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On Bilateral Matching between Multisets

  • Maciej KrawczakEmail author
  • Grażyna Szkatuła
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 400)

Abstract

In the paper we defined a new measure of remoteness between multisets. The development of the measure is based on the definition of sets perturbation originally developed by the authors. The sets perturbation definition is here extended to multisets perturbation, it means perturbation of one multiset by another multiset and/or vice-versa. In general these two measures are different, it means asymmetrical, and therefore can be called the bilateral measure of matching between two multisets. Therefore the measure cannot be considered as a distance between multisets.

Keywords

Multisets Nominal values Measure of remoteness Measure of perturbation 

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References

  1. 1.
    Abo-Tabl, A.E.-S.: Topological approximations of multisets. Journal of the Egyptian Mathematical Society 21, 123–132 (2013)CrossRefMathSciNetzbMATHGoogle Scholar
  2. 2.
    Girish, K.P., Sunil, J.J.: Multiset topologies induced by multiset relations. Information Sciences 188, 298–313 (2012)CrossRefMathSciNetzbMATHGoogle Scholar
  3. 3.
    Krawczak, M., Szkatuła, G.: On perturbation measure of clusters: application. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part II. LNCS, vol. 7895, pp. 176–183. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  4. 4.
    Krawczak, M., Szkatuła, G.: An approach to dimensionality reduction in time series. Information Sciences 260, 15–36 (2014)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Krawczak, M., Szkatuła, G.: On Perturbation Measure of Sets – Properties. Journal of Automation, Mobile Robotics & Intelligent Systems 8, 41–44 (2014)CrossRefGoogle Scholar
  6. 6.
    Krawczak, M., Szkatuła, G.: On asymmetric matching between sets. Information Sciences 312, 89–103 (2015)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Petrovsky, A.B.: Cluster analysis in multiset spaces. In: Goldevsky, M., Mayr, H. (eds.) Information Systems Technology and its Applications, pp. 199–206. Gesellschaft fur Informatik, Bonn (2003)Google Scholar
  8. 8.
    Petrovsky, A.B.: Methods for the Group Classification of multi-attribute Objects. Scientific and Technical Information Processing 37(5), 357–368 (2010)CrossRefGoogle Scholar
  9. 9.
    Singh, D., Ibrahim, A.M., Yohanna, T., Singh, J.N.: A systematization of fundamentals of multisets. Lecturas Matematicas 29, 33–48 (2008)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Singh, D., Ibrahim, A.M., Yohanna, T., Singh, J.N.: An overview of the applications of multisets. Novi Sad J. Math. 37(2), 73–92 (2007)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Systems Research InstitutePolish Academy of SciencesWarsawPoland
  2. 2.Warsaw School of Information TechnologyWarsawPoland

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