메뉴 건너뛰기




Volumn 34, Issue 2, 2004, Pages 961-977

Geometry of Dempster's Rule of Combination

Author keywords

Belief space; Commutativity; Constant mass loci; Convex decomposition; Dempster's rule; Geometric orthogonal sum; Theory of evidence

Indexed keywords

APPROXIMATION THEORY; COMPUTATION THEORY; DECOMPOSITION; FUNCTIONS; HIERARCHICAL SYSTEMS; KNOWLEDGE BASED SYSTEMS; MATHEMATICAL OPERATORS; PROBABILITY; THEOREM PROVING;

EID: 1842483360     PISSN: 10834419     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSMCB.2003.818431     Document Type: Article
Times cited : (32)

References (26)
  • 2
    • 0014171914 scopus 로고
    • Upper and lower probability inferences based on a sample from a finite univariate population
    • A. P. Dempster, "Upper and lower probability inferences based on a sample from a finite univariate population," Biometrika, vol. 54, pp. 515-528, 1967.
    • (1967) Biometrika , vol.54 , pp. 515-528
    • Dempster, A.P.1
  • 3
    • 0000582933 scopus 로고
    • Upper and lower probabilities generated by a random closed interval
    • _, "Upper and lower probabilities generated by a random closed interval," Ann. Math. Stat., vol. 39, pp. 957-966, 1968.
    • (1968) Ann. Math. Stat. , vol.39 , pp. 957-966
  • 4
    • 0000140767 scopus 로고
    • Upper and lower probabilities inferences for families of hypothesis with monotone density ratios
    • _, "Upper and lower probabilities inferences for families of hypothesis with monotone density ratios," Ann. Math. Stat., vol. 40, pp. 953-969, 1969.
    • (1969) Ann. Math. Stat. , vol.40 , pp. 953-969
  • 5
    • 1842561095 scopus 로고    scopus 로고
    • Geometric analysis of belief space and conditional subspaces
    • June 26-29
    • F. Cuzzolin and R. Frezza, "Geometric analysis of belief space and conditional subspaces," in Proc. ISIPTA'01, June 26-29, 2001.
    • (2001) Proc. ISIPTA'01
    • Cuzzolin, F.1    Frezza, R.2
  • 6
    • 1842613120 scopus 로고    scopus 로고
    • Geometrical structure of belief space and conditional sub-spaces
    • Nov., submitted for publication
    • F. Cuzzolin, "Geometrical structure of belief space and conditional sub-spaces," IEEE Trans. Syst., Man, Cybern., C, Nov. 2002, submitted for publication.
    • (2002) IEEE Trans. Syst., Man, Cybern. , vol.100
    • Cuzzolin, F.1
  • 7
    • 0345682512 scopus 로고    scopus 로고
    • Geometric foundations for interval-based probability
    • Cohn, Schubert, and Shapiro, Eds. San Mateo, CA: Morgan Kaufmann
    • V. Ha and P. Haddawy, "Geometric foundations for interval-based probability," in KR98: Principles of Knowledge Representation and Reasoning, Cohn, Schubert, and Shapiro, Eds. San Mateo, CA: Morgan Kaufmann, 1998, pp. 582-593.
    • (1998) KR98: Principles of Knowledge Representation and Reasoning , pp. 582-593
    • Ha, V.1    Haddawy, P.2
  • 8
    • 0012705922 scopus 로고
    • Bayes's two arguments for the rule of conditioning
    • December
    • G. Shafer, "Bayes's two arguments for the rule of conditioning," Ann. Stat., vol. 10, no. 4, pp. 1075-1089, December 1982.
    • (1982) Ann. Stat. , vol.10 , Issue.4 , pp. 1075-1089
    • Shafer, G.1
  • 9
    • 0023314059 scopus 로고
    • Bayesian and non-Bayesian evidential updating
    • H. Kyburg, "Bayesian and non-Bayesian evidential updating," Artif. Intell., vol. 31, no. 3, pp. 271-294, 1987.
    • (1987) Artif. Intell. , vol.31 , Issue.3 , pp. 271-294
    • Kyburg, H.1
  • 10
    • 0002692915 scopus 로고    scopus 로고
    • A probabilistic analysis of Dempster combination rule
    • Timothy, Ed. Prague
    • I. Kramosil, "A probabilistic analysis of Dempster combination rule," in The Logica. Yearbook 1997, C. Timothy, Ed. Prague, 1997, pp. 174-187.
    • (1997) The Logica. Yearbook 1997 , vol.100 , pp. 174-187
    • Kramosil, I.1
  • 11
    • 0012829231 scopus 로고
    • Steps toward an efficient implementation of Dempster-Shafer theory
    • R. Yager, M. Fedrizzi, and J. Kacprzyk, Eds. New York: Wiley
    • H. Xu and R. Kennes, "Steps toward an efficient implementation of Dempster-Shafer theory," in Advances in the Dempster-Shafer Theory of Evidence, R. Yager, M. Fedrizzi, and J. Kacprzyk, Eds. New York: Wiley, 1994, pp. 153-174.
    • (1994) Advances in the Dempster-shafer Theory of Evidence , pp. 153-174
    • Xu, H.1    Kennes, R.2
  • 14
    • 0025460756 scopus 로고
    • Dempster's rule of combination is np-complete
    • P. Orponen, "Dempster's rule of combination is np-complete," Artif. Intell., vol. 44, pp. 245-253, 1990.
    • (1990) Artif. Intell. , vol.44 , pp. 245-253
    • Orponen, P.1
  • 15
    • 0023446625 scopus 로고
    • Implementing Dempster's rule for hierarchical evidence
    • G. Shafer and R. Logan, "Implementing Dempster's rule for hierarchical evidence," Artif. Intell., vol. 33, pp. 271-298, 1987.
    • (1987) Artif. Intell. , vol.33 , pp. 271-298
    • Shafer, G.1    Logan, R.2
  • 16
    • 0024662329 scopus 로고
    • A computationally efficient approximation of Dempster-Shafer theory
    • F. Voorbraak, "A computationally efficient approximation of Dempster-Shafer theory," Int. J. Man-Machine Studies, vol. 30, pp. 525-536, 1989.
    • (1989) Int. J. Man-machine Studies , vol.30 , pp. 525-536
    • Voorbraak, F.1
  • 18
    • 16644376697 scopus 로고
    • The nature of the unnormalized beliefs encountered in the transferable belief model
    • D. B. D. Dubois, M. P. Wellmann, and S. Ph., Eds.
    • S. Philippe, "The nature of the unnormalized beliefs encountered in the transferable belief model," in Proc. Conf. Uncertainty in Artificial Intelligence (AI92), D. B. D. Dubois, M. P. Wellmann, and S. Ph., Eds., 1992, pp. 292-297.
    • (1992) Proc. Conf. Uncertainty in Artificial Intelligence (AI92) , pp. 292-297
    • Philippe, S.1
  • 19
    • 0025434991 scopus 로고
    • The combination of evidence in the transferable belief models
    • P. Smets, "The combination of evidence in the transferable belief models," IEEE Trans. Pattern Anal. Machine Intell., vol. 12, pp. 447-458, 1990.
    • (1990) IEEE Trans. Pattern Anal. Machine Intell. , vol.12 , pp. 447-458
    • Smets, P.1
  • 20
    • 1842508699 scopus 로고    scopus 로고
    • Ph.D., Università di Padova, Dipartimento di Elettronica e Informatica
    • F. Cuzzolin, "Visions of a Generalized Probability Theory," Ph.D., Università di Padova, Dipartimento di Elettronica e Informatica, 2001.
    • (2001) Visions of a Generalized Probability Theory
    • Cuzzolin, F.1
  • 21
    • 85032146143 scopus 로고
    • The canonical decomposition of a weighted belief
    • Montréal, Canada
    • P. Smets, "The canonical decomposition of a weighted belief," in Proc. Int. Joint Conf. on AI, IJCAI 95, Montréal, Canada, 1995, pp. 1896-1901.
    • (1995) Proc. Int. Joint Conf. on AI, IJCAI 95 , pp. 1896-1901
    • Smets, P.1
  • 22
    • 0346937171 scopus 로고    scopus 로고
    • Measure-theoretic approach to the inversion problem for BFs
    • Prague, Academia, June
    • I. Kramosil, "Measure-theoretic approach to the inversion problem for BFs," in Proc. IFSA, Seventh Int. Fuzzy Systems Association World Congress, vol. 1, Prague, Academia, June 1997, pp. 454-459.
    • (1997) Proc. IFSA, Seventh Int. Fuzzy Systems Association World Congress , vol.1 , pp. 454-459
    • Kramosil, I.1
  • 23
    • 0004033326 scopus 로고
    • New York: Springer-Verlag, Classics in Mathematics
    • A. Martin, Combinatorial Theory. New York: Springer-Verlag, 1979, Classics in Mathematics.
    • (1979) Combinatorial Theory
    • Martin, A.1
  • 24
    • 0031206656 scopus 로고    scopus 로고
    • Approximation algorithms and decision making in the Dempster-Shafer theory of evidence-an empirical study
    • M. Bauer, "Approximation algorithms and decision making in the Dempster-Shafer theory of evidence-an empirical study," Int. J. Approx. Reason., vol. 17, no. 2-3, pp. 217-237, 1997.
    • (1997) Int. J. Approx. Reason. , vol.17 , Issue.2-3 , pp. 217-237
    • Bauer, M.1
  • 25
    • 0027609211 scopus 로고
    • Approximations for efficient computation in the theory of evidence
    • B. Tessem, "Approximations for efficient computation in the theory of evidence," Artif. Intell., vol. 61, no. 2, pp. 315-329, 1993.
    • (1993) Artif. Intell. , vol.61 , Issue.2 , pp. 315-329
    • Tessem, B.1
  • 26
    • 1842613122 scopus 로고    scopus 로고
    • Geometry of upper probabilities
    • Bernard, Seidenfeld, and Zaffalon, Eds.
    • F. Cuzzolin, "Geometry of upper probabilities," in Proc. ISIPTA, Bernard, Seidenfeld, and Zaffalon, Eds., 2003, pp. 188-203.
    • (2003) Proc. ISIPTA , pp. 188-203
    • Cuzzolin, F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.