# A fuzzy if-then rule-based nonlinear classifier

International Journal of Applied Mathematics and Computer Science (2003)

- Volume: 13, Issue: 2, page 215-223
- ISSN: 1641-876X

## Access Full Article

top## Abstract

top## How to cite

topŁęski, Jacek. "A fuzzy if-then rule-based nonlinear classifier." International Journal of Applied Mathematics and Computer Science 13.2 (2003): 215-223. <http://eudml.org/doc/207638>.

@article{Łęski2003,

abstract = {This paper introduces a new classifier design method that is based on a modification of the classical Ho-Kashyap procedure. The proposed method uses the absolute error, rather than the squared error, to design a linear classifier. Additionally, easy control of the generalization ability and robustness to outliers are obtained. Next, an extension to a nonlinear classifier by the mixture-of-experts technique is presented. Each expert is represented by a fuzzy if-then rule in the Takagi-Sugeno-Kang form. Finally, examples are given to demonstrate the validity of the introduced method.},

author = {Łęski, Jacek},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {classifier design; mixture of experts; fuzzy if-then rules; generalization control},

language = {eng},

number = {2},

pages = {215-223},

title = {A fuzzy if-then rule-based nonlinear classifier},

url = {http://eudml.org/doc/207638},

volume = {13},

year = {2003},

}

TY - JOUR

AU - Łęski, Jacek

TI - A fuzzy if-then rule-based nonlinear classifier

JO - International Journal of Applied Mathematics and Computer Science

PY - 2003

VL - 13

IS - 2

SP - 215

EP - 223

AB - This paper introduces a new classifier design method that is based on a modification of the classical Ho-Kashyap procedure. The proposed method uses the absolute error, rather than the squared error, to design a linear classifier. Additionally, easy control of the generalization ability and robustness to outliers are obtained. Next, an extension to a nonlinear classifier by the mixture-of-experts technique is presented. Each expert is represented by a fuzzy if-then rule in the Takagi-Sugeno-Kang form. Finally, examples are given to demonstrate the validity of the introduced method.

LA - eng

KW - classifier design; mixture of experts; fuzzy if-then rules; generalization control

UR - http://eudml.org/doc/207638

ER -

## References

top- Abe S. and Lan M.-S. (1995): A method for fuzzy rules extraction directly from numerical data and its application to pattern classification. - IEEE Trans. Fuzzy Syst., Vol. 3, No. 1, pp. 18-28.
- Bellman R., Kalaba K. and Zadeh L.A. (1966): Abstraction and pattern classification. - J. Math. Anal. Appl., Vol. 13, No. 1, pp. 1-7. Zbl0134.15305
- Bezdek J.C. (1982): Pattern Recognition with Fuzzy Objective Function Algorithms. - New York: Plenum Press. Zbl0503.68069
- Bezdek J.C. and Pal S.K. (Eds.) (1992): Fuzzy Models for Pattern Recognition. - New York: IEEE Press.
- Bezdek J.C., Reichherzer T.R., Lim G.S. and Attikiouzel Y.(1998): Multiple-prototype classifier design. - IEEE Trans.Syst. Man Cybern., Part C, Vol. 28, No. 1, pp. 67-78.
- Czogal a E. and L ęski J.M. (2000): Fuzzy and Neuro-Fuzzy Intelligent Systems. - Heidelberg: Physica-Verlag.
- Duda R.O. and Hart P.E. (1973): Pattern Classification and Scene Analysis. - New York: Wiley. Zbl0277.68056
- Herbrich R., Graepel T. and Campbell C. (2001): Bayes point machines. - J. Mach. Res., Vol. 1, No. 2, pp. 245-279. Zbl1008.68104
- Ho Y.-C. and Kashyap R.L. (1965): An algorithmfor linear inequalities and its applications. - IEEE Trans. Elec. Comp., Vol. 14, No. 5, pp. 683-688. Zbl0173.17902
- Ho Y.-C. and Kashyap R.L. (1966): A class of iterative procedures for linear inequalities. - J. SIAM Contr., Vol. 4, No. 2, pp. 112-115. Zbl0143.37503
- Ishibuchi H., Nakashima T. and Murata T. (1999): Performance evaluation of fuzzy classifier systems for multidimensional pattern classification problems. - IEEE Trans. Syst. Man Cybern., Part B, Vol. 29, No. 5, pp. 601-618.
- Huber P.J. (1981): Robust Statistics. - New York: Wiley. Zbl0536.62025
- Keller J.M., Gray M.R. and Givens J.A. (1985): Afuzzy k-nearest neighbors algorithm. - IEEE Trans. Syst. Man Cybern., Vol. 15, No. 3, pp. 580-585.
- Krishnapuram R. and Keller J.M. (1993): A possibilistic approach to clustering. - IEEE Trans. Fuzzy Syst., Vol. 1, No. 2, pp. 98-110.
- Kim E., Park M., Ji S. and Park M. (1997): A new approach to fuzzy modeling. - IEEE Trans. Fuzzy Syst., Vol. 5, No. 3, pp. 328-337.
- Kuncheva L.I. and Bezdek J.C. (1999): Presupervised and postsupervised prototype classifier design. - IEEE Trans. Neural Netw., Vol. 10, No. 5, pp. 1142-1152.
- Kuncheva L.I. (2000a): How good are fuzzy if-then classifiers? - IEEE Trans. Syst. Man Cybern., Part B, Vol. 30, No. 4, pp. 501-509.
- Kuncheva L.I. (2000b): Fuzzy Classifier Design.- Heidelberg: Physica-Verlag. Zbl0992.68183
- Kuncheva L.I. (2001): Using measures of similarity and inclusion for multiple classifier fusion by decision templates. -Fuzzy Sets Syst., Vol. 122, No. 3, pp. 401-407. Zbl1006.68127
- Kuncheva L.I. (2002): Switching between selection and fusion in combining classifiers: An experiment. - IEEE Trans. Syst. Man Cybern.. Part B, Vol. 32, No. 2, pp. 146-156.
- Łęski J. and Henzel N. (2001): A neuro-fuzzy system based on logical interpretation of if-then rules, In: Fuzzy Learning and Applications (Russo M. and Jain L.C., Eds.). - New York: CRC Press, pp. 359-388. Zbl0972.68135
- Łęski J. (2002): Robust weighted averaging.- IEEE Trans. Biomed. Eng., Vol. 49, No. 8, pp. 796-804.
- Malek J.E., Alimi A.M. and Tourki R. (2002): Problems in pattern classification in high dimensional spaces: Behavior of aclass of combined neuro-fuzzy classifiers. - Fuzzy Sets Syst., Vol. 128, No. 1, pp. 15-33. Zbl1002.68550
- Mangasarian O.L. and Musicant D.R. (2000): Lagrangian support vector machines. - Technical Report 00-06, Data Mining Institute, Computer Sciences Department, University of Wisconsin, Madison, available at ftp://ftp.cs.wisc.edu/pub/dmi/tech-reports/00-06.ps Zbl0997.68108
- Marin-Blazquez J. and Shen Q. (2002): From approximative to descriptive fuzzy classifiers. - IEEE Trans. FuzzySyst., Vol. 10, No. 4, pp. 484-497.
- Miller D., Rao A.V., Rose K. and Gersho A. (1996): A global optimization technique for statistical classifier design.- IEEE Trans. Signal Process., Vol. 44, No. 12, pp. 3108-3121.
- Nath A.K. and Lee T.T. (1982): On the design of a classifier with linguistic variables as inputs. - Fuzzy Sets Syst., Vol. 11, No. 2, pp. 265-286. Zbl0538.68069
- Ripley B.D. (1996): Pattern Recognition and Neural Networks. - Cambridge: Cambridge University Press. Zbl0853.62046
- Runkler T.A. and Bezdek J.C. (1999): Alternating cluster estimation: A new tool for clustering and function approximation.- IEEE Trans. Fuzzy Syst., Vol. 7, No. 4, pp. 377-393.
- Rutkowska D. (2002): Neuro-Fuzzy Architectures and Hybrid Learning. - Heidelberg: Physica-Verlag. Zbl1005.68127
- Setnes M. and Babuvska R. (1999): Fuzzy relational classifier trained by fuzzy clustering. - IEEE Trans. Syst. Man Cybern., Part B, Vol. 29, No. 5, pp. 619-625.
- Tipping M.E. (2001): Sparse Bayesian learning andthe relevance vector machine. - J. Mach. Res., Vol. 1, No. 2, pp. 211-244. Zbl0997.68109
- Tou J.T. and Gonzalez R.C. (1974): Pattern Recognition Principles. - London: Addison-Wesley. Zbl0299.68058
- Vapnik V. (1998): Statistical Learning Theory. -New York: Wiley. Zbl0935.62007
- Vapnik V. (1999): An overview of statistical learning theory. - IEEE Trans. Neural Netw., Vol. 10, No. 5, pp. 988-999.
- Webb A. (1999): Statistical Pattern Recognition.- London: Arnold. Zbl0968.68540

## Citations in EuDML Documents

top- Norbert Jankowski, Graph-based generation of a meta-learning search space
- Hoai Linh Tran, Van Nam Pham, Hoang Nam Vuong, Multiple neural network integration using a binary decision tree to improve the ECG signal recognition accuracy
- Łukasz Bartczuk, Andrzej Przybył, Krzysztof Cpałka, A new approach to nonlinear modelling of dynamic systems based on fuzzy rules

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.