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
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)
Atanassov, K.: Intuitionistic Fuzzy Sets: Theory and Applications. Springer, Heidelberg (1999)
Bock, H.-H., Diday, E.: Analysis of Symbolic Data. Springer, Heidelberg (2000)
Cheng, V., Li, C.-H., Kowk, J.T., Li, C.-K.: Dissimilarity learning for nominal data. Pattern Recognition 37, 1471–1477 (2004)
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)
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)
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)
Fisher, D., Langley, P.: Conceptual Clustering and its Relation to Numerical Taxonomy. Addison-Wesley Longman, Boston (1986)
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)
Goodall, D.W.: A new similarity index based on probability. Biometrics 22, 882–907 (1966)
Ichino, M., Yaguchi, H.: Generalized Minkowsky metrics for mixed feature type data analysis. IEEE Trans. on Syst., Man and Cybern. 24, 698–708 (1994)
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)
Li, C., Biswas, G.: Unsupervised learning with mixed numeric and nominal data. IEEE Trans. On Knowledge and Data Eng. 14(4), 673–690 (2002)
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)
Quinlan, J.R.: Induction of decision trees. Machine Learning 1, 81–106 (1986)
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)
Szmidt, E., Kacprzyk, J.: Distances between intuitionistic fuzzy sets. Fuzzy Sets and Systems 114(3), 505–518 (2000)
Szmidt, E., Kacprzyk, J.: Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems 118(3), 467–477 (2001)
Szmidt, E., Kacprzyk, J.: Similarity of intuitionistic fuzzy sets and the Jaccard coefficient. In: Proc. IPMU 2004, Perugia, pp. 1405–1412 (2004)
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)
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)
Yamada, K.: Probability–Possibility Transformation Based on Evidence Theory. In: IFSA–NAFIPS’2001, Vancouver, pp. 70–75 (2001)
Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)
Zadrożny, S.: Imprecise queries and linguistic summarisation of the data bases (in Polish). Exit Publishers, Warsaw (2006)
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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
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