Öz
Kaynakça
- Alefeld, G., Mayer, G., “Interval Analysis: Theory and Applications”, Journal of Computational and Applied Mathematics, 121: 421-464 (2000).
- Benedetti, J.K., “On the Nonparametric Estimation of Regression Functions”, Journal of the Royal Statistical Society Series B, 39: 248-253 (1977).
- Cheng, C.B., Lee, E.S., “Fuzzy Regression with Radial Basis Function Network”, Fuzzy Sets and Systems, 119: 291-301 (2001).
- Choi, S.W., Lee, D., Park, J.H., Lee, I.B., “Nonlinear Regression Using RBFN with Linear Submodels”, Chemometrics and Intelligent Laboratory Systems, 65: 191-208 (2003).
- Chu, C.K., Marron, J.S., “Choosing a Kernel Regression Estimator”, Statistical Science, 6(4): 404-436 (1991).
- Eubank, R.L., “Spline Smoothing and
- Nonparametric Regression”, Marcel Dekker Inc., New York, 1-8 (1988).
- Fu, L., “Neural Networks in Computer Intelligence”, McGraw Hill Inc., Singapure, 94-98 (1996).
- Gamgam, H., “Parametrik Olmayan İstatistiksel Teknikler”, Gazi Üniversitesi, Fen-Edebiyat Fakültesi Yayınları, Ankara, 232-249 (1998).
- Gürbüz, Ü., Doğruer, Y., Nizamlıoğlu, M., “Pastırma Üretiminde Dumanlama İşleminin Uygulanabilme İmkanları ve Kaliteye Etkisi”, Veteriner Bilimleri Dergisi, 13(2): 57-68 (1997).
- Györfi, L., Kohler, M., Krzyak, A., Walk, H., “Distribution Free Theory of Nonparametric Regression”, Springer-Verlag, New York, 329- 332 (2002).
- Hardle, W., “Applied Nonparametric Regression”, Cambridge University Press, New York, 14-30 (1990).
- Ishibuchi, H., Kwon, K., Tanaka, H., “A Learning Algorithm of Fuzzy Neural Networks with Triangular Fuzzy Weights”, Fuzzy Sets and Systems, 71: 277-293 (1995).
- Klir, G.J., Yuan, B., “Fuzzy Sets and Fuzzy Logic: Theory and Application”, Prentice Hall International Inc., New Jersey, 102-104 (1995).
- Lai, Y.J., Hwang, C.L., “Fuzzy Mathematical Programming: Method and Applications”, Springer-Verlag, Berlin Heidelberg, 20-66 (1992).
- Lin, C.T., Duh, F.B., Liu, D.J., “A Neural Fuzzy Network for Word Information Processing”, Fuzzy Sets and Systems, 127: 37-48 (2002).
- Moore, R.E., “Methods and Application of Interval Analysis”, SIAM, Philadelphia, 9-14 (1979).
- Rice, J., “Bandwidth Choice for Nonparametric Regression”, The Annals of Statistics, 12(4): 1215-1230 (1984).
- Terano, T., Asai, K., Sugeno, M., “Fuzzy Systems Theory and Its Applications”, Academic Press Inc., San Diego, 19-37 (1992).
- Yapıcı Pehlivan, N., “Parametrik Olmayan Regresyonda Bulanık Tahmin Ediciler”, Doktora Tezi, Selçuk Üniversitesi Fen Bilimleri Enstitüsü, Konya (2005).
- Zadeh, L.A., “Fuzzy Sets”, Information and Control, 8: 338-353 (1965).
Öz
In this paper, we suggest two fuzzy estimators in nonparametric regression: fuzzy kernel regression (FNPR) estimator and fuzzy radial basis function (FRBF) networks. Both FNPR estimator and FRBF networks are applied to original data taken from an experiment. We obtain MSE values of the FNPR estimator and FRBF networks and then compare them. We show that the FNPR estimator is more efficient than the FRBF networks.
Key Words: Fuzzy number, Fuzzy kernel regression estimator, Nonparametric regression, Neural networks, Fuzzy radial basis function networks.
Anahtar Kelimeler
Fuzzy number Fuzzy kernel regression estimator Nonparametric regression Neural networks Fuzzy radial basis function networks
Kaynakça
- Alefeld, G., Mayer, G., “Interval Analysis: Theory and Applications”, Journal of Computational and Applied Mathematics, 121: 421-464 (2000).
- Benedetti, J.K., “On the Nonparametric Estimation of Regression Functions”, Journal of the Royal Statistical Society Series B, 39: 248-253 (1977).
- Cheng, C.B., Lee, E.S., “Fuzzy Regression with Radial Basis Function Network”, Fuzzy Sets and Systems, 119: 291-301 (2001).
- Choi, S.W., Lee, D., Park, J.H., Lee, I.B., “Nonlinear Regression Using RBFN with Linear Submodels”, Chemometrics and Intelligent Laboratory Systems, 65: 191-208 (2003).
- Chu, C.K., Marron, J.S., “Choosing a Kernel Regression Estimator”, Statistical Science, 6(4): 404-436 (1991).
- Eubank, R.L., “Spline Smoothing and
- Nonparametric Regression”, Marcel Dekker Inc., New York, 1-8 (1988).
- Fu, L., “Neural Networks in Computer Intelligence”, McGraw Hill Inc., Singapure, 94-98 (1996).
- Gamgam, H., “Parametrik Olmayan İstatistiksel Teknikler”, Gazi Üniversitesi, Fen-Edebiyat Fakültesi Yayınları, Ankara, 232-249 (1998).
- Gürbüz, Ü., Doğruer, Y., Nizamlıoğlu, M., “Pastırma Üretiminde Dumanlama İşleminin Uygulanabilme İmkanları ve Kaliteye Etkisi”, Veteriner Bilimleri Dergisi, 13(2): 57-68 (1997).
- Györfi, L., Kohler, M., Krzyak, A., Walk, H., “Distribution Free Theory of Nonparametric Regression”, Springer-Verlag, New York, 329- 332 (2002).
- Hardle, W., “Applied Nonparametric Regression”, Cambridge University Press, New York, 14-30 (1990).
- Ishibuchi, H., Kwon, K., Tanaka, H., “A Learning Algorithm of Fuzzy Neural Networks with Triangular Fuzzy Weights”, Fuzzy Sets and Systems, 71: 277-293 (1995).
- Klir, G.J., Yuan, B., “Fuzzy Sets and Fuzzy Logic: Theory and Application”, Prentice Hall International Inc., New Jersey, 102-104 (1995).
- Lai, Y.J., Hwang, C.L., “Fuzzy Mathematical Programming: Method and Applications”, Springer-Verlag, Berlin Heidelberg, 20-66 (1992).
- Lin, C.T., Duh, F.B., Liu, D.J., “A Neural Fuzzy Network for Word Information Processing”, Fuzzy Sets and Systems, 127: 37-48 (2002).
- Moore, R.E., “Methods and Application of Interval Analysis”, SIAM, Philadelphia, 9-14 (1979).
- Rice, J., “Bandwidth Choice for Nonparametric Regression”, The Annals of Statistics, 12(4): 1215-1230 (1984).
- Terano, T., Asai, K., Sugeno, M., “Fuzzy Systems Theory and Its Applications”, Academic Press Inc., San Diego, 19-37 (1992).
- Yapıcı Pehlivan, N., “Parametrik Olmayan Regresyonda Bulanık Tahmin Ediciler”, Doktora Tezi, Selçuk Üniversitesi Fen Bilimleri Enstitüsü, Konya (2005).
- Zadeh, L.A., “Fuzzy Sets”, Information and Control, 8: 338-353 (1965).
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Bölüm | Statistics |
| Yazarlar | |
| Yayımlanma Tarihi | 1 Nisan 2010 |
| Yayımlandığı Sayı | Yıl 2008 Cilt: 21 Sayı: 3 |