Models for Approximate Reasoning in Expert Systems

  • Didier Dubois
  • Henri Prade


In the expert systems of artificial intelligence, the facts and/or the rules to be represented may often be uncertain or imprecise.


Fuzzy Logic Expert System Inference Engine Confidence Measure Modus Ponens 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    ADLASSNIG, K. P.,and KOLARZ, G. (1982). CADIAG-2: Computer-assisted medical diagnosis using fuzzy subsets. In Approximate Reasoning in Decision Analysis (M. M. Gupta and E. Sanchez, eds.). North-Holland, Amsterdem, pp. 219–247.Google Scholar
  2. 2.
    BALDWIN, J. F. (1979). A new approach to approximate reasoning using a fuzzy logic. Fuzzy Sets Syst., 2, 309–325.MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    BALDWIN, J. F.,and PILSWORTH, B. W. (1980). Axiomatic approach to implication for approximate reasoning with fuzzy logic. Fuzzy Sets Syst., 3, 193–219.MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    BELLMAN, R. E., and ZADEH, L. A. (1977). Local and fuzzy logics. In Modern Uses of Multiple-Valued Logic (J. M. Dunn and G. Epstein, eds.). D. Reidel, Dordrecht, pp. 103–165 . CrossRefGoogle Scholar
  5. 5.
    CAYROL, M.,FARRENY,H., and PRADE, H. (1982). Fuzzy pattern matching. Kybernetes, 11, 103–116.CrossRefGoogle Scholar
  6. 6.
    DEMPSTER, A. P. (1967). Upper and lower probabilities induced by a multivalued mapping. Ann. Math. Stat., 38, 325–339.MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    DUBOIS, D.,and PRADE, H. (1979). Operations in a fuzzy-valued logic. Inf. Control, 43(2), 224–240.MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    DUBOIS, D.,and PRADE, H. (1982).A class of fuzzy measures based on triangular norms—A general framework for the combination of uncertain information. Int. J. Gen. Syst., 8(1), 43–61.MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    .DUBOIS, D.,and PRADE, H. (1982). Degree of truth and truth-functionality.Proc. 2nd World Conf. on Maths at the Service of Man, Las Palmas, Spain, June 28-July 3, 1982, pp. 262–265.Google Scholar
  10. 10.
    DUBOIS, D.,and PRADE, H. (1982). On several representations of an uncertain body of evidence. In Fuzzy Information and Decision Processes (M. M. Gupta and E. Sanchez, eds.), North-Holland, Amsterdam, pp. 167–181.Google Scholar
  11. 11.
    DUBOIS, D., and PRADE, H. (1983). On distances between fuzzy points and their use for plausible reasoning. Proc. IEEE Int. Conf. on Cybernetics and Society, Bombay-New Dehli, Dec. 30, 1983-Jan. 7, 1984, pp. 300–303.Google Scholar
  12. 12.
    DUBOIS, D.,and PRADE, H. (1984). Fuzzy logics and the generalized modus ponens revisited. Cybern. Syst., 15, 293–331.MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    DUBOIS, D.,and PRADE, H. (1985). The generalized modus ponens under sup-min composition. A theoretical study. In Approximate Reasoning in Expert Systems (M. M. Gupta, A. Kandel, W. Bandler, and J. B. Kiszka, eds.), North-Holland, Amsterdam, pp. 217–232.Google Scholar
  14. 14.
    DUBOIS, D., and PRADE, H. (1987). The management of uncertainty in fuzzy expert systems and some applications. In The Analysis of Fuzzy Information, Volume 2: Artificial Intelligence and Decision Systems (J. C. Bezdek, éd.). CRC Press, Boca Raton, Florida, pp. 39–58.Google Scholar
  15. 15.
    DUDA, R., GASCHNIG, J.,and HART, P. (1981). Model design in the PROSPECTOR consultant system for mineral exploration. Expert Systems in the Micro-Electronic Age (D. Michie, ed.). Edingurgh University Press, pp. 153–167.Google Scholar
  16. 16.
    ERNST, C. (1982). Le modèle de raisonnement approché du système MANAGER. BUSEFAL, Report No. 9, L.S.I., University P. Sabatier, Toulose, pp. 93–99.Google Scholar
  17. 17.
    FRIEDMAN, L. (1981). Extended plausible inference. Proc. 7th Int. Joint. Conf Artificial Intelligence. Vancouver, August 1981, pp. 487–495.Google Scholar
  18. 18.
    GAINES, B. R. (1976). Foundations of fuzzy reasoning. Int. J. Man-Machine Stud., 8, 623–668.MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    GOGUEN, J. A. (1969). The logic of inexact concepts. Synthese, 19, 325–373.MATHCrossRefGoogle Scholar
  20. 20.
    ISHIZUKA, M. (1983). Inference methods based on extended Dempster and Shafer’s theory for problems with uncertainty/fuzziness. New Generation Comp., 1, 159–168.CrossRefGoogle Scholar
  21. 21.
    ISHIZUKA, M., FU, K. S.,and YAO, J. T. P. (1981). Inexact inference for rule-based damage assessment of existing structures. Proc. 7th Int. Joint Conf on Artificial Intelligence. Vancouver, pp. 837–842.Google Scholar
  22. 22.
    ISHIZUKA,M., Fu, K. S., and YAO, J. T. P. (1982). Inference procedures with uncertainty for problem reduction method. Inf. Sci., 28, 179–206.MathSciNetMATHCrossRefGoogle Scholar
  23. 23.
    KAYSER, D. (1979). Vers une modélisation du raisonnement “approximatif.” Proc. of the Colloquium Représentation des Connaissances et Raisonnement dans les Sciences de l’Homme (M. Borillo, éd.), Saint-Maximin, September 1979, Published by INRIA, pp. 440–457.Google Scholar
  24. 24.
    LESMO, L., SAITTA, L.,and TORASSO, P. (1983). Fuzzy production rules: A learning methodology. In Advances in Fuzzy Set Theory and Applications, (P. P. Wang, ed.). Plenum Press, New York, pp. 181–198.CrossRefGoogle Scholar
  25. 25.
    MAMDANI, E. H. (1977). Application of fuzzy logic to approximate reasoning using linguistic systems. IEEE Trans. Comput, C-26, 1182–1191.CrossRefGoogle Scholar
  26. 26.
    DUBOIS, D., MARTIN-CLOU AIRE, R.,and PRADE, H. (1988). Practical computing in fuzzy logics. In Fuzzy Computing (M. M. Gupta and T. Yamakawa, eds.), North- Holland, Amsterdam, to be published.Google Scholar
  27. 27.
    MARTIN-CLOUAIRE, R.,and PRADE, H. (1985). On the problems of representation and propagation of uncertainty in expert systems. Int. J. Man-Machine Stud., 22, 251–264.CrossRefGoogle Scholar
  28. 28.
    LEBAILLY, J., MARTIN-CLOUAIRE, R.,and PRADE, H. (1987). Use of fuzzy logic in a rule-based system in petroleum geology. In Approximate Reasoning in Intelligent Systems, Decision and Control (E. Sanchez and L. A. Zadeh, eds.), Pergamon, Oxford, pp. 125–144.Google Scholar
  29. 29.
    MIZUMOTO,M.,FUKAMI, S.,and TANAKA, K. (1979). Fuzzy conditional inferences and fuzzy inferences with fuzzy quantifiers. Proc. 6th Int. Joint Conf. on Artificial Intelligence, Tokyo, pp. 589–591.Google Scholar
  30. 30.
    MIZUMOTO, M.,and ZIMMERMANN,H.J. (1982). Comparison of fuzzy reasoning methods. Fuzzy Sets Syst., 8, 253–283.MathSciNetMATHCrossRefGoogle Scholar
  31. 31.
    POLYA,G. (1954). Mathematics and Plausible Reasoning. Vol. II: Patterns of Plausible Inference. Princeton University Press, Princeton, New Jersey, 2nd edition 1968.Google Scholar
  32. 32.
    PRADE, H. (1982). Modèles mathématiques de l’imprécis et de l’incertain en vue d’applications au raisonnement naturel. Thesis University of Toulose III, June 1982 (358 pp.).Google Scholar
  33. 33.
    PRADE, H. (1983). A synthetic view of approximate reasoning techniques. Proc. 8th Int. Joint Conf. Artificial Intelligence, Karlsruhe, August 1983, pp. 130–136.Google Scholar
  34. 34.
    PRADE, H. (1983). Data bases with fuzzy information and approximate reasoning in expert systems. Proc. IFAC Int. Symp. Artificial Intelligence. Leningrad, USSR, October 4–6, 1983, pp. 113–120.Google Scholar
  35. 35.
    PRADE, H. (1984). Modèles de raisonnement approché pour les systèmes experts. Proc 4ème Congrès AFCET Reconnaissance des Formes & Intelligence Artificielle, Paris, January 25–27, 1984, pp. 355–373.Google Scholar
  36. 36.
    PRADE, H. (1985).A computational approach to approximate and plausible reasoning, with applications to expert systems. IEEE Trans. Pattern Anal. Machine Intell, 7, 260–283. Corrections in 7, 747–748.Google Scholar
  37. 37.
    RESCHER, N. (1969). Many-Valued Logic. McGraw-Hill, New York.MATHGoogle Scholar
  38. 38.
    SANCHEZ, E. (1976). Resolution of composite fuzzy relation equations. Inf. Control, 30, 38–48.MATHCrossRefGoogle Scholar
  39. 39.
    SHAFER, G. (1976). A Mathematical Theory of Evidence. Princeton University Press, Princeton, New Jersey.MATHGoogle Scholar
  40. 40.
    SHORTLIFFE, E. H., and BUCHANAN, B. G. (1975). A model of inexact reasoning in medicine. Math. Biosci., 23, 351–379.MathSciNetCrossRefGoogle Scholar
  41. 41.
    SOULA, G., and SANCHEZ, E. (1982). Soft deduction rules in medical diagnosis processes. In Approximate Reasoning in Decision Analysis, (M. M. Gupta and E. Sanchez, eds.), North-Holland, Amsterdam, pp. 77–88.Google Scholar
  42. 42.
    SOULA, G., VIALETTES, B., and SAN MARCO, J. L. (1983). PROTIS, a fuzzy deduction-rule system: Application to the treatment of diabetes. Proc. Medinfo 83, (Van Bemmel, Ball, and Wigertz, eds.), IFIP-INIA, Amsterdam, pp. 553–536.Google Scholar
  43. 43.
    SUPPES, P. (1966). Probabilistic inference and the concept of total evidence. In Aspects of Inductive Logic (J. Hintikka and P. Suppes, eds.), North-Holland, Amsterdam, pp. 49–65.CrossRefGoogle Scholar
  44. 44.
    TONG, R. M., SHAPIRO, D. G., DEAN, J. S.,and MCCUNE, B. P. (1983). A comparison of uncertainty calculi in an expert system for information retrieval. Proc. 8th Int. Joint Conf Artificial Intelligence, Karlsruhe, August 1983, pp. 194–197.Google Scholar
  45. 45.
    TRILLAS, E., and VALVERDE, L. (1981). On some functionally expressible implications for fuzzy set theory. Proc. 3rd Int. Seminar on Fuzzy Set Theory (E. P. Klement, ed.), J. Kepler Univ., Linz, Austria, September 7–12, 1981, pp. 173–190.Google Scholar
  46. 46.
    TSUKAMOTO, Y. (1979). An approach to fuzzy reasoning method. In Advances in Fuzzy Set Theory and Applications (M. M. Gupta, R. K. Ragade, and R. R. Yager, eds.). North-Holland, Amsterdam, pp. 137–149.Google Scholar
  47. 47.
    WEBER, S. (1983).A general concept of fuzzy connectives, negations and implications based on t-norms and t-co-norms. Fuzzy Sets and Syst., 11, 115–134.MATHCrossRefGoogle Scholar
  48. 48.
    WHALEN, T., and SCHOTT, B. (1983). Issues in fuzzy production systems. Int. J. Man-Machine Stud., 19, 57–71.CrossRefGoogle Scholar
  49. 49.
    YAGER, R. R. (1980). An approach to inference in approximate reasoning. Int. J. Man-Machine Stud., 13, 323–338.MathSciNetCrossRefGoogle Scholar
  50. 50.
    ZADEH, L. A. Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans. Syst., Man Cybernet., 3, 28–44.MathSciNetGoogle Scholar
  51. 51.
    ZADEH, L. A. (1978). PRUF-A meaning representation language for natural languages. Int. J. Man-Machine Stud., 10(4), 395–460.MathSciNetMATHCrossRefGoogle Scholar
  52. 52.
    ZADEH, L. A.(1979).A theory of approximate reasoning.Machine Intelligence, Vol. 9, (J. E. Hayes, D. Mitchie, and L. I. Mikulich, eds.). Elsevier, New York, pp. 149–194.Google Scholar
  53. 53.
    ZADEH, L. A. (1983). The role of fuzzy logic in the management of uncertainty in expert systems. Fuzzy Sets Syst., 11(3), 199–228.MathSciNetMATHCrossRefGoogle Scholar
  54. 54.
    ZADEH, L. A. (1984). Review of “ A Mathematical Theory of Evidence,” by G. Shafer. The AI Magazine, Fall 1984, 81–83.MathSciNetGoogle Scholar
  55. 55.
    APPELBAUM, L., RUSPINI, E. H. (1985). ARIES: An approximate reasoning inference engine. In Approximate Reasoning in Expert Systems, (M. M. Gupta, A. Kandel, W. Bandler, and J. B. Kiszka, eds.). North-Holland, Amsterdam, pp. 745–765.Google Scholar
  56. 56.
    BUCKLEY, J., SILVER, W.,and TUCKER, D. (1986).FLOPS: A fuzzy expert system: applications and perspectives. In Fuzzy Logic in Knowledge Engineering (C. V. Negoita and H. Prade, eds.). Verlag TUV Rheinland, Cologne.Google Scholar
  57. 57.
    CHATALIC, P., DUBOIS, D.,and PRADE, H. An approach to approximate reasoning based on Dempster rule of combination. Proc. 8th IASTED Inter. Symp. Robotics and Artificial Intelligence, Toulouse, France, June 18–20, pp. 333–343.Google Scholar
  58. 58.
    DUBOIS, D.,and PRADE, H. (1984). A theorem on implication functions defined from triangular norms. Stochastica, VIII, 267–279.MathSciNetGoogle Scholar
  59. 59.
    DUBOIS, D.,and PRADE, H. (1985). Combination and propagation of uncertainty with belief functions. A reexamination. Proc. 9th Inter. Joint Conf Artificial Intelligence, Los Angeles, pp. 111–113.Google Scholar
  60. 60.
    DUBOIS, D.,and PRADE, H. (1986). Possibilistic inference under matrix form. In Fuzzy Logic in Knowledge Engineering (C. V. Negoita, and H. Prade, eds.), Verlag TUV Rheinland, Cologne, pp. 112–126.Google Scholar
  61. 61.
    .FARRENY, H.,and PRADE, H. (1986). Default and inexact reasoning with possibility degrees. IEEE Trans. Syst., Man. Cybernet., 16, 270–276.MATHCrossRefGoogle Scholar
  62. 62.
    FARRENY, H., PRADE, H.,and WYSS, E. (1986). Approximate reasoning in a rule-based expert system using possibility theory: A case study. Proc. 10th IFIP World Computer Cong., Dublin, Ireland, September, 1–5.Google Scholar
  63. 63.
    GARVEY,T.D., LOWRANCE, J. D.,and FISCHLER, M. A. (1985). An inference technique for integrating knowledge from disparate sources. Proc. 7th Inter. Joint Conf. Artificial Intelligence, Vancouver, August 1981, pp. 319–325.Google Scholar
  64. 64.
    HISDAL, E. (1978). Conditional possibilities. Independence and non-interactivity. Fuzzy Sets Syst., 1, 283–297.MATHCrossRefGoogle Scholar
  65. 65.
    MARTIN-CLOUAIRE, R.,and PRADE, H. SPII-1: A simple inference engine for accommodating both imprecision and uncertainty. In Computer-Assisted Decision Making, North-Holland, Amsterdam, pp. 117–131.Google Scholar
  66. 66.
    NEGOITA, C. V., and PRADE, H. (eds.). (1986). Fuzzy Logic in Knowledge Engineering. Verlag TÙV Rheinland, Cologne.MATHGoogle Scholar
  67. 67.
    .FIESCHI, M. (1984). Intelligence artificielle en médecine. Des systèmes experts. Méthode + Programmes series. Masson, Paris.Google Scholar
  68. 68.
    WEBER,S. (1984). 1-decomposable measures and integrals for Archimedean t-conorms 1. J. Math. Anal. Appl., 101, 114–138.Google Scholar
  69. 69.
    DUBOIS, D.,and PRADE, H. (1988). On the combination of uncertain or imprecise pieces of information in rule-based systems. Inter. J. of Approximate Reasoning, to be published.Google Scholar
  70. 70.
    PEDRYCZ, W. (1985). On generalized fuzzy relational equations and their applications. J. Math. Anal. Appl., 107, 520–536.MathSciNetMATHCrossRefGoogle Scholar
  71. 71.
    SUGENO, M. (ed). (1985). Industrial Applications of Fuzzy Control. North-Holland, Amsterdam.Google Scholar
  72. 72.
    BUISSON, J. C., FARRENY, H., PRADE, H., TURNIN, M. C., TAUBER J. P., and BAYARD, F. (1987). TOULMED, an inference engine which deals with imprecise and uncertain aspects of medical knowledge. Proc. AIME 87, (J. Fox, M. Fieschi, and R. Engelbrecht, eds.), Lecture Notes in Medical Informatics, Vol. 33, Springer Verlag, Berlin, 123–140.Google Scholar
  73. 73.
    SANCHEZ,E.,ZADEH, L. A. (eds.). (1987). Approximate Reasoning in Intelligent Systems, Decision and Control. Pergamon, Oxford.Google Scholar

Copyright information

© Plenum Press, New York 1988

Authors and Affiliations

  • Didier Dubois
    • 1
  • Henri Prade
    • 1
  1. 1.CNRS, Languages and Computer Systems (LSI)University of Toulouse IIIToulouseFrance

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