Learning Membership Functions for Fuzzy Sets through Modified Support Vector Clustering

  • Dario Malchiodi
  • Witold Pedrycz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8256)


We propose an algorithm for inferring membership functions of fuzzy sets by exploiting a procedure originated in the realm of support vector clustering. The available data set consists of points associated with a quantitative evaluation of their membership degree to a fuzzy set. The data are clustered in order to form a core gathering all points definitely belonging to the set. This core is subsequently refined into a membership function. The method is analyzed and applied to several real-world data sets.


Membership Function Membership Grade Information Granule Obese Class Machine Learn Research 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Dubois, D., Prade, H.: The three semantics of fuzzy sets. Fuzzy Sets and Systems 90, 141–150 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Pedrycz, W.: Granular Computing: Analysis and Design of Intelligent Systems. CRC Press/Francis Taylor, Boca Raton (2013)CrossRefGoogle Scholar
  3. 3.
    Nguyen, H., Walker, E.: A First Course in Fuzzy Logic. Chapman Hall, CRC Press, Boca Raton (1999)Google Scholar
  4. 4.
    Pedrycz, W.: Why triangular membership functions? Fuzzy Sets & Systems 64, 21–30 (1994)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Linde, Y., Buzo, A., Gray, R.: An algorithm for vector quantizer design. IEEE Transactions on Communications COM-28(1), 84–95 (1988)Google Scholar
  6. 6.
    Ben-Hur, A., Horn, D., Siegelmann, H.T., Vapnik, V.: Support vector clustering. Journal of Machine Learning Research 2, 125–137 (2001)Google Scholar
  7. 7.
    Fletcher, R.: Practical methods of optimization, 2nd edn. Wiley-Interscience, New York (1987)zbMATHGoogle Scholar
  8. 8.
    Guyon, I., Saffari, A., Dror, G., Cawley, G.: Model selection: Beyond the bayesian/frequentist divide. J. of Machine Learning Research 11, 61–87 (2010)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Evangelista, P.F., Embrechts, M.J., Szymanski, B.K.: Some properties of the gaussian kernel for one class learning. In: Marques de Sá, J., Alexandre, L.A., Duch, W., Mandic, D.P. (eds.) ICANN 2007. LNCS, vol. 4668, pp. 269–278. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  10. 10.
    Consultation, W.E.: Appropriate body-mass index for asian populations and its implications for policy and intervention strategies. Lancet 363(9403), 157–163 (2004)CrossRefGoogle Scholar
  11. 11.
    McDowell, M.A., Fryar, C., Ogden, C.L., Flegal, K.M.: Anthropometric reference data for children and adults: United states, 2003–2006. National health statistics reports, vol. 10. National Center for Health Statistics, Hyattsville, MD (2008), accessed (May 2012)
  12. 12.
    Fisher, R.A.: The use of multiple measurements in taxonomic problems. Annals of Eugenics 7(2), 179–188 (1936)CrossRefGoogle Scholar
  13. 13.
    Abdi, H., Williams, L.J.: Principal component analysis. Wiley Interdisciplinary Reviews: Computational Statistics 2, 433–459 (2010)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Dario Malchiodi
    • 1
  • Witold Pedrycz
    • 2
  1. 1.Università degli Studi di MilanoItaly
  2. 2.University of AlbertaCanada

Personalised recommendations