Abstract
The problem of handling imperfect information has turned out to be a very important issue in the practical use of artificial intelligence for many industrial applications [Luo and Kay, 1995; Pfleger et al., 1993].
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References
[Berenstein et al., 19863] C. Berenstein, L.N. Kanal, and P. Lavine. Consensus rules. In L.N. Kanal and J.F. Lemmer, editors, Uncertainty in Artificial Intelligence, Vol. I, pages 27–32. North Holland, Amsterdam, 1986.
A. Chateauneuf. Combination of compatible belief functions and relation of specificity. In M. Fedrizzi, J. Kacprzyk, and R.R. Yager, editors, Advances in Dempster-Shafer Theory of Evidence, pages 97–114. Wiley, new York, 1994.
Y Cheng and R. L. Kashyap. A study of associative evidential reasoning. IEEE Trans. on Pattern Analysis and Machnie Intelligence, 11: 623–631, 1989.
L. Cholvy. Proving theorems in a multisource environment. In Proc. 13th Intern. Joint Conf. on Artificial Intelligence, pages 66–71, Chambery, France, 1993.
P.R. Cohen. Heuristic Reasoning about Uncertainty: An Artificial Intelligence Approach. Pitman, Boston, MA, 1985.
R.M. Cooke. Uncertainty in risk assessment: A probabilist’s manifesto. Reliability Eng. and Syst. Safety, 23: 277–283, 1988.
R.M. Cooke. Experts in Uncertainty. Oxford University Press, Oxford, 1991.
R.M. Cooke, M. Mendel, and W. Thijs. Calibration and information in expert resolution: A classical approach. Automatica, 24: 87–94, 1988.
R. Cox. Probability, frequency and reasonable expectation. American J. of Physics, 14: 1–13, 1946.
J. Kampé de Fériet. Interpretation of membership functions of fuzzy sets in terms of plausibility and belief. In M.M. Gupta and E. Sanchez, editors, Fuzzy Information and Decision Processes, pages 13–98. North-Holland, 1982.
A.P. Dempster. Upper and lower probabilities induced by a multivalued mapping. Ann. Math. Stat., 38: 325–339, 1967.
A.P. Dempster. Upper and lower probabilities generated by a random closed interval. Ann. Math. Stat., 39: 957–966, 1968.
D. Driankov. Uncertainty calculus with verbally defined belief intervals. Intern. J. of Intelligent Systems, 1: 219–246, 1986.
D. Dubois, S. Moral, and H. Prade. A semantics for possibility theory based on likelihoods. Annual report, CEC-ESPRIT III BRA 6156 DRUMS II, 1993.
D. Dubois and H. Prade. A review of fuzzy set aggregation connectives. Information Sciences, 36: 85–121, 1985.
D. Dubois and H. Prade. On the unicity of Dempster’s rule of combination. Int. J. of Intelligent Systems, 1: 133–142, 1986.
D. Dubois and H. Prade. Weighted minimum and maximum operations in fuzzy set theory. Information Sciences, 39: 205–210, 1986.
D. Dubois and H. Prade. On the combination of uncertain or imprecise pieces of information in rule-based systems. Int. J. of Approximate Reasoning, 2: 65–87, 1988.
D. Dubois and H. Prade. Possibility Theory. Plenum Press, New York, 1988.
D. Dubois and H. Prade. Representation and combination of uncertainty with belief functions and possibility measures. Computational Intelligence, 4(4):244–264, 1988.
D. Dubois and H. Prade. Aggregation of possibility measures. In J. Kacprzyk and M. Fedrizzi, editors, Multiperson Decision Making Models Using Fuzzy Sets and Possibility Theory. Kluwer, Dordrecht, 1990.
D. Dubois and H. Prade. Belief change and possibility theory. In P. Gärdenfors, editor, Belief Revision, pages 142–182. Cambridge University Press, 1992.
D. Dubois and H. Prade. Combination of fuzzy information in the framework of possibility theory. In M.A. Abidi and R.C. Gonzales, editors, Data Fusion in Robotics and Machine Intelligence, pages 481–505. Academic Press, New York, 1992.
D. Dubois and H. Prade. On the combination of evidence in various mathematical frameworks. In J. Flamm and T. Luisi, editors, Reliability Data Collection and Analysis, pages 213–241. ECSC, EEC, EAEC, Brussels and Luxemburg, 1992.
D. Dubois and H. Prade. Possibility theory and data fusion in poorly informed environments. Control Eng. Practice, 2: 811–823, 1994.
T.L. Fine. Theories of Probability: An Examination of Foundations. Academic Press, New York, 1973.
B. De Finetti. Foresight: Its logical laws, its subjective sources. In H.E. Kyburg and H.E. Smokier, editors, Studies in Subjective Probability, pages 93–158. Wiley, New York, 1964. First time published in: Annales de l’Institut H. Poincaré 7.
P.C. Fishburn. The axioms of subjective probability. Statistical Science, 1: 335–358, 1986.
S. French. Group consensus probability distributions: A critical survey. In J.M. Bernardo, M.H. DeGroot, D.V. Lindley, and A.F.M. Smith, editors, Bayesian Statistics, volume 2, pages 183–202. North-Holland, Amsterdam, 1985.
J. Gebhardt and R. Kruse. A possibilistic interpretation of fuzzy sets by the context model. In Proc. FUZZr-IEEE′92, pages 1089–1096, San Diego, 1992.
J. Gebhardt and R. Kruse. The context model — an integrating view of vagueness and uncertainty. Int. Journal of Approximate Reasoning, 9: 283–314, 1993.
J. Gebhardt and R. Kruse. A new approach to semantic aspects of possibilistic reasoning. In M. Clarke, R. Kruse, and S. Moral, editors, Symbolic and Quantitative Approaches to Reasoning and Uncertainty, Lecture Notes in Computer Science, 747, pages 151–160. Springer, Berlin, 1993.
J. Gebhardt and R. Kruse. On an information compression view of possibility theory. In Proc. 3rd IEEE Int. Conf. on Fuzzy Systems, pages 1285–1288, Orlando, 1994.
I.R. Goodman and H.T. Nguyen. Uncertainty Models for Knowledge-Based Systems. North-Holland, Amsterdam, 1985.
P. Hajek. Combining functions for certainty degrees in consulting systems. International Journal of Man-Machine Studies, 22: 59–76, 1985.
K. Hestir, H.T. Nguyen, and G.S. Rogers. A random set formalism for evidential reasoning. In I.R. Goodman, M.M. Gupta, H.T. Nguyen, and G.S. Rogers, editors, Conditional Logic in Expert Systems, pages 209–344. North-Holland, 1991.
F. Klawonn and E. Schwecke. On the axiomatic justification of Dempster’s rule of combination. Int. J. of Intelligent Systems, 7(7):469–478, 1992.
J. Kohlas and P.A. Monney. A Mathematical Theory of Hints: An Approach to Dempster-Shafer Theory of Evidence. Lecture Notes in Economics and Mathematical Systems. 425, Springer, Berlin, 1995.
R. Kruse, J. Gebhardt, and F. Klawonn. Foundations of Fuzzy Systems. Wiley, Chichester, 1994.
R. Kruse, E. Schwecke, and J. Heinsohn. Uncertainty and Vagueness in Knowledge Based Systems: Numerical Methods. Series: Artificial Intelligence. Springer, Berlin, 1991.
H.E. Kyburg. The Logical Foundations of Statistical Inference. Reidel, Dordrecht, The Netherlands, 1974.
H.E. Kyburg. Bayesian and non-Bayesian evidential updating. Artificial Intelligence, 31: 271–293, 1987.
R.P. Loui. Computing reference classes. In L.N. Kanal and J.F. Lemmer, editors, Uncertainty in Artificial Intelligence, Vol. 2, pages 273–289. North-Holland, Amsterdam, 1988.
R.C. Luo and M.G. Kay, editors. Multisensor Integration and Fusion for Intelligent Machines and Systems. Ablex Publishing Corporation, Norwood, NJ, 1995.
H.T. Nguyen. On random sets and belief functions. J. of Mathematical Analysis and Applications, 65: 531–542, 1978.
J. Pearl. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, New York, 1988.
S. Pfleger, J. Goncalves, and D. Vernon, editors. Data Fusion Applications. Research Reports ESPRIT. Springer-Verlag, Berlin, 1995.
H. Prade. A computational approach to approximate and plausible reasoning, with applications to expert systems. IEEE Transactions on Pattern Analysis and Machine Intelligence, 7: 260–283 (Corrections, 7, 747–748), 1985.
E.H. Ruspini. The logical foundations of evidential reasoning. Technical Note 408, SRI International, Menlo Park, CA, 1986.
S. Sandri, D. Dubois, and H. Kalfsbeek. Elicitation, assessment and pooling of expert judgement using possibility theory. Technical Report IRIT-93-24, University Paul Sabatier, Toulouse, France, 1993.
B. Schweizer and A. Sklar. Probabilistic Metric Spaces. North-Holland, New York, 1983.
G. Shafer. A Mathematical Theory of Evidence. Princeton University Press, Princeton, 1976.
G. Shafer. The combination of evidence. Int. J. of Intelligent Systems, 1: 155–180, 1986.
G. Shafer. Belief functions and possibility measures. In The Analysis of Fuzzy Information, Vol. I, pages 51–84. CRC Press, Boca Raton, Fl., 1987.
G. Shafer and J. Pearl. Readings in Uncertain Reasoning. Morgan Kaufmann, San Mateo, CA, 1990.
W. Silvert. Symmetric summation: A class of operations on fuzzy sets. IEEE Trans. on Systems, Man and Cybernetics, 9(10):657–659, 1979.
P. Smets. Belief functions. In P. Smets, A. Mamdani, D. Dubois, and H. Prade, editors, Nonstandard Logics for Automated Reasoning, pages 253–286. Academic Press, London, 1988.
P. Smets. The combination of evidence in the transferable belief model. IEEE Pattern Analysis and Machine Learning, 12: 447–458, 1990.
P. Smets. Belief functions: The disjunctive rule of combination and the generalized Bayesian theorem. Int. Journal of Approximate Reasoning, 9: 1–36, 1993.
P. Smets. Probability of deductibility and belief functions. In M. Clarke, R. Kruse, and S. Moral, editors, Symbolic and Quantitative Approaches to Reasoning and Uncertainty, Lecture Notes in Computer Science, 747, pages 332–340. Springer, Berlin, 1993.
P. Smets and R. Kennes. The transferable belief model. Artificial Intelligence, 66: 191–234, 1994.
W. Spohn. Ordinal conditional functions: A dynamic theory of epistemic states. In W. Harper and B. Skyrms, editors, Causation in Decision, Belief Change and Statistics, pages 105–134. 1988.
W. Spohn. A general non-probabilistic theory of inductive reasoning. In R.D. Shachter, T.S. Levitt, L.N. Kanal, and J.F. Lemmer, editors, Uncertainty in Artificial Intelligence, pages 149–158. North Holland, Amsterdam, 1990.
V. Strassen. Meßfehler und Information. Zeitschrift Wahrscheinlichkeitstheorie und verwandte Gebiete, 2: 273–305, 1964.
CG. Wagner. Consensus for belief functions and related uncertainty measures. Theory and Decision, 26: 295–304, 1989.
P. Walley. Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, 1991.
P. Walley and T. Fine. Towards a frequentist theory of upper and lower probability. The Annals of Statistics, 10: 741–761, 1982.
S. Weber. A general concept for fuzzy connectives, negation, and implication based on t-norms and t-conorms. Fuzzy Sets and Systems, 11: 115–134, 1983.
R.R. Yager. Approximate reasoning as a basis for rule based expert systems. IEEE Trans. on Systems, Man, and Cybernetics, 14: 636–643, 1984.
R.R. Yager. On the relationships of methods of aggregation evidence in expert systems. Cybernetics and Systems, 16: 1–21, 1985.
R.R. Yager. Quasi associative operations in the combination of evidence. Kybernetes, 16: 37–41, 1987.
R.R. Yager. Prioritized, non-pointwise, non-monotonic intersection and union for commonsense reasoning. In B. Bouchon, L. Saitta, and R.R. Yager, editors, Uncertainty and Intelligent Systems, volume 313 of Lecture Notes in Computer Science, pages 359–365. Springer-Verlag, Berlin, 1988.
L.A. Zadeh. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1: 3–28, 1978.
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Gebhardt, J., Kruse, R. (1998). Parallel Combination of Information Sources. In: Dubois, D., Prade, H. (eds) Belief Change. Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5054-5_9
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