Abstract:

Abstract The classification problem is the assignment an object with certain features to one of classes. Various engineering, management, economic, political, medical, sport, and other problems are reduced to classification. In fuzzy classifiers «inputs – output» relation is described by linguistic rules. Antecedents of these rules contain fuzzy terms «low», «average», «high» etc. To increase the correctness it is necessary to tune the fuzzy classifier on experimental data. The new criteria for fuzzy classifier learning that take into account the difference of membership degrees to the main competitors only are proposed. When the classification is correct, the main competitor of the decision is the class with the second largest membership degree. In cases of misclassification the wrong decision is the main competitor to the correct class. Computer experiments with learning the fuzzy classifier of 3 kinds of Italian wines recognition showed a significant advantage of the new criteria. Among new learning criteria the criterion in the form of squared distance between main competitors with the penalty for wrong decision has minor advantage. New criteria can be used not only for tuning fuzzy classifiers but for tuning some other models, such as neural networks. References Kuncheva L. I. Fuzzy classifier design / L. I. Kuncheva //Studies in Fuzziness and Soft Computing. – Berlin – Heidelberg: Springer- Verlag, 2000. – Vol. 49. – 314 p. 2. Shtovba S. Analyzing the criteria for fuzzy classifier learning / S. Shtovba, O. Pankevich, A. Nagorna // Automatic Control and Computer Sciences. – 2015. – Vol. 49, № 3. – P. 123–132. 3. Madala H. R. Inductive learning algorithms for complex systems modeling / H. R. Madala, A. G. Ivakhnenko. – Boca Raton : CRC Press, 1994. – 368 p. 4. Bellman R. Abstraction and pattern classification / R. Bellman, R. Kalaba, L. Zadeh // Journal of Mathematical Analysis and Applications. – 1966. – Vol. 13, № 1. – P. 1–7. 5. Construction of fuzzy classification systems with rectangular fuzzy rules using genetic algorithms / [Ishibuchi H., Nozaki K., Yamomoto N., Tanaka H.] // Fuzzy sets and systems. – 1994. – Vol. 65, № 2. – P. 237–253. 6. Ishibuchi H. Classification and modeling with linguistic information granules: advanced approaches advanced approaches to linguistic data mining / H. Ishibuchi, T. Nakashima, M. Nii. – Berlin-Heidelberg : Springer-Verlag, 2005. – 307 p. 7. Штовба С. Д. Порівняння критеріїв навчання нечіткого класифікатора / С. Д. Штовба // Вісник Вінницького політехнічного інституту. – 2007. – № 6. – С. 84–91. 8. Abe S. Tuning of a fuzzy classifier derived from data / S. Abe, M. S. Lan, R. Thawonmas // International Journal of Approximate Reasoning. – 1996. – Vol. 14. – P. 1–24. 9. Nauck D. A neuro-fuzzy method to learn fuzzy classification rules from data / D. Nauck, R. Kruse // Fuzzy Sets and Systems. – 1997. – Vol. 89, № 3. – P. 277–288. 10. Rotshtein A. P. Design and Tuning of Fuzzy If – Then Rules for Automatic Classification / A. P. Rotshtein, D. I. Katelnikov // Proc. of NAFIPS’98 – International Conf. «Annual Meeting of North American Fuzzy Information Processing Society», Tampa, USA, 1998. – P. 50–55.

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