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Flexible Query Answering Using Distance-Based Fuzzy Relations

  • Ulrich Bodenhofer
  • Josef Küng
  • Susanne Saminger
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4342)

Abstract

This paper addresses the added value that is provided by using distance-based fuzzy relations in flexible query answering. To use distances and/or concepts of gradual similarity in that domain is not new. Within the last ten years, however, results in the theory of fuzzy relations have emerged that permit a smooth and pragmatic, yet expressive and effective, integration of ordinal concepts too. So this paper primarily highlights the benefits of integrating fuzzy orderings in flexible query answering systems, where the smooth interplay of fuzzy equivalence relations and fuzzy orderings allows to use simple distances as a common basis for defining both types of relations. As one case study, we discuss a pragmatic variant of a flexible query answering system—the so-called Vague Query System (VQS). The integration of fuzzy orderings into that system is provided in full detail along with the necessary methodological background and demonstrative examples.

Keywords

Aggregation Operator Fuzzy Relation Structure Query Language Query Answering Triangular Norm 
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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References

  1. 1.
    Bodenhofer, U.: A similarity-based generalization of fuzzy orderings preserving the classical axioms. Internat. J. Uncertain. Fuzziness Knowledge-Based Systems 8(5), 593–610 (2000)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bodenhofer, U., Bogdanowicz, P., Lanzerstorfer, G., Küng, J.: Distance-based fuzzy relations in flexible query answering systems: Overview and experiences. In: Düntsch, I., Winter, M. (eds.) Proc. 8th Int. Conf. on Relational Methods in Computer Science, St. Catharines, ON, Brock University, pp. 15–22 (February 2005)Google Scholar
  3. 3.
    Bodenhofer, U., Küng, J.: Fuzzy orderings in flexible query answering systems. Soft Computing 8(7), 512–522 (2004)MATHCrossRefGoogle Scholar
  4. 4.
    Bosc, P., Buckles, B., Petry, F., Pivert, O.: Fuzzy databases: Theory and models. In: Bezdek, J., Dubois, D., Prade, H. (eds.) Fuzzy Sets in Approximate Reasoning and Information Systems. The Handbooks of Fuzzy Sets, vol. 5, pp. 403–468. Kluwer Academic Publishers, Boston (1999)Google Scholar
  5. 5.
    Bosc, P., Duval, L., Pivert, O.: Value-based and representation-based querying of possibilistic databases. In: Bordogna, G., Pasi, G. (eds.) Recent Issues on Fuzzy Databases. Studies in Fuzziness and Soft Computing, vol. 53, pp. 3–27. Physica-Verlag, Heidelberg (2000)Google Scholar
  6. 6.
    Bosc, P., Galibourg, M., Hamon, G.: Fuzzy querying with SQL: Extension and implementation aspects. Fuzzy Sets and Systems 28(3), 333–349 (1988)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Bosc, P., Pivert, O.: Fuzzy querying in conventional databases. In: Zadeh, L.A., Kacprzyk, J. (eds.) Fuzzy Logic for the Management of Uncertainty, pp. 645–671. John Wiley & Sons, New York (1992)Google Scholar
  8. 8.
    Bosc, P., Pivert, O.: SQLf: A relational database language for fuzzy querying. IEEE Trans. Fuzzy Systems 3, 1–17 (1995)CrossRefGoogle Scholar
  9. 9.
    Buckles, B.P., Petry, F.E.: Fuzzy databases and their applications. In: Gupta, M.M., Sanchez, E. (eds.) Fuzzy Information and Decision Processes, pp. 361–371. North-Holland, New York (1982)Google Scholar
  10. 10.
    Buckles, B.P., Petry, F.E.: Query languages for fuzzy databases. In: Kacprzyk, J., Yager, R.R. (eds.) Management Decision Support Systems Using Fuzzy Sets and Possibility Theory, pp. 241–252. Verlag TÜV Rheinland, Köln (1985)Google Scholar
  11. 11.
    Buckles, B.P., Petry, F.E., Sachar, H.: Design of similarity-based relational databases. In: Negotia, C.V., Prade, H. (eds.) Fuzzy Logic in Knowledge Engineering, pp. 3–17. Verlag TÜV Rheinland, Cologne (1986)Google Scholar
  12. 12.
    Calvo, T., Mayor, G., Mesiar, R.: Aggregation Operators. Studies in Fuzziness and Soft Computing, vol. 97. Physica-Verlag, Heidelberg (2002)MATHGoogle Scholar
  13. 13.
    B. C. Csáji, J. Küng, J. Palkoska, and R. Wagner. On the automation of similarity information maintenance in flexible query answering systems. In F. Galindo, M. Takizawa, and R. Traunmüller, editors, Proc. 15th Int. Conf. on Database and Expert Systems Applications, volume 3180 of Lecture Notes in Computer Science, pages 130–140. Springer, Berlin, 2004.CrossRefGoogle Scholar
  14. 14.
    De Baets, B., Mesiar, R.: Pseudo-metrics and T-equivalences. J. Fuzzy Math. 5(2), 471–481 (1997)MATHMathSciNetGoogle Scholar
  15. 15.
    Dubois, D., Prade, H.: Similarity-based approximate reasoning. In: Zurada, J.M., Marks, R.J., Robinson, C.J. (eds.) Computational Intelligence Imitating Life, pp. 69–80. IEEE Press, New York (1994)Google Scholar
  16. 16.
    Dubois, D., Prade, H.: Using fuzzy sets in flexible querying: Why and how? In: Proc. Workshop on Flexible Query-Answer Systems (FQAS 1996), Roskilde, May 1996, pp. 89–103 (1996)Google Scholar
  17. 17.
    Fodor, J., Roubens, M.: Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer Academic Publishers, Dordrecht (1994)MATHGoogle Scholar
  18. 18.
    Höhle, U., Blanchard, N.: Partial ordering in L-underdeterminate sets. Inform. Sci. 35, 133–144 (1985)MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Ichikawa, T., Hirakawa, M.: ARES: A relational database with the capability of performing flexible interpretation of queries. IEEE Trans. Software Eng. 12(5), 624–634 (1986)Google Scholar
  20. 20.
    Kacprzyk, J., Zadrozny, S.: Implementation of OWA operators in fuzzy querying for Microsoft Access. In: Yager, R.R., Kacprzyk, J. (eds.) The Ordered Weighted Averaging Operators: Theory and Applications, pp. 293–306. Kluwer Academic Publishers, Boston (1997)Google Scholar
  21. 21.
    Kacprzyk, J., Zadrozny, S., Ziolkowski, A.: FQUERY III+: a “human-consistent” database querying system based on fuzzy logic with linguistic quantifiers. Inform. Sci. 14(6), 443–453 (1989)Google Scholar
  22. 22.
    Kacprzyk, J., Ziolkowski, A.: Database queries with fuzzy linguistic quantifiers. IEEE Trans. Syst. Man Cybern. 16, 474–479 (1986)CrossRefGoogle Scholar
  23. 23.
    Klawonn, F.: Fuzzy sets and vague environments. Fuzzy Sets and Systems 66, 207–221 (1994)MATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Trends in Logic, vol. 8. Kluwer Academic Publishers, Dordrecht (2000)MATHGoogle Scholar
  25. 25.
    Kruse, R., Gebhardt, J., Klawonn, F.: Foundations of Fuzzy Systems. John Wiley & Sons, New York (1994)Google Scholar
  26. 26.
    Küng, J., Palkoska, J.: VQS—a vague query system prototype. In: Proc. 8th Int. Workshop on Database and Expert Systems Applications, pp. 614–618. IEEE Computer Society Press, Los Alamitos (1997)Google Scholar
  27. 27.
    Küng, J., Palkoska, J.: Vague joins—an extension of the vague query system VQS. In: Proc. 9th Int. Workshop on Database and Expert Systems Applications, pp. 997–1001. IEEE Computer Society Press, Los Alamitos (1998)CrossRefGoogle Scholar
  28. 28.
    Medina, J.M., Pons, O., Vila, M.A.: GEFRED: a generalized model of fuzzy relational databases. Inform. Sci. 76(1–2), 87–109 (1994)CrossRefGoogle Scholar
  29. 29.
    Motro, A.: VAGUE: A user interface to relational databases that permits vague queries. ACM Trans. Off. Inf. Syst. 6(3), 187–214 (1988)CrossRefGoogle Scholar
  30. 30.
    Ovchinnikov, S.V.: Similarity relations, fuzzy partitions, and fuzzy orderings. Fuzzy Sets and Systems 40(1), 107–126 (1991)MATHCrossRefMathSciNetGoogle Scholar
  31. 31.
    Palkoska, J., Dunzendorfer, A., Küng, J.: Vague queries in tourist information systems. In: Information and Communication Technologies in Tourism (ENTER 2000), pp. 61–70. Springer, Vienna (2000)Google Scholar
  32. 32.
    Petry, F.E., Bosc, P.: Fuzzy Databases: Principles and Applications. International Series in Intelligent Technologies. Kluwer Academic Publishers, Boston (1996)MATHGoogle Scholar
  33. 33.
    Pradera, A., Trillas, E.: A note of pseudometrics aggregation. Int. J. General Systems 31(1), 41–51 (2002)MATHCrossRefMathSciNetGoogle Scholar
  34. 34.
    Rosado, A., Kacprzyk, J., Ribeiro, R.A., Zadrozny, S.: Fuzzy querying in crisp and fuzzy relational databases: An overview. In: Proc. 9th Int. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems, Annecy, July 2002, vol. 3, pp. 1705–1712 (2002)Google Scholar
  35. 35.
    Saminger, S., Mesiar, R., Bodenhofer, U.: Domination of aggregation operators and preservation of transitivity. Internat. J. Uncertain. Fuzziness Knowledge-Based Systems 10(Suppl.), 11–35 (2002)MATHCrossRefMathSciNetGoogle Scholar
  36. 36.
    Schweizer, B., Sklar, A.: Probabilistic Metric Spaces. North-Holland, Amsterdam (1983)MATHGoogle Scholar
  37. 37.
    Tahani, V.: A conceptual framework for fuzzy query processing: A step towards very intelligent database systems. Inf. Proc. and Manag. 13, 289–303 (1977)MATHCrossRefGoogle Scholar
  38. 38.
    Takahashi, Y.: Fuzzy database query languages and their relational completeness theorem. IEEE Trans. Knowl. Data Eng. 5(1), 122–125 (1993)CrossRefGoogle Scholar
  39. 39.
    Trillas, E., Valverde, L.: An inquiry into indistinguishability operators. In: Skala, H.J., Termini, S., Trillas, E. (eds.) Aspects of Vagueness, pp. 231–256. Reidel, Dordrecht (1984)Google Scholar
  40. 40.
    Valverde, L.: On the structure of F-indistinguishability operators. Fuzzy Sets and Systems 17(3), 313–328 (1985)MATHCrossRefMathSciNetGoogle Scholar
  41. 41.
    Yager, R.R.: On ordered weighted averaging aggregation operators in multicriteria decisionmaking. IEEE Trans. Syst. Man Cybern. B 18(1), 183–190 (1988)MATHCrossRefMathSciNetGoogle Scholar
  42. 42.
    Yager, R.R.: Interpreting linguistically quantified propositions. Int. J. Intell. Syst. 9, 149–184 (1994)CrossRefGoogle Scholar
  43. 43.
    Yager, R.R., Kacprzyk, J. (eds.): The Ordered Weighted Averaging Operators: Theory and Applications. Kluwer Academic Publishers, Boston (1997)Google Scholar
  44. 44.
    Zadeh, L.A.: Similarity relations and fuzzy orderings. Inform. Sci. 3, 177–200 (1971)MATHCrossRefMathSciNetGoogle Scholar
  45. 45.
    Zadeh, L.A.: A computational approach to fuzzy quantifiers in natural languages. Comput. Math. Appl. 9, 149–184 (1983)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ulrich Bodenhofer
    • 1
  • Josef Küng
    • 2
  • Susanne Saminger
    • 3
  1. 1.Institute of BioinformaticsJohannes Kepler UniversityLinzAustria
  2. 2.Institute for Applied Knowledge ProcessingJohannes Kepler UniversityLinzAustria
  3. 3.Dept. of Knowledge-Based Mathematical SystemsJohannes Kepler UniversityLinzAustria

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