On The Validation of Fuzzy Knowledge Bases

  • Didier Dubois
  • Henri Prade
Part of the International Series on Microprocessor-Based and Intelligent Systems Engineering book series (ISCA, volume 11)


Roughly speaking, a knowledge base is “potentially inconsistent” or incoherent if there exists a piece of input data which respects integrity constraints and which leads to inconsistency when added to the knowledge base. In the paper we use the framework of possibility theory in order to discuss this problem for fuzzy knowledge bases. More particularly we consider the case where such bases are made of parallel fuzzy rules. There exist several kinds of fuzzy rules: certainty rules, gradual rules, possibility rules. For each kind, the problem of “potential consistency” appears to be different. Only certainty and gradual rules pose serious coherence problems. In each case we caracterize what conditions parallel rules have to satisfy in order to avoid inconsistency problem with input facts. The expression of a fuzzy integrity constraint in terms of impossibility qualification is discussed. The problem of redundancy, which is also of interest for fuzzy knowledge base validation, is briefly addressed for certainty and gradual rules.


Knowledge Base Fuzzy Rule Belief Revision Integrity Constraint Possibility Distribution 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ayel M., Rousset M.C. (1990) La Cohérence dans les Bases de Connaissances. Cepadues-Editions, Toulouse, France.Google Scholar
  2. 2.
    Beauvieux A., Dague P. (1990) A general consistency (checking and restoring) engine for knowledge bases. Proc. of the 9th Europ. Conf. on Artificial Intelligence (ECAI’90) (L.C. Aiello, ed.), Stockholm, Sweden, Aug. 6-10, 77–82.Google Scholar
  3. 3.
    Benferhat S., Dubois D., Lang J., Prade H. (1992) Hypothetical reasoning in possibilistic logic: basic notions, applications and implementation issues. In: Advances in Fuzzy Systems: Applications and Theory Vol. I (P.Z. Wang, K.F. Loe, eds.), to appear.Google Scholar
  4. 4.
    Bourrelly L., Chouraqui E., Portafaix V. (1992) Les topoï pour la validation structurelle d’une base de connaissances. Journée Francophone de la Validation et de la Vérification des Systèmes à Bases de Connaissances, Dourdan, France, Apr. 16.Google Scholar
  5. 5.
    Dubois D., Lang J., Prade H. (1989) Automated reasoning using possibilistic logic: semantics, belief revision, and variable certainty weights. Preprints of the 5th Workshop on Uncertainty in Artificial Intelligence, Windsor, Ont., 81–87. Revised version in IEEE Trans. on Data and Knowledge Engineering, to appear.Google Scholar
  6. 6.
    Dubois D., Lang J., Prade H. (1991a) A possibilistic assumption-based truth maintenance system with uncertain justifications, and its application to belief revision. Proc. of the ECAI Workshop on Truth-Maintenance Systems (J.P. Martins, M. Reinfranck, eds.), Stockholm, Aug. 6, 1990, Lecture Notes in Computer Sciences, n° 515, Springer Verlag, Berlin, 87–106.Google Scholar
  7. 7.
    Dubois D., Lang J., Prade H. (1991b) Fuzzy sets in approximate reasoning — Part 2: Logical approaches. Fuzzy Sets and Systems, 40, 203–244.MATHCrossRefGoogle Scholar
  8. 8.
    Dubois D., Martin-Clouaire R., Prade H. (1988) Practical computing in fuzzy logic. In: Fuzzy Computing (M.M. Gupta, T. Yamakawa, eds.), North-Holland, Amsterdam, 11–34.Google Scholar
  9. 9.
    Dubois D., Prade H. (1982) Towards the analysis and the synthesis of fuzzy mappings. In: Fuzzy Sets and Possibility Theory ROSE Recent Developments (R.R. Yager, ed.), Pergamon Press, New York, 316–326.Google Scholar
  10. 10.
    Dubois D., Prade H. (1991a) Fuzzy sets in approximate reasoning — Part 1: Inference with possibility distributions. Fuzzy Sets and Systems, 40, 143–202.MATHCrossRefGoogle Scholar
  11. 11.
    Dubois D., Prade H. (1991b) A note on the validation of possibilistic knowledge bases. BUSEFAL (IRIT, Univ. P. Sabatier, Toulouse,France), 48, 114–116.Google Scholar
  12. 12.
    Dubois D., Prade H. (1992) Gradual inference rules in approximate reasoning. Information Sciences, 61(1,2), 103–122.CrossRefGoogle Scholar
  13. 13.
    Hall L.O., Friedman M., Kandel A. (1988) On the validation and testing of fuzzy expert systems. IEEE Trans, on Systems, Man and Cybernetics, 18, 1023–1028.CrossRefGoogle Scholar
  14. 14.
    Kinkiélélé D. (1992) Détection des incohérences potentielles dans les bases de connaissances floues: vers un modèle conceptuel. Presented at “1ères Rencontres Nationales des Jeunes Chercheurs en Intelligence Artificielle”, Rennes, France, Sept. 7-9.Google Scholar
  15. 15.
    Larsen H.L., Nonfjall H. (1989) Modeling in the design of a KBS validation system. Proc. of the 3rd Inter. Fuzzy Systems Assoc. (IFSA) Congress, Seattle, Aug. 6-11, 341–344.Google Scholar
  16. 16.
    Larsen H.L., Nonfjall H. (1991) Modeling in the design of a KBS validation system. Int. J. of Intelligent Systems, 6, 759–775; Erratum: 7, 1992, p. 391.CrossRefGoogle Scholar
  17. 17.
    Loiseau S. (1992) Refinement of knowledge bases based on consistcncy. Proc. of the 10th Europ. Conf. on Artificial Intelligence (ECAI’92) (B. Neumann, ed.), Vienna, Austria, Aug. 3-7, 845–849.Google Scholar
  18. 18.
    Meseguer P. (1991) Verification of multi-level rule-based expert systems. Proc. of the 9th National Conf. on Artificial Intelligence (AAAI’91), July 14-19, 323–328.Google Scholar
  19. 19.
    Nguyen T.A., Perkins W.A., Laffery T.J., Pecora D. (1985) Checking an expert systems knowledge base for consistency and completeness. Proc. of the 9th Inter. Joint Conf. on Artificial Intelligence (IJCAI’85), Los Angeles, CA, 375–378.Google Scholar
  20. 20.
    Nguyen T.A., Perkins W.A., Laffery T.J., Pecora D. (1987) Knowledge base verification. AI Magazine, 8(2), 69–75.Google Scholar
  21. 21.
    Turksen I.B., Wang Q. (1992) Consistency of fuzzy expert systems with interval-valued fuzzy sets. Proc. of the Abstracts and Summaries of the 1st Inter. Conf. on Fuzzy Theory and Technology (FT&T’92) (P.P. Wang, ed.), 225–230.Google Scholar
  22. 22.
    Yager R.R., Larsen H.L. (1991) On discovering potential inconsistencies in validating uncertain knowledge bases by reflecting on the input. IEEE Trans. on Systems, Man and Cybernetics, 21, 790–801.MATHCrossRefGoogle Scholar
  23. 23.
    Zadeh L.A. (1979) A theory of approximate reasoning. In: Machine Intelligence, Vol. 9 (J.E. Hayes, D. Michie, L.I. Mikulich, eds.), Elsevier, New York, 149–194.Google Scholar

Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Didier Dubois
    • 1
  • Henri Prade
    • 1
  1. 1.Institut de Recherche en Informatique de ToulouseUniversite Paul SabatierToulouse CedexFrance

Personalised recommendations