Abstract
This paper presents type-2 fuzzy decision trees (T2FDTs) that employ type-2 fuzzy sets as values of attributes. A modified fuzzy double clustering algorithm is proposed as a method for generating type-2 fuzzy sets. This method allows to create T2FDTs that are easy to interpret and understand. To illustrate performace of the proposed T2FDTs and in order to compare them with results obtained for type-1 fuzzy decision trees (T1FDTs), two benchmark data sets, available on the internet, have been used.
This work was partly supported by the Foundation for Polish Science (Professorial Grant 2005-2008) and the Polish State Committee for Scientific Research (Grant N518 035 31/3292), Special Research Project 2006-2009, Polish-Singapore Research Project 2008-2010, Research Project 2008-2010.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Adamo, J.M.: Fuzzy decision trees. Fuzzy Sets and Systems 4, 207–219 (1980)
Bezdek, C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York (1981)
Bartczuk, Ł., Rutkowska, D.: The new version of Fuzzy-ID3 algorithm. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Żurada, J.M. (eds.) ICAISC 2006. LNCS (LNAI), vol. 4029, pp. 1060–1070. Springer, Heidelberg (2006)
Bartczuk Ł., Rutkowska D., Fuzzy decision trees of type-2, in: Some Aspects of Computer Science. EXIT Academic Publishing House, Warsaw, Poland (2007) (in Polish)
Bilski, J.: The UD RLS algorithm for training feedforward neural networks. International Journal of Applied Mathematics and Computer Science 15(1), 115–123 (2005)
Blake, C., Keogh, E., Merz, C.: UCI repository of machine learning databases
Canfora, G., Troiano, L.: Fuzzy ordering of fuzzy numbers. In: Proc. Fuzz-IEEE, Budapest, Ungheria, pp. 669–674 (2004)
Castellano, G., Fanelli, A.M., Mencar, C.: A double-clustering approach for interpretable granulation of data. In: Proc. IEEE International Conference on Systems, Man and Cybernetics, pp. 483–487 (2002)
Czekalski, P.: Evolution-Fuzzy rule based system with parameterized consequences. International Journal of Applied Mathematics and Computer Science 16(3), 373–385 (2006)
Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications. Academic Press, San Diego (1980)
Haykin, S.: Neural Networks: A Comprehensive Foundation, Macmilan (1994)
Hwang., C., Rhee, F.C.-H.: Uncertain fuzzy clustering: interval type-2 fuzzy approach to C-Means. IEEE Transactions on Fuzzy Systems 15(1), 107–120 (2007)
Jager, R.: Fuzzy Logic in Control, Ph.D. Dissertation, Technische Universiteit Delft (1995)
Janikow, C.Z.: Fuzzy decision trees: issues and methods. IEEE Transactions on Systems, Man, and Cybernetics 28(3), 1–14 (1998)
Janikow, C.Z.: Exemplar learning in fuzzy decision trees. In: Proc. IEEE International Conference on Fuzzy Systems, Piscataway, NJ, pp. 1500–1505 (1996)
Łȩski, J., Henzel, N.: A neuro-nuzzy system based on logical interpretation of if-then rules. International Journal of Applied Mathematics and Computer Science 10(4), 703–722 (2000)
Mendel, J.M.: Uncertain Rule-Based Fuzzy Logic Systems - Introduction and new directions. Prentice Hall PTR, Englewood Cliffs (2001)
Quinlan, J.R.: Induction of decision trees. Machine Learning 1, 81–106 (1986)
Quinlan, J.R.: C4.5: Programs for Machine Learning. Morgan Kaufmann Publishers, Inc., Los Altos (1993)
Quinlan, J.R.: Learning with continuous classes. In: Proc. 5th Australian Joint Conference on Artificial Intelligence, pp. 343–348. World Scientific, Singapore (1992)
Piegat, A.: Fuzzy Modeling and Control. Physica-Verlag (2001)
Rutkowska, D.: Neuro-Fuzzy Architectures and Hybrid Learning. Physica-Verlag, Springer, New York (2002)
Rutkowska, D., Nowicki, R.: Implication-based neuro-fuzzy architectures. International Journal of Applied Mathematic and Computer Science 10(4), 675–701 (2000)
Rutkowski, L.: Methods and Techniques of Artificial Intelligence, PWN, Warsaw, Poland (in Polish) (2005)
Yager, R.R.: Ranking fuzzy subsets over the unit interval. In: Proc. CDC pp. 1435–1437 (1978)
Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)
Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning - I. Information Sciences 8, 199–249 (1975)
Żurada, J.M.: Introduction to Artificial Nueral Systems. West Publishing Company (1992)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bartczuk, Ł., Rutkowska, D. (2008). Type-2 Fuzzy Decision Trees. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing – ICAISC 2008. ICAISC 2008. Lecture Notes in Computer Science(), vol 5097. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69731-2_20
Download citation
DOI: https://doi.org/10.1007/978-3-540-69731-2_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69572-1
Online ISBN: 978-3-540-69731-2
eBook Packages: Computer ScienceComputer Science (R0)