Generalizing the Dempster-Shafer Theory to Fuzzy Sets.- Bayesian Updating and Belief Functions.- Belief-Function Formulas for Audit Risk.- Decision Making Under Dempster-Shafer Uncertainties.- Belief Functions: The Disjunctive Rule of Combination and the Generalized Bayesian Theorem.- Representation of Evidence by Hints.- Combining the Results of Several Neural Network Classifiers.- The Transferable Belief Model.- A k-Nearest Neighbor Classification Rule Based on Dempster-Shafer Theory.- Logicist Statistics II: Inference.