Advertisement

Fuzzy Type Powerset Operators and F-Transforms

  • Jiří Močkoř
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11144)

Abstract

We introduce two types of aggregation operators for lattice-valued fuzzy sets, called fuzzy type powerset operators and fuzzy type F-transforms, which are derived from classical powerset operators and F-transforms, respectively. We prove that, in contrast with classical powerset operators, fuzzy type powerset operators form a subclass of fuzzy type F-transforms. Some examples of fuzzy type powerset operators are presented.

References

  1. 1.
    Calvo, T., Kolesárová, A., Komorníková, M., Mesiar, R.: Aggregation operators: properties, classes and construction methods. In: Calvo, T., Mayor, G., Mesiar, R. (eds.) Aggregation Operators, pp. 3–107. Physica-Verlag, Heidelberg (2002)CrossRefGoogle Scholar
  2. 2.
    Dubois, E., Prade, H.: A review of fuzzy set aggregation connectives. Inf. Sci. 36, 85–121 (1985)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University Press, Cambridge (2009)CrossRefGoogle Scholar
  4. 4.
    Höhle, U.: Many Valued Topology and its Applications. Kluwer Academic Publishers, Boston (2001)CrossRefGoogle Scholar
  5. 5.
    Močkoř, J.: Closure theories of powerset theories. Tatra Mountains Math. Publ. 64, 101–126 (2015)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Močkoř, J.: Cut systems in sets with similarity relations. Fuzzy Sets Syst. 161, 3127–3140 (2010)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Močkoř, J.: Powerset operators of extensional fuzzy sets. Iran. J. Fuzzy Syst. 15(2), 143–163 (2017)zbMATHGoogle Scholar
  8. 8.
    Močkoř, J., Holčapek, M.: Fuzzy objects in spaces with fuzzy partitions. Soft Comput. 21(24), 7269–7284 (2017)CrossRefGoogle Scholar
  9. 9.
    Močkoř, J.: Spaces with fuzzy partitions and fuzzy transform. Soft Comput. 21, 3479–3492 (2017)CrossRefGoogle Scholar
  10. 10.
    Novák, V., Perfilieva, I., Močkoř, J.: Mathematical Principles of Fuzzy Logic. Kluwer Academic Publishers, Boston (1999)CrossRefGoogle Scholar
  11. 11.
    Perfilieva, I.: Fuzzy transforms and their applications to image compression. In: Bloch, I., Petrosino, A., Tettamanzi, A.G.B. (eds.) WILF 2005. LNCS (LNAI), vol. 3849, pp. 19–31. Springer, Heidelberg (2006).  https://doi.org/10.1007/11676935_3CrossRefzbMATHGoogle Scholar
  12. 12.
    Perfilieva, I.: Fuzzy transforms: a challenge to conventional transform. In: Hawkes, P.W. (ed.) Advances in Image and Electron Physics, vol. 147, pp. 137–196. Elsevies Acad. Press, San Diego (2007)Google Scholar
  13. 13.
    Perfilieva, I., Novak, V., Dvořak, A.: Fuzzy transforms in the analysis of data. Int. J. Approximate Reasoning 48, 36–46 (2008)CrossRefGoogle Scholar
  14. 14.
    Perfilieva, I.: Fuzzy transforms: theory and applications. Fuzzy Sets Syst. 157, 993–1023 (2006)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Perfilieva, I., Singh, A.P., Tiwari, S.P.: On the relationship among \(F\)-transform, fuzzy rough set and fuzzy topology. In: Proceedings of IFSA-EUSFLAT, pp. 1324–1330. Atlantis Press, Amsterdam (2015)Google Scholar
  16. 16.
    Rodabaugh, S.E.: Powerset operator foundation for poslat fuzzy SST theories and topologies. In: Höhle, U., Rodabaugh, S.E. (eds.) Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory, The Handbook of Fuzzy Sets Series, vol. 3, pp. 91–116. Kluwer Academic Publishers, Boston (1999)Google Scholar
  17. 17.
    Rodabaugh, S.E.: Relationship of algebraic theories to powerset theories and fuzzy topological theories for lattice-valued mathematics. Int. J. Math. Math. Sci. 2007, 1–71 (2007)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Solovyov, S.A.: Powerset oeprator foundations for catalg fuzzy set theories. Iran. J. Fuzzy Syst. 8(2), 1–46 (2001)zbMATHGoogle Scholar
  19. 19.
    Takači, A.: General aggregation operators acting on fuzzy numbers induced by ordinary aggregation operators. Novi Sad J. Math. 33(2), 67–76 (2003)MathSciNetzbMATHGoogle Scholar
  20. 20.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Institute for Research and Applications of Fuzzy ModelingUniversity of OstravaOstrava 1Czech Republic

Personalised recommendations