Paper:

# Constructing Cost-Sensitive Fuzzy-Rule-Based Systems for Pattern Classification Problems

## Tomoharu Nakashima^{*}, Yasuyuki Yokota^{*}, Hisao Ishibuchi^{*},

Gerald Schaefer^{**}, Aleš Drastich^{***}, and Michal Závišek^{***}

^{*}Department of Computer Science and Intelligent Systems, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531, Japan

^{**}School of Engineering and Applied Science, Aston University, Aston Triangle, Birmingham B4 7ET, U.K.

^{***}Faculty of Electrical Engineering and Communication, Brno University of Technology, 61200 Brno, Královo Pole, Kolejní 4, Czech Republic

We evaluate the performance of cost-sensitive fuzzy-rule-based systems for pattern classification problems. We assume that a misclassification cost is given a priori for each training pattern. The task of classification thus becomes to minimize both classification error and misclassification cost. We examine the performance of two types of fuzzy classification based on fuzzy if-then rules generated from training patterns. The difference is whether or not they consider misclassification costs in rule generation. In our computational experiments, we use several specifications of misclassification cost to evaluate the performance of the two classifiers. Experimental results show that both classification error and misclassification cost are reduced by considering the misclassification cost in fuzzy rule generation.

Gerald Schaefer, Aleš Drastich, and Michal Závišek, “Constructing Cost-Sensitive Fuzzy-Rule-Based Systems for Pattern Classification Problems,”

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.11, No.6, pp. 546-553, 2007.

- [1] C. C. Lee, “Fuzzy Logic in Control Systems: Fuzzy Logic Controller Part I and Part II,” IEEE Trans. Syst., Man, Cyberetics, Vol.20, pp. 404-435, 1990.
- [2] C. T. Leondes, “Fuzzy theory Systems,” Techniques and Applications. Academic Press, San Diego, Vol.1-4, 1999.
- [3] M. Sugeno, “An Introductory Survey of Fuzzy Control,” Information Science, Vol.30, No.1/2, pp. 59-83, 1985.
- [4] H. Ishibuchi, T. Nakashima, and M. Nii, “Fuzzy IF-THEN Rules for Pattern Classification,” Fuzzy If-Then Rules in Computational Intelligence: Theory and Applications, Kluwer Academic Publishers, pp. 267-295, May, 2000.
- [5] H. Ishibuchi, T. Nakashima, and T. Morisawa, “Voting in Fuzzy Rule-Based Systems for Pattern Classification Problems,” Fuzzy Sets and Systems, Vol.103, No.2, pp.223-238, April, 1999.
- [6] H. Ishibuchi and T. Nakashima, “Performance evaluation of fuzzy classifier systems for multi-dimensional pattern classification problems,” IEEE Trans. on Syst., Man, Cybernetics, Part B, Vol.29, pp. 601-618, 1999.
- [7] H. Ishibuchi and T. Nakashima, “Improving the performance of fuzzy classifier systems for pattern classification problems with continuous attributes,” IEEE Trans. on Industrial Electronics, Vol.46, No.6, pp. 1057-1068, 1999.
- [8] H. Ishibuchi, K. Nozaki, N. Yamamoto, and H. Tanaka, “Selecting fuzzy if-then rules for classification problems using genetic algorithms,” IEEE Trans. on Fuzzy Systems, Vol.3, No.3, pp. 260-270, 1995.
- [9] Y. Yuan and H. Zhang, “A genetic algorithms for generating fuzzy classification rules,” Fuzzy Sets and Systems, Vol.84, No.1, pp. 1-19, 1996.
- [10] R. O. Duda, P. E. Hart, and D. G. Stork, “Pattern Classification,” Wiley Interscience, 2001.
- [11] P. Domingos, “Metacost: A General Method for Making Classifiers Cost Sensitive,” In Proceedings Fifth International Conference on Knowledge Discovery and Data Mining, pp. 155-164, 1999.
- [12] S. Beck, R. Mikut, and J. Jakel, “A Cost-Sensitive Learning,” Algorithm for Fuzzy Rule – Based Classifiersh Mathware & soft computing, Vol.11, No.2/3, pp. 179-195, 2005.
- [13] K. Nozaki, H. Ishibuchi, and H. Tanaka, “Adaptive fuzzy rule-based classification systems,” IEEE Trans. on Fuzzy Systems, Vol.4, No.3, pp. 238-250, 1996.
- [14] G. J. Klir and B. Yuan, “Fuzzy Sets and Fuzzy Logic,” Prentice-Hall, 1995.
- [15] H. Ishibuchi, K. Nozaki, and H. Tanaka, “Distributed representation of fuzzy rules and its application to pattern classification,” Fuzzy Sets and Systems, Vol.52, No.1, pp. 21-32, 1992.
- [16] M. Grabisch, “The representation of importance and interaction of features by fuzzy measures,” Pattern Recognition Letters, Vol.17, pp. 567-575, 1996.
- [17] M. Grabisch and F. Dispot, “A comparison of some methods of fuzzy classification on real data,” Proc. of 2nd Intl. Conf. on Fuzzy Logic and Neural Networks, pp. 659-662, 1992.
- [18] M. Grabisch and J.-M. Nicolas, “Classification by fuzzy integral: performance and tests,” Fuzzy Sets and Systems, Vol.65, No.2/3, pp. 255-271, 1994.
- [19] H. Ishibuchi and T. Nakashima, “The Effect of rule weights in fuzzy rule-based classification systems,” IEEE Trans. on Fuzzy Systems, Vol.9, No.4, pp. 506-515, 2001.
- [20] D. J. Newman, S. Hettich, C. L. Blake, and C. J. Merz, UCI Repository of machine learning databases, 1998.