On sup — * Compositions of Fuzzy Implications

  • Michał Baczyński
  • Józef Drewniak
  • Jolanta Sobera
Conference paper
Part of the Advances in Soft Computing book series (AINSC, volume 19)


Recently we have examined properties of sup-min compositions of fuzzy implications [3]. However, in many applications, another connectives are used for composition of fuzzy implications. Now, we generalize these results to the case of sup —* composition with a triangular norm *.


Distributive Lattice Binary Operation Fuzzy Logic Controller Truth Table Zero Element 
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  1. 1.
    Baczynski, M., Drewniak, J. (1999): Conjugacy classes of fuzzy implication, In: Reusch, B. (Eds.): Computational Intelligence: Theory and Applications, Springer-Verlag, Berlin, (LNCS Vol. 1625), 287–298.Google Scholar
  2. 2.
    Baczylíski, M., Drewniak, J. (2000): Monotonic fuzzy implications, In: Szczepaniak, P., Lisboa, P., Kacprzyk, J. (Eds.): Fuzzy Systems in Medicine, PhysicaVerlag, Heidelberg, (Studies in Fuzzines and Soft Computing, Vol. 41), 90–111.Google Scholar
  3. 3.
    Baczynski, M., Drewniak, J., Sobera, J. (2001): Semigroups of fuzzy implications, Tatra Mt. Math. Publ. 21, 61–71.MathSciNetzbMATHGoogle Scholar
  4. 4.
    Baldwin, J.F., Pilsworth, B.W. (1980): Axiomatic approach to implication for approximate reasoning with fuzzy logic, Fuzzy Sets Syst. 3, 193–219.MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Drewniak, J., Kula, K. (2002): Generalized compositions of fuzzy relations, Presented in FSTA 2002, Liptovsky Jan, Slovakia.Google Scholar
  6. 6.
    Cordon, O., Herrera, F., Peregrin, A. (1997): Applicability of the fuzzy operators in the design of fuzzy logic controllers, Fuzzy Sets Syst. 86, 15–41.zbMATHCrossRefGoogle Scholar
  7. 7.
    Fodor, J.C., Roubens, M.C. (1994): Fuzzy Preference Modelling and Multicriteria Decision Support, Kluwer, Dordrecht.zbMATHCrossRefGoogle Scholar
  8. 8.
    Goguen, J.A. (1967): L-fuzzy sets, J. Math. Anal. Appl. 18, 145–174.MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Klement, E.P., Mesiar, R., Pap, E. (2000): Triangular Norms, Kluwer, Dordrecht.zbMATHGoogle Scholar
  10. 10.
    Schweizer, B., Sklar, A. (1961): Associative functions and statistical triangle inequalities, Publ. Math. Debrecen 8, 169–186.MathSciNetzbMATHGoogle Scholar
  11. 11.
    Zadeh, L.A. (1965): Fuzzy sets, Inform. Control 8, 338–353.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Michał Baczyński
    • 1
  • Józef Drewniak
    • 1
    • 2
  • Jolanta Sobera
    • 1
  1. 1.Institute of MathematicsUniversity of SilesiaBankowa 14Poland
  2. 2.Institute of MathematicsUniversity of RzeszówRejtana 16aPoland

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