Elements of the Type-2 Semantics in Summarizing Databases

  • Adam Niewiadomski
  • Michał Bartyzel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4029)


Modern and effective methods of knowledge extraction from databases and information systems are required to provide rather linguistic than numerical information. The so-called linguistic summaries of databases by Yager [1], exemplified by Many children like sweet ice cream, and further improvements by George and Srikanth [2] and by Kacprzyk and Yager [3], are discussed in this paper. The use of type-2 fuzzy sets is an original contribution to the domain, since only ordinary fuzzy sets have been originally employed. Elements of type-2 semantics are shown to handle effectively pieces of imprecise information (e.g. fuzzy sets) stored in databases. An application on sample data is provided.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Yager, R.R.: A new approach to the summarization of data. Information Sciences 28, 69–86 (1982)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    George, R., Srikanth, R.: Data summarization using genetic algorithms and fuzzy logic. In: Herrera, F., Verdegay, J.L. (eds.) Genetic Algorithms and Soft Computing, pp. 599–611. Physica–Verlag, Heidelberg (1996)Google Scholar
  3. 3.
    Kacprzyk, J., Yager, R.R.: Linguistic summaries of data using fuzzy logic. International Journal of General Systems 30, 133–154 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Turksen, I.B.: Interval-valued fuzzy sets based on normal forms. Fuzzy Sets and Systems, 191–210 (1986)Google Scholar
  6. 6.
    Gorzalczany, M.B.: A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets and Systems 21, 1–17 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Gorzalczany, M.B.: An interval-valued fuzzy inference method in approximate reasoning. Fuzzy Sets and Systems 31, 243–251 (1989)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Karnik, N.N., Mendel, J.M.: An Introduction to Type-2 Fuzzy Logic Systems. University of Southern California, Los Angeles (1998)Google Scholar
  9. 9.
    Karnik, N.N., Mendel, J.M.: Type-2 fuzzy logic systems. IEEE Transactions on Fuzzy Systems 7, 643–658 (1999)CrossRefGoogle Scholar
  10. 10.
    Mendel, J.M.: Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions. Prentice-Hall, Upper Saddle River (2001)zbMATHGoogle Scholar
  11. 11.
    Jang, L.-C., Ralescu, D.: Cardinality concept for type-two fuzzy sets. Fuzzy Sets and Systems 118, 479–487 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Liang, Q., Mendel, J.M.: Equalization of non-linear time-varying channels using type-2 fuzzy adaptive filters. IEEE Transactions on Fuzzy Systems 8, 551–563 (2000)CrossRefGoogle Scholar
  13. 13.
    de Tre, G., de Caluwe, R.: Level-2 fuzzy sets and their usefulness in object-oriented database modelling. Fuzzy Sets and Systems 140, 29–49 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Wu, H., Mendel, J.M.: Uncertainty bounds and their use in the design of interval type–2 fuzzy logic systems. IEEE Transactions on Fuzzy Systems 10, 622–639 (2002)CrossRefGoogle Scholar
  15. 15.
    Karnik, N.N., Mendel, J.M.: Operations on type-2 fuzzy sets. Fuzzy Sets and Systems 122, 327–348 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Liang, Q., Mendel, J.M.: Interval type-2 fuzzy logic systems. theory and design. IEEE Transactions on Fuzzy Systems 8, 535–550 (2000)CrossRefGoogle Scholar
  17. 17.
    de Korvin, A., Hu, C., Sirisaengtaksin, O.: On firing rules of fuzzy sets of type ii. International J. of Applied Mathematics 3(2), 151–159 (2000)zbMATHGoogle Scholar
  18. 18.
    Zadeh, L.A.: A computational approach to fuzzy quantifiers in natural languages. Computers and Maths with Applications 9, 149–184 (1983)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Kacprzyk, J., Yager, R.R., Zadrożny, S.: Fuzzy linguistic summaries of databases for an efficient business data analysis and decision support. In: Abramowicz, W., Żurada, J. (eds.) Discovery for Business Information Systems, pp. 129–152. Kluwer Academic Publishers, B. V., Boston (2001)Google Scholar
  20. 20.
    Zadeh, L.A.: The concept of linguistic variable and its application for approximate reasoning (i). Information Sciences 8, 199–249 (1975)CrossRefMathSciNetGoogle Scholar
  21. 21.
    Niewiadomski, A.: On two possible roles of type-2 fuzzy sets in linguistic summaries. In: Szczepaniak, P.S., Kacprzyk, J., Niewiadomski, A. (eds.) AWIC 2005. LNCS (LNAI), vol. 3528, pp. 341–347. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  22. 22.
    Niewiadomski, A.: Interval-valued linguistic variables. an application to linguistic summaries. In: Hryniewicz, O., Kacprzyk, J., Koronacki, J., Wierzchoń, S.T. (eds.) Issues in Intelligent Systems. Paradigms, pp. 167–184. EXIT Academic Press, Warsaw (2005)Google Scholar
  23. 23.
    Niewiadomski, A.: Interval-valued quality measures for linguistic summaries. In: Grzegorzewski, P., Krawczak, M., Zadrożny, S. (eds.) Issues in Soft Computing. Theory and Applications, pp. 211–224. Academic Press, London (2005)Google Scholar
  24. 24.
    Niewiadomski, A., Ochelska, J., Szczepaniak, P.S.: Interval-valued linguistic summaries of databases. Control and Cybernetics (2005) (in print) Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Adam Niewiadomski
    • 1
  • Michał Bartyzel
    • 1
  1. 1.Institute of Computer ScienceTechnical University of ŁódźŁódźPoland

Personalised recommendations