Advertisement

Handling Incomplete or Uncertain Data and Vague Queries in Database Applications

  • Didier Dubois
  • Henri Prade

Abstract

One often has to handle data that are far from precise and certain. In fact, the value of an attribute of an object may be completely unknown, incompletely known (i.e., only a subset of possible values of the attribute is known), or uncertain (e.g., a probability or possibility distribution for its value is known). In addition, the attribute may not be applicable to some of the objects being considered and, in certain cases, we may not know whether the value even exists, or whether it is simply not known.

Keywords

Membership Function Fuzzy Number Fuzzy Subset Relational Algebra Uncertain Data 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    ADIBA, M., and DELOBEL, C. (1982). Bases de Données et Systèmes Relationnels. Dunod, Paris.Google Scholar
  2. 2.
    BALDWIN, J. F. (1983). A fuzzy relational inference language for expert systems. Proc. 13th IEEE Int. symp. on Multiple-Valued Logic, Kyoto, Japan, pp. 416–423.Google Scholar
  3. 3.
    BALDWIN, J. F. (1983). Knowledge engineering using a fuzzy relational inference language. Proc. IF AC Symposium on Fuzzy Information, Knowledge Representation and Decision Processes, Marseille, July 19–21, pp. 15–20.Google Scholar
  4. 4.
    BISKUP, J. (1980). A formal approach to null values in database relations. Workshop: Formal Bases for Databases. December, 12–14, 1979, CERT-DERI. Toulouse (H. Gallaire and J. M. Nicolas, eds.). Plenum Press, New York.Google Scholar
  5. 5.
    Bossu, G., and SIEGEL, P. (1985). Saturation, nonomonotonic reasoning, and the closed world assumption. Artif. Intell. 25, 13–63.MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    BUCKLES, B. P., and PETRY, F. E. (1982). A fuzzy representation of data for relational databases. Fuzzy Sets Syst., 7, 213–226.MATHCrossRefGoogle Scholar
  7. 7.
    BUCKLES, B. P., and PETRY, F. E. (1982). Fuzzy databases and their applications. In Fuzzy Information and Decision Processes (M. M. Gupta and E. Sanchez, eds.). North-Holland, Amsterdam, pp. 361–371.Google Scholar
  8. 8.
    BUCKLES, B. P., and PETRY, F. E. (1983). Extension of the fuzzy database with fuzzy arithmetic. Proc. IFAC Symposium, Fuzzy Information, Knowledge Representation and Decision Processes, Marseille, July 19–21, pp. 409–414.Google Scholar
  9. 9.
    CAYROL, M., FARRENY, H., and PRADE, H. (1980). Possibility and necessity in a pattern matching process. Proc. IXth. Int. Cong, on Cybernetics, Namur, Belgium, September 8–13, pp. 53–65.Google Scholar
  10. 10.
    CAYROL, M., FARRENY, H., and PRADE, H., (1982). Fuzzy pattern matching. Kybernetes, 11, 103–116.CrossRefGoogle Scholar
  11. 11.
    CODD, E. F. (1979). Extending the database relational model to capture more meaning ACM Trans. Database Syst. 4(4), 397–434.CrossRefGoogle Scholar
  12. 12.
    DATE, D. J. (1977). An Introduction to Data Base Systems. Addison-Wesley, Reading, Massachusetts.Google Scholar
  13. 13.
    DUBOIS, D., and PRADE, H. (1983). Twofold fuzzy sets: An approach to the representation of sets with fuzzy boundaries based on possibility and necessity measures. Fuzzy Math. (.Huazhong, China), 3(4), 53–76.MathSciNetMATHGoogle Scholar
  14. 14.
    DUBOIS, D., and PRADE, H. (1985). Fuzzy cardinality and the modeling of imprecise quantification. Fuzzy Sets Syst., 16, 199–230.MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    WINSTON, P. H. and HORN, B. K. P. (1981). LISP. Addison-Wesley, Reading, Massachusetts.MATHGoogle Scholar
  16. 16.
    FRESKA, C. (1980). L-FUZZY—An A.I. language with linguistic modification of patterns. AISB Conf. Amsterdam. (Also UCB/ERL M80/10, Univ. of California, Berkeley.)Google Scholar
  17. 17.
    GELENBE, E. (1983). Incomplete representations of information in data bases. Research, Report, No 9, ISEM, Univ. Paris-Sud.Google Scholar
  18. 18.
    GRANT, J. (1979). Null values in a relational data base. Inf. Process. Lett., 6(5), 156–157.MathSciNetCrossRefGoogle Scholar
  19. 19.
    GRANT, J. (1979). Partial values in a tabular database. Inf. Process. Lett., 9(2), 97–99.MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    HAAR, R. L. (1977). A fuzzy relational data base system. University of Maryland. Computer Center. TR-586, September.Google Scholar
  21. 21.
    LE FAIVRE, R. (1974). The representation of fuzzy knowledge. J. Cybernet., 4(2), 57–66.CrossRefGoogle Scholar
  22. 22.
    LIPSKI, W., Jr. (1979). On semantic issues connected with incomplete information data bases. ACM Trans. Database Syst., 4(3), 262–296.CrossRefGoogle Scholar
  23. 23.
    LIPSKI, W., Jr. (1981). On databases with incomplete information. J. Assoc. Comput. Machinery, 28(1), 41–70.MathSciNetMATHCrossRefGoogle Scholar
  24. 24.
    MONTGOMERY, C. A., and RUSPINI, E. H. (1981). The active information system: A data driven system for the analysis of imprecise data.Proc. VHth. Int. Conf. on Very Large Databases, Cannes, September.Google Scholar
  25. 25.
    NARIN’YANI, A. S. (1980). Sub-definite set—New data-type for knowledge representation. (in Russian). Memo No 4–232 Computer Center. Novosibirsk. URSS.Google Scholar
  26. 26.
    PHILIPS, R. J., BEAUMONT, M. J., and RICHARDSON, D. (1979). AESOP. An Architectural relational database. Comput. Aided Des., 11(4), 217–226.CrossRefGoogle Scholar
  27. 27.
    PRADE, H. The connection between Lipski’s approach to incomplete information data bases and Zadeh’s possibility theory. Proc. Int. Conf. Systems Methodology, Washington, D.C., January, 5–9, pp. 402–408.Google Scholar
  28. 28.
    PRADE, H. (1982). Possibility sets, fuzzy sets and their relation to Lukasiewicz logic. Proc. 12th. Symp. on Multiple-Valued Logic, Paris, May 24–27, pp. 223–227.Google Scholar
  29. 29.
    PRADE, H. (1982). Modèles mathématiques de l’imprécis et de l’incertain en vue d’applications au raisonnement naturel (358 p.). Thèse d’Etat, Univ. Paul Sabatier, Toulouse.Google Scholar
  30. 30.
    PRADE, H. (1983). Représentation d’informations incomplètes dans une base de données à l’aide de la théorie des possibilités. Proc. Convention Informatique Latine 83, Barcelona, Spain, June 6–9, pp. 378–392.Google Scholar
  31. 31.
    PRADE, H. (1984). Lipski’s approach to incomplete information databases restated and generalized in the setting of Zadeh’s possibility theory. Inf. Syst. 9(1), 27–42.MathSciNetMATHCrossRefGoogle Scholar
  32. 32.
    PRADE, H. (1983). Do we need a precise definition of membership functions? BUSEFAL, No. 14, LSI, University Paul Sabatier, Toulouse, p. 127.Google Scholar
  33. 33.
    PRADE, H., and TESTEMALE, C. (1984). Generalizing database relational algebra for the treatment of incomplete/uncertain information and vague queries. Inf. Sci., 34, 115–143.MathSciNetMATHCrossRefGoogle Scholar
  34. 34.
    PRADE, H., and TESTEMALE, C. (1987). Representation of soft constraints and fuzzy attribute values by means of possibility distributions in databases. In The Analysis of Fuzzy Information, Volume 2: Artificial Intelligence and Decision Systems (J. Bezdek, ed.), CRC Press, Boca Raton, Florida, pp. 213–229.Google Scholar
  35. 35.
    RUSPINI, E. (1982). Possibilistic data structures for the representation of uncertainty. In Approximate Reasoning in Decision Analysis (M. M. Gupta and E. Sanchez, eds.), North-Holland, Amsterdam, pp. 411–415.Google Scholar
  36. 36.
    SIKLOSSY, L., and LAURIERE, J. L. (1982). Removing restrictions in the relational database model: An application of problem-solving techniques. Proc. National Conf in Artificial Intelligence Pittsburg, August.Google Scholar
  37. 37.
    TAHANI, V. (1977). A conceptual framework for fuzzy query processing —A step toward very intelligent database systems. Inf. Process. Manage., 13, 289–303.MATHCrossRefGoogle Scholar
  38. 38.
    UMANO, M. (1982). FREEDOM-O: A fuzzy database system. In Fuzzy Information and Decision Processes (M. M. Gupta and E. Sanchez, eds.), North-Holland, Amsterdam, pp. 339–349.Google Scholar
  39. 39.
    UMANO, M. (1983). Retrieval from fuzzy data base by fuzzy relational algebra. Proc. IFAC Symposium, Fuzzy Information, Knowledge Representation and Decision Processes, Marseille, July 19–21, pp. 1–6.Google Scholar
  40. 40.
    WINSTON, P. H. (1977). Artificial Intelligence. Addison-Wesley, Reading, Massachusetts.MATHGoogle Scholar
  41. 41.
    WONG, E. A. (1982). Statistical approach to incomplete information in database systems. ACM Trans. Database Syst., 7(3), 470–488.MATHCrossRefGoogle Scholar
  42. 42.
    YAGER, R. (1982). A new approach to the summarization of data. Inf. Sci., 28, 69–86.MathSciNetMATHCrossRefGoogle Scholar
  43. 43.
    ZADEH, L. A. (1978). Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst., 1(1), 3–28.MathSciNetMATHCrossRefGoogle Scholar
  44. 44.
    ZADEH, L. A. (1978). PRÜF: A meaning representation language for natural languages. Int. J. Man-Machine Stud., 10, 395–460.MathSciNetMATHCrossRefGoogle Scholar
  45. 45.
    ZADEH, L. A. (1981). Test-score semantics for natural languages and meaning representation via PRÜF. SRI International Technical Note No. 247, May 1981, Menlo Park, California. Also in Empirical Semantics, Vol. 1 (B. B. Rieger, ed.). Brockmeyer, Bochum, pp. 281–349.Google Scholar
  46. 46.
    PRADE, H., and TESTEMALE, C. (1987). Fuzzy relational data bases: Representational issues and reduction using similarity measures. J. Am. Soc. Inf Sci. 38(2), 118–126.CrossRefGoogle Scholar
  47. 47.
    KUNII, T. L. (1976) DATAPLAN: an interface generator for database semantics. Inf Sci., 10, 279–298Google Scholar
  48. 48.
    ZEMANKOVA, M. and KANDEL, A. (1984). Fuzzy Relational Data Bases: A Key to Expert Systems. Verlag TÜV Rheinland, Köln.MATHGoogle Scholar
  49. 49.
    KACPRZYK, J., and ZIOLKOWSKI, A. (1986). Retrieval from data bases using queries with fuzzy linguistic quantifiers. In Fuzzy Logic in Knowledge Engineering (H. Prade and C. V. Negoita, eds.), Verlag TÜV Rheinland Köln, pp. 46–57.Google Scholar
  50. 50.
    Bosc, P., CHAUFFAUT, A. GALIBOURG, M., and HAMON, G. (1986). Une extension de SEQUEL pour permettre l’interrogation floue. Modèles et Bases de Données, no. 4. AFCET, Paris, pp. 17–24.Google Scholar
  51. 51.
    DOCKERY, J. (1982). Fuzzy design of military information systems. Int. J. Man-Machine Studies, 16, 1–38.CrossRefGoogle 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

Personalised recommendations