Uni-norm Fuzzy Pattern Trees for Evolving Classification by Imperialist Competitive Algorithm

Volume 4, Issue 3, pp 502--513 http://dx.doi.org/10.22436/jmcs.04.03.25

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Authors

S. Rajaeipour - Department of Industrial Engineering, Shomal University of Amol, Iran G. Shojatalab - Department of Industrial Engineering, Shomal University of Amol, Iran

Abstract

Fuzzy pattern trees induction was recently introduced as a novel machine learning method for classification. Roughly speaking, a pattern tree is a hierarchical, tree-like structure, whose inner nodes are marked with generalized fuzzy logical or arithmetic operators and whose leaf nodes are associated with fuzzy predicates on input attributes. Operators perform an important role in fuzzy pattern trees. These operators include arithmetic and logical operators. Unlike arithmetic operators,logical operators that were used in these trees are not parameterized. As arithmetic operators, we can choose weighted arithmetic mean and ordered weighted arithmetic mean. There are several families which contain the standard triangular norms and conorms as special cases. This way, we would implicitly select from an infinite number of operators, just like in the case of arithmetic operators. We develop this algorithm by proposing a method to using parameterized logical operators and tuning their parameters by imperialist competitive algorithm. In experimental studies, we compare our method to previous version of algorithm, showing that our method is significantly outperformsthe previous method in terms of predictive accuracy andflexibilityin operator selection.

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Keywords

• machine learning
• classification
• fuzzy operators
• parameter tuning

MSC

•  90C27
•  90C59
•  68T05
•  03E72

References

• [1] Z. Huang, Tamas D. Gedeon, M. Nikravesh, Pattern Trees Induction: A New Machine Learning Method, IEEE Transactions on Fuzzy Systems, 16 (2008), 958--970
  • View Article
  • Google Scholar


• [2] Y. Yi, T. Fober, E. Hullermeier, Fuzzy operator trees for modeling rating functions, International Journal of Computational Intelligence and Applications, 8 (2008), 413--428
  • View Article
  • Google Scholar


• [3] R. Senge, E. Hullermeier, Top-Down Induction of fuzzy Pattern Trees, IEEE Transactions On Fuzzy Systems, Vol. 19, 241--252, (2010)
  • View Article
  • Google Scholar


• [4] R. Senge, E. Hullermeier, Pattern Trees for Regression and Fuzzy Systems Modeling, World Congress on Computational, 1--7 (2010)
  • View Article
  • Google Scholar


• [5] B. Schweizer, A. Sklar, Probabilistic Metric Spaces, North-Holland, New York (1983)
  • Google Scholar


• [6] R. Yager, On ordered weighted averaging aggregation operators in multi criteria decision making, IEEE Transactions on Systems, Man and Cybernetics, 18 (1988), 183--190
  • View Article
  • Google Scholar


• [7] E. P. Klement, R. Mesiar, E. Pap, Triangular Norms, Kluwer Academic Publishers, New York (2000)
  • View Article
  • Google Scholar


• [8] J. R. Quinlan, Decision trees and decision making, IEEE Transactions on Systems, Man, and Cybernetics, 20 (1990), 185--208
  • View Article
  • Google Scholar


• [9] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338--353
  • View Article
  • Google Scholar


• [10] D. Dubois, H. Prade, A review of fuzzy set aggregation connectives, Inform. Sci., 36 (1985), 85--121
  • View Article
  • Google Scholar


• [11] G. Klir, T. Folger, Fuzzy sets, uncertainty, and information, Prentice-Hall, Englewood Cliffs (1988)
  • View Article
  • Google Scholar


• [12] H-X. Li, V. C. Yen, Fuzzy sets and fuzzy decision-making, CRC Press, Boca Raton (1995)
  • View Article
  • Google Scholar


• [13] H. J. Zimmermann, Fuzzy Set Theory and its Applications, Kiuwer Academic Publishers, Massachusetts (1991)
  • Google Scholar


• [14] H-J. Zimmermann, P. Zysno, Latent connectives in human decision making, Fuzzy Sets and Systems, 4 (1980), 37--51
  • View Article
  • Google Scholar


• [15] G. Beliakov, Numerical construction of membership functions and aggregation operators from empirical data, Proceedings of the Third International Conference on Information Fusion, 143--154 (2000)
  • View Article
  • Google Scholar


• [16] H. Dyckhoff, W. Pedrycz, Generalized means as model of compensative connectives, Fuzzy Sets and Systems, 14 (1984), 143--154
  • View Article
  • Google Scholar


• [17] G. Beliakov, How to build aggregation operators from data, International Journal Of Intelligent Systems, 18 (2003), 903--923
  • View Article
  • Google Scholar


• [18] E. Atashpaz Gargari, C. Lucas, Imperialist Competitive Algorithm: An Algorithm for Optimization Inspired by Imperialistic Competition, IEEE Congress on Evolutionary Computation (CEC 2007), 2007 (2007), 4661--4667
  • View Article
  • Google Scholar


• [19] http://archive.ics.uci.edu/ml/datasets.html, Machine Learning Repository, UCI University, ()
  • View Article


• [20] http://www.mathworks.com/products/matlab/, MATHWORKS, , ()
  • View Article


• [21] W. H. Kruskal, W. A. Wallis, Use of ranks in one-criterion variance analysis, American Statistical Association, 47 (1952), 583--621
  • View Article
  • Google Scholar


• [22] J. Jaccard, M. A. Becker, G. Wood, Pairwise multiple comparison procedures: A review, Psychological Bulletin, 96 (1984), 589--596
  • View Article
  • Google Scholar


• [23] R. R. Yager, A. Rybalov, Uninorm aggregation operators, Fuzzy Sets and Systems, 80 (1996), 111--120
  • View Article
  • Google Scholar