Powers with Respect to t-Norms and t-Conorms and Aggregation Functions

  • D. Boixader
  • J. RecasensEmail author
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 339)


Aggregation functions A stable with respect to powers of t-norms and t-conorms (i.e.: satisfying \(A(x^{(r)},y^{(r)})=(A(x,y))^{(r)}\)) where \(x^{(r)}\) is the r-th power of \(x \in [0,1]\) with respect to a t-norm or t-conorm) are characterized. This result generalizes the characterization of power stable aggregation functions in [5].


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  1. 1.
    J. Aczél, Lectures on Functional Equations and Their Applications (Academic Press, NY-London, 1966)zbMATHGoogle Scholar
  2. 2.
    G. Beliakov, A. Pradera, T. Calvo, Aggregation Functions: A Guide for Practitioners. Studies in Fuzziness and Soft Computing, vol. 221 (Springer, 2007)Google Scholar
  3. 3.
    T. Calvo, A. Kolesárova, M. Komorníková, R. Mesiar, Aggregation operators: properties, classes and construction methods, in Aggregation Operators: New Trends and Applications, Studies in Fuzziness and Soft Computing, ed. by R. Mesiar, T. Calvo, G. Mayor (Springer, 2002), pp. 3–104Google Scholar
  4. 4.
    E.P. Klement, R. Mesiar, E. Pap, Triangular Norms (Kluwer Academic Publishers, Dordrecht, 2000)CrossRefzbMATHGoogle Scholar
  5. 5.
    A. Kolesárová, R. Mesiar, T. Rückschlossová, Power stable aggregation functions. Fuzzy Sets Syst. 240, 39–50 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    E.A. Walker, C.L. Walker, Powers of t-norms. Fuzzy Sets Syst. 129, 1–18 (2002)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Secció Matemàtiques i Informàtica, ETS Arquitectura del VallèsUniversitat Politècnica de CatalunyaSant Cugat Del VallèsSpain

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