Towards a Fuzzy Extension of the López de Mántaras Distance

  • Eva Armengol
  • Pilar Dellunde
  • Àngel García-Cerdaña
Part of the Communications in Computer and Information Science book series (CCIS, volume 297)


In this paper we introduce FLM, a divergence measure to compare a fuzzy and a crisp partition. This measure is an extension of LM, the López de Mántaras distance. This extension allows to handle domain objects having attributes with continuous values. This means that for some domains the use of fuzzy sets may report better results than the discretization that is the usual way to deal with continuous values. We experimented with both FLM and LM in the context of the lazy learning method called Lazy Induction of Descriptions useful for classification tasks.


Machine learning partitions fuzzy partitions entropy measures López de Mántaras distance 


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  1. 1.
    López de Mántaras, R.: A distance-based attribute selection measure for decision tree induction. Machine Learning 6, 81–92 (1991)CrossRefGoogle Scholar
  2. 2.
    Armengol, E., Plaza, E.: Lazy Induction of Descriptions for Relational Case-Based Learning. In: Flach, P.A., De Raedt, L. (eds.) ECML 2001. LNCS (LNAI), vol. 2167, pp. 13–24. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  3. 3.
    Quinlan, J.R.: Induction of decision trees. Machine Learning 1, 81–106 (1986)Google Scholar
  4. 4.
    Pfitzner, D., Leibbrandt, R., Powers, D.M.W.: Characterization and evaluation of similarity measures for pairs of clusterings. Knowledge Information Systems 19(3), 361–394 (2009)CrossRefGoogle Scholar
  5. 5.
    Armengol, E.: Discovering plausible explanations of carcinogenecity in chemical compounds. In: Perner, P. (ed.) MLDM 2007. LNCS (LNAI), vol. 4571, pp. 756–769. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  6. 6.
    Armengol, E., Puig, S.: Combining two lazy learning methods for classification and knowledge discovery. a case study for malignant melanoma diagnosis. In: Proceedings of the International Conference on Knowledge Discovery and Information Retrieval, pp. 200–207 (2011)Google Scholar
  7. 7.
    Kuwajima, I., Nojima, Y., Ishibuchi, H.: Effects of constructing fuzzy discretization from crisp discretization for rule-based classifiers. Artificial Life and Robotics 13(1), 294–297 (2008)CrossRefGoogle Scholar
  8. 8.
    Rand, W.M.: Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association 66(336), 846–850 (1971)CrossRefGoogle Scholar
  9. 9.
    Campello, R.J.G.B.: A fuzzy extension of the Rand index and other related indexes for clustering and classification assessment. Pattern Recognition Letters 28(7), 833–841 (2007)CrossRefGoogle Scholar
  10. 10.
    Hüllermeier, E., Rifqi, M.: A fuzzy variant of the Rand index for comparing clustering structures. In: Proceedings of IFSA/EUSFLAT Conference, pp. 1294–1298 (2009)Google Scholar
  11. 11.
    Armengol, E., García-Cerdaña, À.: Lazy Induction of Descriptions Using Two Fuzzy Versions of the Rand Index. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds.) IPMU 2010, Part I. CCIS, vol. 80, pp. 396–405. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  12. 12.
    Zimmermann, H.: Fuzzy Set Theory and its applications, 2nd edn. Kluver Academic Publishers (1992)Google Scholar
  13. 13.
    Asuncion, A., Newman, D.J.: UCI machine learning repository (2007)Google Scholar
  14. 14.
    Witten, I., Frank, E., Trigg, L., Hall, M., Holmes, G., Cunningham, S.: Weka: Practical machine learning tools and techniques with java implementations (1999)Google Scholar
  15. 15.
    de Luca, A., Termini, S.: A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory. Information and Control 20(4), 301–312 (1972)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Montes, S., Couso, I., Gil, P., Bertoluzza, C.: Divergence measure between fuzzy sets. International Journal Approximate Reasoning 30(2), 91–105 (2002)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Eva Armengol
    • 1
  • Pilar Dellunde
    • 1
    • 2
  • Àngel García-Cerdaña
    • 1
    • 3
  1. 1.Artificial Intelligence Research Institute (IIIA - CSIC)BellaterraSpain
  2. 2.Departament de FilosofiaUniversitat Autònoma de BarcelonaBellaterraSpain
  3. 3.Departament de Lògica, Història i Filosofia de la CiènciaUniversitat de BarcelonaBarcelonaSpain

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