Incorporation of Excluding Features in Fuzzy Relational Compositions Based on Generalized Quantifiers

  • Nhung CaoEmail author
  • Martin Štěpnička
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 641)


The concepts of incorporation of excluding features in fuzzy relational compositions and the compositions based on generalized quantifiers are useful tools for improving relevance and precision of the suspicion provided by the standard fuzzy relational compositions initial studied by Willis Bandler and Ladislav Kohout. They are independently extended from the standard compositions. However, it may become a very effective tool if they are used together. Taking this natural motivation leads us to introduce the concept of incorporation of excluding features in fuzzy relational compositions based on generalized quantifiers. Most of valid properties preserved for the two mentioned approaches will be proved for the new concept as well. Furthermore, an illustrative example will be presented for showing the usefulness of the approach.


Fuzzy relational compositions Fuzzy relational products Bandler-Kohout products Fuzzy measures Generalized (fuzzy) quantifiers Medical diagnosis Classification 



This research was partially supported by the NPU II project LQ1602 “IT4Innovations excellence in science” provided by the MŠMT.


  1. 1.
    Bandler, W., Kohout, L.J.: Semantics of implication operators and fuzzy relational products. Int. J. Man Mach. Stud. 12(1), 89–116 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Bandler, W., Kohout, L.J.: Relational-product architectures for information processing. Inf. Sci. 37, 25–37 (1985)CrossRefGoogle Scholar
  3. 3.
    Belohlavek, R.: Sup-t-norm and inf-residuum are one type of relational product: unifying framework and consequences. Fuzzy Sets Syst. 197, 45–58 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Burda, M.: Linguistic fuzzy logic in R. In: Proceedings of IEEE International Conference on Fuzzy Systems, Istanbul, Turkey (2015)Google Scholar
  5. 5.
    Běhounek, L., Daňková, M.: Relational compositions in fuzzy class theory. Fuzzy Sets Syst. 160(8), 1005–1036 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Cao, N., Štěpnička, M.: How to incorporate excluding features in fuzzy relational compositions and what for. In: Proceedings of 16th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems. Communications in Computer and Information Science, vol. 611, pp. 470–481. Springer, Heidelberg (2016)Google Scholar
  7. 7.
    Cao, N., Štěpnička, M.: Properties of ‘excluding symptoms’ in fuzzy relational compositions. In: Proceedings of 12th Conference on Uncertainty Modelling in Knowledge Engineering and Decision Making (FLINS), vol. 10, pp. 555–560. World Scientific (2016)Google Scholar
  8. 8.
    Cao, N., Štěpnička, M., Burda, M., Dolný, A.: Excluding features in fuzzy relational compositions. Expert Syst. Appl. 81, 1–11 (2017)CrossRefGoogle Scholar
  9. 9.
    Cao, N., Štěpnička, M., Holčapek, M.: An extension of fuzzy relational compositions using generalized quantifiers. In: Proceedings of 16th World Congress of the International Fuzzy Systems Association (IFSA) and 9th Conference of the European Society for Fuzzy-Logic and Technology (EUSFLAT). Advances in Intelligent Systems Research, vol. 89, pp. 49–58. Atlantis press, Gijón (2015)Google Scholar
  10. 10.
    Cao, N., Štěpnička, M., Holčapek, M.: Non-preservation of chosen properties of fuzzy relational compositions based on fuzzy quantifiers. In: IEEE International Conference on Fuzzy Systems (2017, in press)Google Scholar
  11. 11.
    Cao, N., Štěpnička, M., Holčapek, M.: Extensions of fuzzy relational compositions based on generalized quantifer. Fuzzy Sets Syst. (submitted)Google Scholar
  12. 12.
    De Baets, B.: Analytical solution methods for fuzzy relational equations. In: Dubois, D., Prade, H. (eds.) The Handbook of Fuzzy Set Series, vol. 1, pp. 291–340. Academic Kluwer Publishers, Boston (2000)Google Scholar
  13. 13.
    De Baets, B., Kerre, E.: Fuzzy relational compositions. Fuzzy Sets Syst. 60, 109–120 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Di Nola, A., Sessa, S., Pedrycz, W., Sanchez, E.: Fuzzy Relation Equations and Their Applications to Knowledge Engineering. Kluwer, Boston (1989)CrossRefzbMATHGoogle Scholar
  15. 15.
    Dubois, D., Prade, H.: Semantics of quotient operators in fuzzy relational databases. Fuzzy Sets Syst. 78, 89–93 (1996)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Lim, C.K., Chan, C.S.: A weighted inference engine based on interval-valued fuzzy relational theory. Exp. Syst. Appl. 42(7), 3410–3419 (2015)CrossRefGoogle Scholar
  17. 17.
    Mandal, S., Jayaram, B.: SISO fuzzy relational inference systems based on fuzzy implications are universal approximators. Fuzzy Sets Syst. 277, 1–21 (2015)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Pedrycz, W.: Fuzzy relational equations with generalized connectives and their applications. Fuzzy Sets Syst. 10, 185–201 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Pedrycz, W.: Applications of fuzzy relational equations for methods of reasoning in presence of fuzzy data. Fuzzy Sets Syst. 16, 163–175 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Pivert, O., Bosc, P.: Fuzzy Preference Queries to Relational Databases. Imperial College Press, London (2012)CrossRefzbMATHGoogle Scholar
  21. 21.
    Sanchez, E.: Resolution of composite fuzzy relation equations. Inf. Control 30, 38–48 (1976)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Štěpnička, M., De Baets, B.: Interpolativity of at-least and at-most models of monotone single-input single-output fuzzy rule bases. Inf. Sci. 234, 16–28 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Štěpnička, M., De Baets, B., Nosková, L.: Arithmetic fuzzy models. IEEE Trans. Fuzzy Syst. 18, 1058–1069 (2010)CrossRefGoogle Scholar
  24. 24.
    Štěpnička, M., Holčapek, M.: Fuzzy relational compositions based on generalized quantifiers. In: Information Processing and Management of Uncertainty in Knowledge-Based Systems, PT II, Communications in Computer and Information Science, IPMU 2014, vol. 443, pp. 224–233. Springer, Berlin (2014)Google Scholar
  25. 25.
    Štěpnička, M., Jayaram, B.: On the suitability of the Bandler-Kohout subproduct as an inference mechanism. IEEE Trans. Fuzzy Syst. 18(2), 285–298 (2010)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Institute for Research and Applications of Fuzzy Modeling, CE IT4InnovationsUniversity of OstravaOstravaCzech Republic

Personalised recommendations