Classic works on the Dempster-Shafer theory of belief functions.

*(English)*Zbl 1135.68051
Studies in Fuzziness and Soft Computing 219. Berlin: Springer (ISBN 978-3-540-25381-5/hbk). xix, 806 p. (2008).

Publisher’s description: 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.

The articles of this volume will not be indexed individually.

Contents: “About the founders” (pp. vii–viii); A. P. Dempster and G. Shafer, “Foreword” (pp. ix–x); R. R. Yager and L. Liu, “Preface” (pp. xi–xii); L. Liu and R. R. Yager, “Classic works on the Dempster-Shafer theory of belief functions: an introduction” (pp. 1–34); A. P. Dempster, “New methods for reasoning towards posterior distributions based on sample data” (pp. 35–56) [reprinted from: Ann. Math. Stat. 37, 355–374 (1966; Zbl 0178.54302)]; A. P. Dempster, “Upper and lower probabilities induced by a multivalued mapping” (pp. 57–72) [reprinted from: Ann. Math. Stat. 38, 325–339 (1967; Zbl 0168.17501)]; A. P. Dempster, “A generalization of Bayesian inference” (pp. 73–103) [reprinted from: J. R. Stat. Soc., Ser. B 30, 205–232 (1968; Zbl 0169.21301)]; H. T. Nguyen, “On random sets and belief functions” (pp. 105–116) [reprinted from: J. Math. Anal. Appl. 65, 531–542 (1978; Zbl 0409.60016)]; G. Shafer, “Non-additive probabilities in the work of Bernoulli and Lambert” (pp. 117–181) [reprinted from: Arch. Hist. Exact Sci. 19, 309–370 (1978; Zbl 0392.01010)]; G. Shafer, “Allocations of probability” (pp. 183–196) [reprinted from: Ann. Probab. 7, 827–839 (1979; Zbl 0414.60002)]; J. A. Barnett, “Computational methods for a mathematical theory of evidence” (pp. 197–216) [reprinted from: Proceedings of the 7th international conference on artificial intelligence. The American Association for Artificial Intelligence. 868–875 (1981)]; G. Shafer, “Constructive probability” (pp. 217–264) [reprinted from: Synthese 48, 1–60 (1981; Zbl 0522.60001)]; G. Shafer, “Belief functions and parametric models” (pp. 265–289) [reprinted from: J. R. Stat. Soc., Ser. B 44, 322–352 (1982; Zbl 0499.62007)]; R. R. Yager, “Entropy and specificity in a mathematical theory of evidence” (pp. 291–309) [reprinted from: Int. J. Gen. Syst. 9, 249–260 (1983; Zbl 0521.94008)]; J. Gordon and E. H. Shortliffe, “A method for managing evidential reasoning in a hierarchical hypothesis space” (pp. 311–344) [reprinted from: Artif. Intell. 26, 323–357 (1985; Zbl 1134.68530)]; G. Shafer and A. Tversky, “Languages and designs for probability judgment” (pp. 345–373) [reprinted from: Cogn. Sci. Soc. 9, 309–339 (1985)]; D. Dubois and H. Prade, “A set-theoretic view of belief functions. Logical operations and approximations by fuzzy sets” (pp. 375–410) [reprinted from: Int. J. Gen. Syst. 12, 193–226 (1986)]; N. L. Zhang, “Weights of evidence and internal conflict for support functions” (pp. 411–417) [reprinted from: Inf. Sci. 38, 205–212 (1986; Zbl 0596.62004)]; J. D. Lowrance, T. D. Garvey and T. M. Strat, “A framework for evidential-reasoning systems” (pp. 419–434) [reprinted from: Proceedings of the 5th national conference on artificial intelligence. The American Association for Artificial Intelligence. 869–901 (1986)]; E. H. Ruspini, “Epistemic logics, probability, and the calculus of evidence” (pp. 435–448) [reprinted from: Proceedings of the 10th international joint conference on artificial intelligence (IJCAI). Elsevier. 924–931 (1987)]; G. Shafer and R. Logan, “Implementing Dempster’s rule for hierarchical evidence” (pp. 449–476) [reprinted from: Artif. Intell. 33, 271–298 (1987; Zbl 0633.68093)]; A. Chateauneuf and J.-Y. Jaffray, “Some characterizations of lower probabilities and other monotone capacities through the use of Möbius inversion” (pp. 477–498) [reprinted from: Math. Soc. Sci. 17, No. 3, 263–283 (1989; Zbl 0669.90003)]; P. P. Shenoy and G. Shafer, “Axioms for probability and belief-function propagation” (pp. 499–528) [reprinted from: R. D. Shachter et al. (eds.), Uncertainty in artificial intelligence. 4. Amsterdam: North-Holland. Machine Intelligence and Pattern Recognition 9, 169–198 (1990)]; J. Yen, “Generalizing the Dempster-Shafer theory to fuzzy sets” (pp. 529–554) [reprinted from: IEEE Trans. Syst. Man Cybern. 20, No. 3, 559–570 (1990; Zbl 1134.68565)]; J.-Y. Jaffray, “Bayesian updating and belief functions” (pp. 555–576) [reprinted from: IEEE Trans. Syst. Man Cybern. 22, No. 5, 1144–1152 (1992; Zbl 0769.62001)]; R. P. Srivastava and G. R. Shafer, “Belief-function formulas for audit risk” (pp. 577–618) [reprinted from: Account. Rev. 67, No. 2, 249–283 (1992)]; R. R. Yager, “Decision making under Dempster-Shafer uncertainties” (pp. 619–632) [reprinted from: Int. J. Gen. Syst. 20, No. 3, 233–245 (1992; Zbl 0756.90005)]; P. Smets, “Belief functions: the disjunctive rule of combination and the generalized Bayesian theorem” (pp. 633–663) [reprinted from: Int. J. Approx. Reasoning 9, No. 1, 1–35 (1993; Zbl 0796.68177)]; J. Kohlas and P.-A. Monney, “Representation of evidence by hints” (pp. 665–681) [reprinted from: R. R. Yager et al. (eds.), Advances in the Dempster-Shafer theory of evidence. Chichester: Wiley. 473–492 (1994; Zbl 0816.68110)]; G. Rogova, “Combining the results of several neural network classifiers” (pp. 683–691) [reprinted from: Neural Netw. 7, No. 5, 777–781 (1994)]; P. Smets and R. Kennes, “The transferable belief model” (pp. 693–736) [reprinted from: Artif. Intell. 66, No. 2, 191–234 (1994; Zbl 0807.68087)]; T. Denœux, “A \(k\)-nearest neighbor classification rule based on Dempster-Shafer theory” (pp. 737–760) [reprinted from: IEEE Trans. Syst. Man Cybern. 25, No. 5, 804–813 (1995)]; A. P. Dempster, “Logicist statistics. II: Inference” (pp. 761–785) [for Part I see Stat. Sci. 13, No. 3, 248–276 (1998; Zbl 1099.62501); Part II is a revised version of the 1998 COPSS R. A. Fisher Memorial Lecture]; “About editors” (pp. 787–788); “About authors” (pp. 789–797); Author index (p. 799); Subject index (pp. 801–806).

The articles of this volume will not be indexed individually.

Contents: “About the founders” (pp. vii–viii); A. P. Dempster and G. Shafer, “Foreword” (pp. ix–x); R. R. Yager and L. Liu, “Preface” (pp. xi–xii); L. Liu and R. R. Yager, “Classic works on the Dempster-Shafer theory of belief functions: an introduction” (pp. 1–34); A. P. Dempster, “New methods for reasoning towards posterior distributions based on sample data” (pp. 35–56) [reprinted from: Ann. Math. Stat. 37, 355–374 (1966; Zbl 0178.54302)]; A. P. Dempster, “Upper and lower probabilities induced by a multivalued mapping” (pp. 57–72) [reprinted from: Ann. Math. Stat. 38, 325–339 (1967; Zbl 0168.17501)]; A. P. Dempster, “A generalization of Bayesian inference” (pp. 73–103) [reprinted from: J. R. Stat. Soc., Ser. B 30, 205–232 (1968; Zbl 0169.21301)]; H. T. Nguyen, “On random sets and belief functions” (pp. 105–116) [reprinted from: J. Math. Anal. Appl. 65, 531–542 (1978; Zbl 0409.60016)]; G. Shafer, “Non-additive probabilities in the work of Bernoulli and Lambert” (pp. 117–181) [reprinted from: Arch. Hist. Exact Sci. 19, 309–370 (1978; Zbl 0392.01010)]; G. Shafer, “Allocations of probability” (pp. 183–196) [reprinted from: Ann. Probab. 7, 827–839 (1979; Zbl 0414.60002)]; J. A. Barnett, “Computational methods for a mathematical theory of evidence” (pp. 197–216) [reprinted from: Proceedings of the 7th international conference on artificial intelligence. The American Association for Artificial Intelligence. 868–875 (1981)]; G. Shafer, “Constructive probability” (pp. 217–264) [reprinted from: Synthese 48, 1–60 (1981; Zbl 0522.60001)]; G. Shafer, “Belief functions and parametric models” (pp. 265–289) [reprinted from: J. R. Stat. Soc., Ser. B 44, 322–352 (1982; Zbl 0499.62007)]; R. R. Yager, “Entropy and specificity in a mathematical theory of evidence” (pp. 291–309) [reprinted from: Int. J. Gen. Syst. 9, 249–260 (1983; Zbl 0521.94008)]; J. Gordon and E. H. Shortliffe, “A method for managing evidential reasoning in a hierarchical hypothesis space” (pp. 311–344) [reprinted from: Artif. Intell. 26, 323–357 (1985; Zbl 1134.68530)]; G. Shafer and A. Tversky, “Languages and designs for probability judgment” (pp. 345–373) [reprinted from: Cogn. Sci. Soc. 9, 309–339 (1985)]; D. Dubois and H. Prade, “A set-theoretic view of belief functions. Logical operations and approximations by fuzzy sets” (pp. 375–410) [reprinted from: Int. J. Gen. Syst. 12, 193–226 (1986)]; N. L. Zhang, “Weights of evidence and internal conflict for support functions” (pp. 411–417) [reprinted from: Inf. Sci. 38, 205–212 (1986; Zbl 0596.62004)]; J. D. Lowrance, T. D. Garvey and T. M. Strat, “A framework for evidential-reasoning systems” (pp. 419–434) [reprinted from: Proceedings of the 5th national conference on artificial intelligence. The American Association for Artificial Intelligence. 869–901 (1986)]; E. H. Ruspini, “Epistemic logics, probability, and the calculus of evidence” (pp. 435–448) [reprinted from: Proceedings of the 10th international joint conference on artificial intelligence (IJCAI). Elsevier. 924–931 (1987)]; G. Shafer and R. Logan, “Implementing Dempster’s rule for hierarchical evidence” (pp. 449–476) [reprinted from: Artif. Intell. 33, 271–298 (1987; Zbl 0633.68093)]; A. Chateauneuf and J.-Y. Jaffray, “Some characterizations of lower probabilities and other monotone capacities through the use of Möbius inversion” (pp. 477–498) [reprinted from: Math. Soc. Sci. 17, No. 3, 263–283 (1989; Zbl 0669.90003)]; P. P. Shenoy and G. Shafer, “Axioms for probability and belief-function propagation” (pp. 499–528) [reprinted from: R. D. Shachter et al. (eds.), Uncertainty in artificial intelligence. 4. Amsterdam: North-Holland. Machine Intelligence and Pattern Recognition 9, 169–198 (1990)]; J. Yen, “Generalizing the Dempster-Shafer theory to fuzzy sets” (pp. 529–554) [reprinted from: IEEE Trans. Syst. Man Cybern. 20, No. 3, 559–570 (1990; Zbl 1134.68565)]; J.-Y. Jaffray, “Bayesian updating and belief functions” (pp. 555–576) [reprinted from: IEEE Trans. Syst. Man Cybern. 22, No. 5, 1144–1152 (1992; Zbl 0769.62001)]; R. P. Srivastava and G. R. Shafer, “Belief-function formulas for audit risk” (pp. 577–618) [reprinted from: Account. Rev. 67, No. 2, 249–283 (1992)]; R. R. Yager, “Decision making under Dempster-Shafer uncertainties” (pp. 619–632) [reprinted from: Int. J. Gen. Syst. 20, No. 3, 233–245 (1992; Zbl 0756.90005)]; P. Smets, “Belief functions: the disjunctive rule of combination and the generalized Bayesian theorem” (pp. 633–663) [reprinted from: Int. J. Approx. Reasoning 9, No. 1, 1–35 (1993; Zbl 0796.68177)]; J. Kohlas and P.-A. Monney, “Representation of evidence by hints” (pp. 665–681) [reprinted from: R. R. Yager et al. (eds.), Advances in the Dempster-Shafer theory of evidence. Chichester: Wiley. 473–492 (1994; Zbl 0816.68110)]; G. Rogova, “Combining the results of several neural network classifiers” (pp. 683–691) [reprinted from: Neural Netw. 7, No. 5, 777–781 (1994)]; P. Smets and R. Kennes, “The transferable belief model” (pp. 693–736) [reprinted from: Artif. Intell. 66, No. 2, 191–234 (1994; Zbl 0807.68087)]; T. Denœux, “A \(k\)-nearest neighbor classification rule based on Dempster-Shafer theory” (pp. 737–760) [reprinted from: IEEE Trans. Syst. Man Cybern. 25, No. 5, 804–813 (1995)]; A. P. Dempster, “Logicist statistics. II: Inference” (pp. 761–785) [for Part I see Stat. Sci. 13, No. 3, 248–276 (1998; Zbl 1099.62501); Part II is a revised version of the 1998 COPSS R. A. Fisher Memorial Lecture]; “About editors” (pp. 787–788); “About authors” (pp. 789–797); Author index (p. 799); Subject index (pp. 801–806).