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Classification with Nominal Data Using Intuitionistic Fuzzy Sets

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Book cover Foundations of Fuzzy Logic and Soft Computing (IFSA 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4529))

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Abstract

The classical classification problem with nominal data is considered. First, to make the problem practically tractable, some transformation into a numerical (real) domain is performed using a frequency based analysis. Then, the use of a fuzzy sets based, and – in particular - an intuitionistic fuzzy sets based technique is proposed. To better explain the procedure proposed, the analysis is heavily based on an example. Importance of the results obtained for other areas exemplified by decision making and case based reasoning is mentioned.

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References

  1. Atanassov, K.: Intuitionistic Fuzzy Sets (in Bulgarian). VII ITKR Session. Sofia (Deposed in Centr. Sci.-Techn. Library of Bulg. Acad. of Sci, 1697/84) (1983)

    Google Scholar 

  2. Atanassov, K.: Intuitionistic Fuzzy Sets: Theory and Applications. Springer, Heidelberg (1999)

    MATH  Google Scholar 

  3. Bock, H.-H., Diday, E.: Analysis of Symbolic Data. Springer, Heidelberg (2000)

    Google Scholar 

  4. Cheng, V., Li, C.-H., Kowk, J.T., Li, C.-K.: Dissimilarity learning for nominal data. Pattern Recognition 37, 1471–1477 (2004)

    Article  Google Scholar 

  5. De Carvalho, F.A.T.: Proximity coefficients between Boolean symbolic objects. In: Diday, E., et al. (eds.) New Approaches in Classification and Data Analysis, pp. 387–394. Springer, Heidelberg (1994)

    Google Scholar 

  6. De Carvalho, F.A.T.: Extension based proximities between Boolean symbolic objects. In: Hayashi, C., et al. (eds.) Data Science, Classification and Related Methods, pp. 370–378. Springer, Tokyo (1998)

    Google Scholar 

  7. De Carvalho, F.A.T., Souza, R.M.C.: Statistical proximity functions of Boolean symbolic objects based on histograms. In: Rizzi, A., Vichi, M., Bock, H.-H. (eds.) Advances in Data Science and Classification, pp. 391–396. Springer, Heidelberg (1998)

    Google Scholar 

  8. Fisher, D., Langley, P.: Conceptual Clustering and its Relation to Numerical Taxonomy. Addison-Wesley Longman, Boston (1986)

    Google Scholar 

  9. Fountoukis, S.G., Bekasos, M.P., Kontos, J.P.: Rule extraction from decision trees with complex nominal data. Neural, Parallel & Scient. Comput. 9, 119–128 (2001)

    MATH  Google Scholar 

  10. Goodall, D.W.: A new similarity index based on probability. Biometrics 22, 882–907 (1966)

    Article  Google Scholar 

  11. Ichino, M., Yaguchi, H.: Generalized Minkowsky metrics for mixed feature type data analysis. IEEE Trans. on Syst., Man and Cybern. 24, 698–708 (1994)

    Article  MathSciNet  Google Scholar 

  12. Ichino, M., Yaguchi, H., Diday, E.: A fuzzy symbolic pattern classifier. In: Diday, E., et al. (eds.) Ordinal and Symbolic Data Analysis, pp. 92–102. Springer, Heidelberg (1996)

    Google Scholar 

  13. Li, C., Biswas, G.: Unsupervised learning with mixed numeric and nominal data. IEEE Trans. On Knowledge and Data Eng. 14(4), 673–690 (2002)

    Article  Google Scholar 

  14. Narazaki, H., Ralescu, A.: Iterative induction of a category membership function. Int. J. of Uncert. Fuzziness and Knowledge-Based Systems 2(1), 91–100 (1994)

    Article  MathSciNet  Google Scholar 

  15. Quinlan, J.R.: Induction of decision trees. Machine Learning 1, 81–106 (1986)

    Google Scholar 

  16. Szmidt, E., Baldwin, J.: Intuitionistic Fuzzy Set Functions, Mass Assignment Theory, Possibility Theory and Histograms. In: 2006 IEEE World Congress on Computational Intelligence, pp. 237–243 (2006)

    Google Scholar 

  17. Szmidt, E., Kacprzyk, J.: Distances between intuitionistic fuzzy sets. Fuzzy Sets and Systems 114(3), 505–518 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  18. Szmidt, E., Kacprzyk, J.: Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems 118(3), 467–477 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  19. Szmidt, E., Kacprzyk, J.: Similarity of intuitionistic fuzzy sets and the Jaccard coefficient. In: Proc. IPMU 2004, Perugia, pp. 1405–1412 (2004)

    Google Scholar 

  20. Szmidt, E., Kacprzyk, J.: Distances Between Intuitionistic Fuzzy Sets: Straightforward Approaches may not work. In: 3rd Int. IEEE Conf. Intelligent Systems, pp. 716–721 (2006)

    Google Scholar 

  21. Szmidt, E., Kacprzyk, J.: An Application of Intuitionistic Fuzzy Set Similarity Measures to a Multi-criteria Decision Making Problem. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Żurada, J.M. (eds.) ICAISC 2006. LNCS (LNAI), vol. 4029, pp. 314–323. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  22. Yamada, K.: Probability–Possibility Transformation Based on Evidence Theory. In: IFSA–NAFIPS’2001, Vancouver, pp. 70–75 (2001)

    Google Scholar 

  23. Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  24. Zadrożny, S.: Imprecise queries and linguistic summarisation of the data bases (in Polish). Exit Publishers, Warsaw (2006)

    Google Scholar 

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Patricia Melin Oscar Castillo Luis T. Aguilar Janusz Kacprzyk Witold Pedrycz

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Szmidt, E., Kacprzyk, J. (2007). Classification with Nominal Data Using Intuitionistic Fuzzy Sets. In: Melin, P., Castillo, O., Aguilar, L.T., Kacprzyk, J., Pedrycz, W. (eds) Foundations of Fuzzy Logic and Soft Computing. IFSA 2007. Lecture Notes in Computer Science(), vol 4529. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72950-1_8

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  • DOI: https://doi.org/10.1007/978-3-540-72950-1_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72917-4

  • Online ISBN: 978-3-540-72950-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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