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Volumn 38, Issue 4, 2008, Pages 522-534

A geometric approach to the theory of evidence

Author keywords

Belief function (b.f.); Belief space; Conditional subspace; Dempster's rule; Simplex; Theory of evidence (ToE)

Indexed keywords

GEOMETRICAL OPTICS; PROBABILITY;

EID: 46849104277     PISSN: 10946977     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSMCC.2008.919174     Document Type: Article
Times cited : (129)

References (54)
  • 2
    • 0014171914 scopus 로고
    • Upper and lower probability inferences based on a sample from a finite univariate population
    • A. 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.1
  • 3
    • 0000582933 scopus 로고
    • Upper and lower probabilities generated by a random closed interval
    • A. Dempster, "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
    • Dempster, A.1
  • 4
    • 0000140767 scopus 로고
    • Upper and lower probabilities inferences for families of hypothesis with monotone density ratios
    • A. Dempster, "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
    • Dempster, A.1
  • 5
    • 33744944512 scopus 로고    scopus 로고
    • The TBM global distance measure for the association of uncertain combat id declarations
    • B. Ristic and P. Smets, "The TBM global distance measure for the association of uncertain combat id declarations," Inf. Fusion, vol. 7, no. 3, pp. 276-284, 2006.
    • (2006) Inf. Fusion , vol.7 , Issue.3 , pp. 276-284
    • Ristic, B.1    Smets, P.2
  • 6
    • 29744464638 scopus 로고    scopus 로고
    • Agreement and stochastic independence of belief functions
    • K. Lo, "Agreement and stochastic independence of belief functions," Math. Soc. Sci., vol. 51, no. 1, pp. 1-22, 2006.
    • (2006) Math. Soc. Sci , vol.51 , Issue.1 , pp. 1-22
    • Lo, K.1
  • 7
    • 33646472889 scopus 로고    scopus 로고
    • Risk assessment based on weak information using belief functions: A case study in water treatment
    • May
    • S. Demotier, W. Schon, and T. Denoeux, "Risk assessment based on weak information using belief functions: A case study in water treatment," IEEE Trans. Syst., Man, Cybern. C, Appl. Rev., vol. 36, no. 3, pp. 382-396, May 2006.
    • (2006) IEEE Trans. Syst., Man, Cybern. C, Appl. Rev , vol.36 , Issue.3 , pp. 382-396
    • Demotier, S.1    Schon, W.2    Denoeux, T.3
  • 8
    • 46849108545 scopus 로고    scopus 로고
    • Refined sensor tuning in the belief function framework using contextual discounting
    • D. Mercier, T. Denoeux, and M. Masson, "Refined sensor tuning in the belief function framework using contextual discounting," in Proc. IPMU, 2006, pp. 1443-1450.
    • (2006) Proc. IPMU , pp. 1443-1450
    • Mercier, D.1    Denoeux, T.2    Masson, M.3
  • 9
    • 46849094143 scopus 로고    scopus 로고
    • B. Quost, T. Denoeux, and M. Masson, One-against-all classifier combination in the framework of belief functions, presented at the IPMU, Paris, France, 2006.
    • B. Quost, T. Denoeux, and M. Masson, "One-against-all classifier combination in the framework of belief functions," presented at the IPMU, Paris, France, 2006.
  • 10
    • 46849106532 scopus 로고    scopus 로고
    • On some results of the set of dominating k-additive belief functions
    • P. Miranda, M. Grabisch, and P. Gil, "On some results of the set of dominating k-additive belief functions," in Proc. IPMU, 2004, pp. 625-632.
    • (2004) Proc. IPMU , pp. 625-632
    • Miranda, P.1    Grabisch, M.2    Gil, P.3
  • 11
    • 6344230871 scopus 로고    scopus 로고
    • Belief function theory on the continuous space with an application to model based classification
    • B. Ristic and P. Smets, "Belief function theory on the continuous space with an application to model based classification," in Proc. IPMU 2004, pp. 1119-1126.
    • (2004) Proc. IPMU , pp. 1119-1126
    • Ristic, B.1    Smets, P.2
  • 13
    • 84937408775 scopus 로고    scopus 로고
    • Coarsening approximations of belief functions
    • S. Benferhat and P. Besnard, Eds, pp
    • A. B. Yaghlane, T. Denoeux, and K. Mellouli, "Coarsening approximations of belief functions," in Proc. ECSQARU'2001, S. Benferhat and P. Besnard, Eds., pp. 362-373.
    • Proc. ECSQARU'2001 , pp. 362-373
    • Yaghlane, A.B.1    Denoeux, T.2    Mellouli, K.3
  • 14
    • 0001127944 scopus 로고    scopus 로고
    • Inner and outer approximation of belief structures using a hierarchical clustering approach
    • T. Denoeux, "Inner and outer approximation of belief structures using a hierarchical clustering approach," Int. J. Uncertainty, Fuzziness Knowl.- Based Syst., vol. 9, no. 4, pp. 437-460, 2001.
    • (2001) Int. J. Uncertainty, Fuzziness Knowl.- Based Syst , vol.9 , Issue.4 , pp. 437-460
    • Denoeux, T.1
  • 15
    • 0036786963 scopus 로고    scopus 로고
    • Approximating the combination of belief functions using the Fast Moebius Transform in a coarsened frame
    • Oct
    • T. Denoeux and A. B. Yaghlane, "Approximating the combination of belief functions using the Fast Moebius Transform in a coarsened frame," Int. J. Approx. Reasoning, vol. 31, no. 1-2, pp. 77-101, Oct. 2002.
    • (2002) Int. J. Approx. Reasoning , vol.31 , Issue.1-2 , pp. 77-101
    • Denoeux, T.1    Yaghlane, A.B.2
  • 16
    • 0036787875 scopus 로고    scopus 로고
    • Resource bounded and anytime approximation of belief function computations
    • Oct
    • R. Haenni and N. Lehmann, "Resource bounded and anytime approximation of belief function computations," Int. J. Approx. Reasoning, vol. 31, no. 1-2, pp. 103-154, Oct. 2002.
    • (2002) Int. J. Approx. Reasoning , vol.31 , Issue.1-2 , pp. 103-154
    • Haenni, R.1    Lehmann, N.2
  • 17
    • 0031206656 scopus 로고    scopus 로고
    • M. Bauer, Approximation algorithms and decision making in the Dempster-Shafer theory of evidence - An empirical study, Int. J. Approx. Reasoning, 17, pp. 217-237, 1997.
    • M. Bauer, Approximation algorithms and decision making in the Dempster-Shafer theory of evidence - An empirical study," Int. J. Approx. Reasoning, vol. 17, pp. 217-237, 1997.
  • 18
    • 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
  • 19
    • 46849110636 scopus 로고    scopus 로고
    • J. Lowrance, T. Garvey, and T. Strat, A framework for evidential-reasoning systems, in Proc. Nat. Conf. Artif. Intell. A. A. for Artificial Intelligence, Ed., 1986, pp. 896-903.
    • J. Lowrance, T. Garvey, and T. Strat, "A framework for evidential-reasoning systems," in Proc. Nat. Conf. Artif. Intell. A. A. for Artificial Intelligence, Ed., 1986, pp. 896-903.
  • 20
    • 0024662329 scopus 로고
    • A computationally efficient approximation of Dempster-Shafer theory
    • F. Voorbraak, "A computationally efficient approximation of Dempster-Shafer theory," Int. J. Man-Mach. Stud., vol. 30, pp. 525-536, 1989.
    • (1989) Int. J. Man-Mach. Stud , vol.30 , pp. 525-536
    • Voorbraak, F.1
  • 21
    • 0344152300 scopus 로고    scopus 로고
    • A comparison of Bayesian and belief function reasoning
    • B. Cobb and P. Shenoy, "A comparison of Bayesian and belief function reasoning," Inf. Syst. Frontiers, vol. 5, no. 4, pp. 345-358, 2003.
    • (2003) Inf. Syst. Frontiers , vol.5 , Issue.4 , pp. 345-358
    • Cobb, B.1    Shenoy, P.2
  • 22
    • 85009438160 scopus 로고
    • Belief functions versus probability functions
    • L. Saitta, B. Bouchon, and R. Yager, Eds. Berlin, Germany: Springer-Verlag
    • P. Smets, "Belief functions versus probability functions," in Uncertainty and Intelligent Systems, L. Saitta, B. Bouchon, and R. Yager, Eds. Berlin, Germany: Springer-Verlag, 1988, pp. 17-24.
    • (1988) Uncertainty and Intelligent Systems , pp. 17-24
    • Smets, P.1
  • 23
    • 0345682512 scopus 로고    scopus 로고
    • Geometric foundations for interval-based probabilities
    • A. G. Cohn, L. Schubert, and S. C. Shapiro, Eds. San Francisco, CA: Morgan Kaufmann
    • V. Ha and P. Haddawy, "Geometric foundations for interval-based probabilities," in Proc. KR'98, A. G. Cohn, L. Schubert, and S. C. Shapiro, Eds. San Francisco, CA: Morgan Kaufmann, 1998, pp. 582-593.
    • (1998) Proc. KR'98 , pp. 582-593
    • Ha, V.1    Haddawy, P.2
  • 24
    • 34547107474 scopus 로고    scopus 로고
    • Geometric structure of lower probabilities
    • Goutsias, Malher, and Nguyen, Eds. New York: Springer-Verlag
    • P. Black, "Geometric structure of lower probabilities," in Random Sets: Theory and Applications, Goutsias, Malher, and Nguyen, Eds. New York: Springer-Verlag, 1997, pp. 361-383.
    • (1997) Random Sets: Theory and Applications , pp. 361-383
    • Black, P.1
  • 25
    • 26944456820 scopus 로고    scopus 로고
    • Consistency of probabilistic transformations of belief functions
    • M. Daniel, "Consistency of probabilistic transformations of belief functions," in Proc. IPMU, 2004, pp. 1135-1142.
    • (2004) Proc. IPMU , pp. 1135-1142
    • Daniel, M.1
  • 26
    • 46849113886 scopus 로고    scopus 로고
    • Degree of imprecision: Geometric and algebraic approaches
    • T. Melkonyan and R. Chambers, "Degree of imprecision: Geometric and algebraic approaches," Int. J. Approximate Reasoning, vol. 24, no. 2, pp. 522-538, 2006.
    • (2006) Int. J. Approximate Reasoning , vol.24 , Issue.2 , pp. 522-538
    • Melkonyan, T.1    Chambers, R.2
  • 27
    • 0033273449 scopus 로고    scopus 로고
    • Calculation of posterior bounds given convex sets of prior probability measures and likelihood functions
    • F. Cozman, "Calculation of posterior bounds given convex sets of prior probability measures and likelihood functions," J. Comput. Graphical Statist., vol. 8, no. 4, pp. 824-838, 1999.
    • (1999) J. Comput. Graphical Statist , vol.8 , Issue.4 , pp. 824-838
    • Cozman, F.1
  • 28
    • 38249019651 scopus 로고
    • Robust Bayesian analysis: Sensitivity to the prior
    • Berger, "Robust Bayesian analysis: Sensitivity to the prior," J. Statist. Planning Inference, vol. 25, pp. 303-328, 1990.
    • (1990) J. Statist. Planning Inference , vol.25 , pp. 303-328
    • Berger1
  • 29
    • 0038363063 scopus 로고    scopus 로고
    • Divisive conditioning: Further results on dilation
    • T. Herron, T. Seidenfeld, and L.Wasserman, "Divisive conditioning: Further results on dilation," Philos. Sci., vol. 64, pp. 411-444, 1997.
    • (1997) Philos. Sci , vol.64 , pp. 411-444
    • Herron, T.1    Seidenfeld, T.2    Wasserman, L.3
  • 30
    • 21344486183 scopus 로고
    • Dilation for convex sets of probabilities
    • T. Seidenfeld and L. Wasserman, "Dilation for convex sets of probabilities," Ann. Statist., vol. 21, pp. 1139-1154, 1993.
    • (1993) Ann. Statist , vol.21 , pp. 1139-1154
    • Seidenfeld, T.1    Wasserman, L.2
  • 31
    • 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
  • 32
    • 0035271128 scopus 로고    scopus 로고
    • A survey of computer vision-based human motion capture
    • T. Moeslund and E. Granum, "A survey of computer vision-based human motion capture," Image Vision Comput., vol. 81, pp. 231-268, 2001.
    • (2001) Image Vision Comput , vol.81 , pp. 231-268
    • Moeslund, T.1    Granum, E.2
  • 33
    • 0029711401 scopus 로고    scopus 로고
    • 3D model-based tracking of humans in action: A multi-view approach
    • San Francisco, CA, pp
    • D. Gavrila and L. Davis, "3D model-based tracking of humans in action: A multi-view approach," in Proc. CVPR'96, San Francisco, CA, pp. 73-80.
    • Proc. CVPR'96 , pp. 73-80
    • Gavrila, D.1    Davis, L.2
  • 36
    • 46849091813 scopus 로고    scopus 로고
    • Some static and dynamic aspects of rubust Bayesian theory
    • Goutsias, Malher, and Nguyen, Eds. New York: Springer-Verlag
    • T. Seidenfeld, "Some static and dynamic aspects of rubust Bayesian theory," in Random Sets: Theory and Application, Goutsias, Malher, and Nguyen, Eds. New York: Springer-Verlag, 1997, pp. 385-406.
    • (1997) Random Sets: Theory and Application , pp. 385-406
    • Seidenfeld, T.1
  • 37
    • 0001598089 scopus 로고
    • Belief functions and parametric models
    • G. Shafer, "Belief functions and parametric models," J. R. Statist. Soc., Series B, vol. 44, pp. 322-352, 1982.
    • (1982) J. R. Statist. Soc., Series B , vol.44 , pp. 322-352
    • Shafer, G.1
  • 38
    • 0002260209 scopus 로고
    • A new approach to updating beliefs
    • L. K. P. P. Bonissone, M. Henrion, and J. Lemmer, Eds
    • R. Fagin and J. Halpern, "A new approach to updating beliefs," in Uncertainty in Artificial Intelligence, vol. 6, L. K. P. P. Bonissone, M. Henrion, and J. Lemmer, Eds., 1991, pp. 347-374.
    • (1991) Uncertainty in Artificial Intelligence , vol.6 , pp. 347-374
    • Fagin, R.1    Halpern, J.2
  • 39
    • 0028711590 scopus 로고
    • Conditional events, conditioning, and random sets
    • M. Spies, "Conditional events, conditioning, and random sets," IEEE Trans. Syst., Man, Cybern., vol. 24, pp. 1755-1763, 1994.
    • (1994) IEEE Trans. Syst., Man, Cybern , vol.24 , pp. 1755-1763
    • Spies, M.1
  • 41
    • 46849088406 scopus 로고    scopus 로고
    • H. Xu and P. Smets, Evidential reasoning with conditional belief functions, in Proc. 10th Uncertainty Artif. Intell., L. de Mantaras R. and P. D., Eds., 1994, pp. 598-605.
    • H. Xu and P. Smets, "Evidential reasoning with conditional belief functions," in Proc. 10th Uncertainty Artif. Intell., L. de Mantaras R. and P. D., Eds., 1994, pp. 598-605.
  • 42
    • 0039462414 scopus 로고    scopus 로고
    • Reasoning in evidential networks with conditional belief functions
    • H. Xu and P. Smets, "Reasoning in evidential networks with conditional belief functions," Int. J. Approx. Reasoning, vol. 14, pp. 155-185, 1996.
    • (1996) Int. J. Approx. Reasoning , vol.14 , pp. 155-185
    • Xu, H.1    Smets, P.2
  • 43
    • 46849089740 scopus 로고    scopus 로고
    • R. G. Almond, Graphical Belief Modeling. London, U.K./Boca Raton, FL: Chapman & Hall/CRC, 1995.
    • R. G. Almond, Graphical Belief Modeling. London, U.K./Boca Raton, FL: Chapman & Hall/CRC, 1995.
  • 44
    • 46849102005 scopus 로고    scopus 로고
    • Belief function propagation in directed evidential networks
    • B. B. Yaghlane and K. Mellouli, "Belief function propagation in directed evidential networks," in Proc. IPMU, 2006, pp. 47-70.
    • (2006) Proc. IPMU , pp. 47-70
    • Yaghlane, B.B.1    Mellouli, K.2
  • 46
    • 34547136700 scopus 로고    scopus 로고
    • Two new Bayesian approximations of belief functions based on convex geometry
    • Aug
    • F. Cuzzolin, "Two new Bayesian approximations of belief functions based on convex geometry," IEEE Trans. Syst., Man Cybern. B, Cybern., vol. 37, no. 4, pp. 993-1008, Aug. 2007.
    • (2007) IEEE Trans. Syst., Man Cybern. B, Cybern , vol.37 , Issue.4 , pp. 993-1008
    • Cuzzolin, F.1
  • 47
    • 16644376697 scopus 로고    scopus 로고
    • The nature of the unnormalized beliefs encountered in the transferable belief model
    • San Mateo, CA: Morgan Kaufmann, pp
    • P. Smets, "The nature of the unnormalized beliefs encountered in the transferable belief model," in Proc. 8th Annu. Conf. Uncertainty Artif. Intell. (UAI-92). San Mateo, CA: Morgan Kaufmann, pp. 292-329.
    • Proc. 8th Annu. Conf. Uncertainty Artif. Intell. (UAI-92) , pp. 292-329
    • Smets, P.1
  • 48
    • 46849121422 scopus 로고    scopus 로고
    • C. Joslyn, Towards an empirical semantics of possibility through maximum uncertainty, in Proc. IFSA 1991, A. R. Lowen and M. Roubens, Eds., pp. 86-89.
    • C. Joslyn, "Towards an empirical semantics of possibility through maximum uncertainty," in Proc. IFSA 1991, vol. A. R. Lowen and M. Roubens, Eds., pp. 86-89.
  • 50
    • 0000158850 scopus 로고
    • Consonant approximations of belief functions
    • D. Dubois and H. Prade, "Consonant approximations of belief functions," Int. J. Approx. Reasoning, vol. 4, pp. 419-449, 1990.
    • (1990) Int. J. Approx. Reasoning , vol.4 , pp. 419-449
    • Dubois, D.1    Prade, H.2
  • 51
    • 27744502171 scopus 로고    scopus 로고
    • Extending consonant approximations to capacities
    • P. Baroni, "Extending consonant approximations to capacities," in Proc. IPMU, 2004, pp. 1127-1134.
    • (2004) Proc. IPMU , pp. 1127-1134
    • Baroni, P.1
  • 52
    • 85032146143 scopus 로고    scopus 로고
    • The canonical decomposition of a weighted belief
    • Montréal, QC, Canada, pp
    • P. Smets, "The canonical decomposition of a weighted belief," in Proc. Int. Joint Conf. AI, IJCAI'95, Montréal, QC, Canada, pp. 1896-1901.
    • Proc. Int. Joint Conf. AI, IJCAI'95 , pp. 1896-1901
    • Smets, P.1
  • 53
    • 0038930703 scopus 로고    scopus 로고
    • Measure-theoretic approach to the inversion problem for belief functions
    • I. Kramosil, "Measure-theoretic approach to the inversion problem for belief functions," Fuzzy Sets Syst., vol. 102, pp. 363-369, 1999.
    • (1999) Fuzzy Sets Syst , vol.102 , pp. 363-369
    • Kramosil, I.1
  • 54
    • 46849117356 scopus 로고    scopus 로고
    • J. Schubert, Managing decomposed belief functions, presented at the IPMU, Paris, France, 2006.
    • J. Schubert, "Managing decomposed belief functions," presented at the IPMU, Paris, France, 2006.


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