On a Reinforced Fuzzy Inclusion and Its Application to Database Querying

  • Patrick Bosc
  • Olivier Pivert
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 297)


This paper introduces a fuzzy inclusion indicator derived from a connective aimed at modulating a fuzzy criterion according to the satisfaction of another one. The idea is to express that one is all the more demanding as to the degree attached to an element x in a set B as this element has a high degree of membership degree to a set A. The use of this reinforced inclusion indicator is illustrated in the context of database querying.


Membership Degree Fuzzy Relation Satisfaction Degree Database Query 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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bosc, P., Pivert, O.: About approximate inclusion and its axiomatization. Fuzzy Sets and Systems 157(11), 1438–1454 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Bosc, P., Pivert, O.: On two qualitative approaches to tolerant inclusion operators. Fuzzy Sets and Systems 159(21), 2786–2805 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Bosc, P., Pivert, O.: On a strengthening connective for flexible database querying. In: Proc. of the 20th IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2011), Taiwan (2011)Google Scholar
  4. 4.
    Bosc, P., Pivert, O.: SQLf: a relational database language for fuzzy querying. IEEE Transactions on Fuzzy Systems 3, 1–17 (1995)CrossRefGoogle Scholar
  5. 5.
    Bosc, P., Buckles, B., Petry, F., Pivert, O.: Fuzzy databases. In: Bezdek, J., Dubois, D., Prade, H. (eds.) Fuzzy Sets in Approximate Reasoning and Information Systems, The Handbook of Fuzzy Sets Series, pp. 403–468. Kluwer Academic Publishers, Dordrecht (1999)CrossRefGoogle Scholar
  6. 6.
    Bosc, P., Pivert, O.: On four noncommutative fuzzy connectives and their axiomatization. Fuzzy Sets and Systems (2012)Google Scholar
  7. 7.
    Bouchon-Meunier, B., Laurent, A., Lesot, M.-J., Rifqi, M.: Strengthening fuzzy gradual rules through ”all the more” clauses. In: Proc. of FUZZ-IEEE 2010, pp. 1–7. IEEE (2010)Google Scholar
  8. 8.
    MacVicar-Whelan, P.J.: Fuzzy sets, the concept of height and the hedge very. IEEE Transactions on Systems, Man, and Cybernetics 8, 507–511 (1978)CrossRefGoogle Scholar
  9. 9.
    Bouchon-Meunier, B., Yao, J.: Linguistic modifiers and imprecise categories. International Journal of Intelligent Systems 7, 25–36 (1992)zbMATHCrossRefGoogle Scholar
  10. 10.
    Bosc, P., Dubois, D., HadjAli, A., Pivert, O., Prade, H.: Adjusting the core and/or the support of a fuzzy set - a new approach to fuzzy modifiers. In: FUZZ-IEEE, pp. 1–6. IEEE (2007)Google Scholar
  11. 11.
    Bouchon-Meunier, B., Dubois, D., Godo, L., Prade, H.: Fuzzy sets and possibility theory in approximate and plausible reasoning. In: Bezdek, J.C., Dubois, D., Prade, H. (eds.) Fuzzy Sets in Approximate Reasoning and Information Systems, pp. 15–190. Kluwer Academic Publishers (1999)Google Scholar
  12. 12.
    Fodor, J., Yager, R.R.: Fuzzy-set theoretic operators and quantifiers. In: Dubois, D., Prade, H. (eds.) The Handbooks of Fuzzy Sets Series, vol. 1: Fundamentals of Fuzzy Sets, pp. 125–193. Kluwer Academic Publishers, Dordrecht (2000)Google Scholar
  13. 13.
    Yager, R.R.: An approach to inference in approximate reasoning. International Journal of Man-Machine Studies 13(3), 323–338 (1980)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Bandler, W., Kohout, L.: Fuzzy power sets and fuzzy implication operators. Fuzzy Sets and Systems 4, 13–30 (1980)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Sinha, D., Dougherty, E.R.: Fuzzification of set inclusion: theory and applications. Fuzzy Sets and Systems 55, 15–42 (1993)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Kitainik, L.: Fuzzy implication and fuzzy inclusion: a comparative axiomatic study. In: Lowen, R., Roubens, M. (eds.) Fuzzy Logic — State of the Art, pp. 441–451. Kluwer Academic Publishers, Dordrecht (1993)Google Scholar
  17. 17.
    Türksen, I.B., Kreinovich, V., Yager, R.R.: A new class of fuzzy implications. Axioms of fuzzy implication revisited. Fuzzy Sets and Systems 100, 267–272 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Cornelis, C., van der Donck, C., Kerre, E.: Sinha-Dougherty approach to the fuzzification of set inclusion revisited. Fuzzy Sets and Systems 134, 283–296 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Bosc, P., Legrand, C., Pivert, O.: About fuzzy query processing — the example of the division. In: Proc. of the 8th IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 1999), Seoul, Korea, pp. 592–597 (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Patrick Bosc
    • 1
  • Olivier Pivert
    • 1
  1. 1.Technopole AnticipaIrisa – Enssat, University of Rennes 1Lannion CedexFrance

Personalised recommendations