Araştırma Makalesi

### COMPARATIVE ANALYSIS FOR FUZZY NONPARAMETRIC REGRESSION MODELS

Yıl 2021, Cilt 22, Sayı 4, 353 - 365, 29.12.2021

### Öz

Statistical modeling is essential in revealing the relationships between variables. These models can be classified as parametric and nonparametric methods in studies using crisp values. However, most of the data collected are inherently fuzzy. In this framework, it has been a subject that has been studied from past to present that the methods derived for exact values are expressed as methods with fuzzy valued input and output variables. The study aims to describe nonparametric local polynomial regression models in fuzzy structure to examine the results for cases where an input variable is a crisp number, and the output variable is a symmetrical triangular and trapezoidal fuzzy number. According to the results, the bandwidth parameter was smaller in models where the degree of the polynomial was taken as one and larger in the case of three. In addition, the bandwidth parameter was found to be larger in models using the Epanechnikov kernel.

### Kaynakça

• [1] Hardle W. Applied Nonparametric Regression. Cambridge University Press, New York, 1994.
• [2] Fox J. Nonparametric Simple Regression: Smoothing Scatterplots. Sage Publications, California, 83 s., 2000.
• [3] Tanaka H, Uejima S, Asai K. Linear Regression Analysis with Fuzzy Model. IEEE Transactions on Systems, Man., and Cybernetics 1982, 12, 903-907.
• [4] Tanaka H. Fuzzy Data Analysis by Possibilistic Linear Models. Fuzzy Sets and Systems 1987, 24, 363-375.
• [5] Tanaka H, Watada J. Possibilistic Linear Systems and Their Application to the Linear Regression Model. Fuzzy Sets and Systems 1988, 27, 275-289.
• [6] Tanaka H, Hayashi I, Watada J. Possibilistic Linear Regression Analysis for Fuzzy Data. European Journal of Operational Research 1989, 40, 389-396.
• [7] Bardossy A. Note on Fuzzy Regression. Fuzzy Sets and Systems 1990, 37, 65-75.
• [8] Savic DA, Pedrycz W. Evaluation of Fuzzy Linear Regression Model. Fuzzy Sets and Systems 1991, 39, 51-63.
• [9] Xizhao W, Minghu H. Fuzzy Linear Regression Analysis. Fuzzy Sets and Systems 1992, 51, 179-188.
• [10] Chang PT, Lee ES. Fuzzy Linear Regression with Spreads Unrestricted in Sign. Computers and Mathematics with Applications 1994, Vol. 28, pp. 61-70.
• [11] Ishibuchi H, Tanaka H. Fuzzy Regression Analysis Using Neural Networks. Fuzzy Sets and Systems 1992, 50, 257-265.
• [12] Nasrabadi M, Nasrabadi E. A Mathematical-Programming Approach to Fuzzy Linear Regression Analysis. Applied Mathem. and Computation 2004, 155, 673-688.
• [13] Diamond P. Fuzzy Least Squares. Information Sciences 1988, 46, 141-157.
• [14] Hong H, Song JK, Do H. Fuzzy Least Squares Linear Regression Analysis Using Shape Preserving Operations. Information Sciences 2001, 138, 185-193.
• [15] Kahraman C, Beskese A, Bozbura TF. Fuzzy Regression Approaches and Applications. StudFuzz 2006 Springer-Verlag Berlin Heidelberg, 201, 589–615.
• [16] Cheng CB, Lee ES. Nonparametric Fuzzy Regression – k-NN and Kernel Smoothing Techniques. Computers and Mathematical with Applications 1999, 38, 239-251.
• [17] Cheng CB, Lee ES. Fuzzy Regression with Radial Basis Function Networks. Fuzzy Sets and Systems 2001, 119, 291-301. [18] Wang N, Zhang WX, Mei CL. Fuzzy Nonparametric Regression Based on Local Linear Smoothing Technique. An International Journal Information Sciences 2007, 177, 3882-3900.
• [19] Yildiz M. Analysis of Nonparametric Fuzzy Regression Models. Ph.D. Dissertation, Anadolu University Graduate School of Sciences Statistical Department, 2013.
• [20] Memmedli M, Yildiz M. Comparison study on smoothing parameter and sample size in nonparametric fuzzy local polynomial regression models. IV International Conference “Problems of Cybernetics and Informatics” (PCI'2012), September 12-14 2012.
• [21] Memmedli M, Yildiz M, Ozdemir O. Parameter Selection of Fuzzy Nonparametric Local Polynomial Regression. 2nd International Symposium on Computing in Science&Engineering, June 1-4 2011, Kusadasi, Aydin, Turkey.
• [22] Razzaghnia T, Danesh S. Nonparametric Regression with Trapezoidal Fuzzy Data. International Journal on Recent and Innovation Trends in Computing and Communication 2015, Volume:3 Issue: 6, 3826-3831.
• [23] Danes S, Farnoosh R, Razzagnia T. Fuzzy nonparametric regression based on an adaptive neuro-fuzzy inference system. Neurocomputing 2016, 173, 1450-1460.
• [24] Hesamian G, Akbari MG. Nonparametric Kernel Estimation Based on Fuzzy Random Variables. IEEE Transactions on Fuzzy Systems February 2017, Vol. 25, No.1.
• [25] Hesamian G, Akbari MG. A fuzzy nonlinear univariate regression model with exact predictors and fuzzy responses. Soft Computing 2021, 25:3247–3262. https://doi.org/10.1007/s00500-020-05375-9
• [26] Naderkhani R, Behzad MH, Razzaghnia T, Farnoosh R. Fuzzy Regression Analysis Based on Fuzzy Neural Networks Using Trapezoidal Data. International Journal of Fuzzy Systems 2021, 23(5):1267–1280.
• [27] Lin CT, Lee GCS. Neural Fuzzy Systems A Neuro-Fuzzy Synergism to Intelligent Systems. Prentice-Hall, Inc., 1996.
• [28] Lee KH. First Course on Fuzzy Theory and Applications. Springer-Verlag, Berlin Heidelberg New York, 2005.
• [29] D’Urso P, Gastaldi T. An “orderwise” Polynomial Regression Procedure for Fuzzy Data. Fuzzy Sets and Systems 2002, 130, 1-19.
• [30] Fan J, Gijbels I. Local Polynomial Modeling and Its Applications. Chapman & Hall/CRC, 1996.
• [31] Cabrera JLO. locpol: Kernel Local Polynomial Regression, R package version 0.7-0. https://CRAN.R-project.org/package=locpol, 2018.

### COMPARATIVE ANALYSIS FOR FUZZY NONPARAMETRIC REGRESSION MODELS

Yıl 2021, Cilt 22, Sayı 4, 353 - 365, 29.12.2021

### Öz

Statistical modeling is essential to revealing the relationships between variables. These statistical models can be classified as parametric and nonparametric methods in studies using crisp values. However, most of the collected data are inherently fuzzy. In this context, the fuzzy expression of methods using precise data is a matter of curiosity for researchers. The methods with fuzzy input and output variables have been developed for a long time. The study aims to describe nonparametric local polynomial regression models in fuzzy structure to examine the results for cases where the input variable is a crisp number, and the output variable is a symmetrical triangular and trapezoidal fuzzy number. According to the results, the bandwidth parameter was smaller in models where the degree of the polynomial was taken as one and larger in the case of three. In addition, the bandwidth parameter was found to be larger in models using the Epanechnikov kernel.

### Kaynakça

• [1] Hardle W. Applied Nonparametric Regression. Cambridge University Press, New York, 1994.
• [2] Fox J. Nonparametric Simple Regression: Smoothing Scatterplots. Sage Publications, California, 83 s., 2000.
• [3] Tanaka H, Uejima S, Asai K. Linear Regression Analysis with Fuzzy Model. IEEE Transactions on Systems, Man., and Cybernetics 1982, 12, 903-907.
• [4] Tanaka H. Fuzzy Data Analysis by Possibilistic Linear Models. Fuzzy Sets and Systems 1987, 24, 363-375.
• [5] Tanaka H, Watada J. Possibilistic Linear Systems and Their Application to the Linear Regression Model. Fuzzy Sets and Systems 1988, 27, 275-289.
• [6] Tanaka H, Hayashi I, Watada J. Possibilistic Linear Regression Analysis for Fuzzy Data. European Journal of Operational Research 1989, 40, 389-396.
• [7] Bardossy A. Note on Fuzzy Regression. Fuzzy Sets and Systems 1990, 37, 65-75.
• [8] Savic DA, Pedrycz W. Evaluation of Fuzzy Linear Regression Model. Fuzzy Sets and Systems 1991, 39, 51-63.
• [9] Xizhao W, Minghu H. Fuzzy Linear Regression Analysis. Fuzzy Sets and Systems 1992, 51, 179-188.
• [10] Chang PT, Lee ES. Fuzzy Linear Regression with Spreads Unrestricted in Sign. Computers and Mathematics with Applications 1994, Vol. 28, pp. 61-70.
• [11] Ishibuchi H, Tanaka H. Fuzzy Regression Analysis Using Neural Networks. Fuzzy Sets and Systems 1992, 50, 257-265.
• [12] Nasrabadi M, Nasrabadi E. A Mathematical-Programming Approach to Fuzzy Linear Regression Analysis. Applied Mathem. and Computation 2004, 155, 673-688.
• [13] Diamond P. Fuzzy Least Squares. Information Sciences 1988, 46, 141-157.
• [14] Hong H, Song JK, Do H. Fuzzy Least Squares Linear Regression Analysis Using Shape Preserving Operations. Information Sciences 2001, 138, 185-193.
• [15] Kahraman C, Beskese A, Bozbura TF. Fuzzy Regression Approaches and Applications. StudFuzz 2006 Springer-Verlag Berlin Heidelberg, 201, 589–615.
• [16] Cheng CB, Lee ES. Nonparametric Fuzzy Regression – k-NN and Kernel Smoothing Techniques. Computers and Mathematical with Applications 1999, 38, 239-251.
• [17] Cheng CB, Lee ES. Fuzzy Regression with Radial Basis Function Networks. Fuzzy Sets and Systems 2001, 119, 291-301. [18] Wang N, Zhang WX, Mei CL. Fuzzy Nonparametric Regression Based on Local Linear Smoothing Technique. An International Journal Information Sciences 2007, 177, 3882-3900.
• [19] Yildiz M. Analysis of Nonparametric Fuzzy Regression Models. Ph.D. Dissertation, Anadolu University Graduate School of Sciences Statistical Department, 2013.
• [20] Memmedli M, Yildiz M. Comparison study on smoothing parameter and sample size in nonparametric fuzzy local polynomial regression models. IV International Conference “Problems of Cybernetics and Informatics” (PCI'2012), September 12-14 2012.
• [21] Memmedli M, Yildiz M, Ozdemir O. Parameter Selection of Fuzzy Nonparametric Local Polynomial Regression. 2nd International Symposium on Computing in Science&Engineering, June 1-4 2011, Kusadasi, Aydin, Turkey.
• [22] Razzaghnia T, Danesh S. Nonparametric Regression with Trapezoidal Fuzzy Data. International Journal on Recent and Innovation Trends in Computing and Communication 2015, Volume:3 Issue: 6, 3826-3831.
• [23] Danes S, Farnoosh R, Razzagnia T. Fuzzy nonparametric regression based on an adaptive neuro-fuzzy inference system. Neurocomputing 2016, 173, 1450-1460.
• [24] Hesamian G, Akbari MG. Nonparametric Kernel Estimation Based on Fuzzy Random Variables. IEEE Transactions on Fuzzy Systems February 2017, Vol. 25, No.1.
• [25] Hesamian G, Akbari MG. A fuzzy nonlinear univariate regression model with exact predictors and fuzzy responses. Soft Computing 2021, 25:3247–3262. https://doi.org/10.1007/s00500-020-05375-9
• [26] Naderkhani R, Behzad MH, Razzaghnia T, Farnoosh R. Fuzzy Regression Analysis Based on Fuzzy Neural Networks Using Trapezoidal Data. International Journal of Fuzzy Systems 2021, 23(5):1267–1280.
• [27] Lin CT, Lee GCS. Neural Fuzzy Systems A Neuro-Fuzzy Synergism to Intelligent Systems. Prentice-Hall, Inc., 1996.
• [28] Lee KH. First Course on Fuzzy Theory and Applications. Springer-Verlag, Berlin Heidelberg New York, 2005.
• [29] D’Urso P, Gastaldi T. An “orderwise” Polynomial Regression Procedure for Fuzzy Data. Fuzzy Sets and Systems 2002, 130, 1-19.
• [30] Fan J, Gijbels I. Local Polynomial Modeling and Its Applications. Chapman & Hall/CRC, 1996.
• [31] Cabrera JLO. locpol: Kernel Local Polynomial Regression, R package version 0.7-0. https://CRAN.R-project.org/package=locpol, 2018.

### Ayrıntılar

Birincil Dil İngilizce Fen Makaleler Münevvere YILDIZ (Sorumlu Yazar) Afyon Kocatepe Üniversitesi 0000-0001-9541-2603 Türkiye 29 Aralık 2021 Yıl 2021, Cilt 22, Sayı 4

### Kaynak Göster

 Bibtex @araştırma makalesi { estubtda1033350, journal = {Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering}, issn = {2667-4211}, address = {btda@anadolu.edu.tr}, publisher = {Eskişehir Teknik Üniversitesi}, year = {2021}, volume = {22}, number = {4}, pages = {353 - 365}, doi = {10.18038/estubtda.1033350}, title = {COMPARATIVE ANALYSIS FOR FUZZY NONPARAMETRIC REGRESSION MODELS}, key = {cite}, author = {Yıldız, Münevvere and Memmedli, Memmedağa} } APA Yıldız, M. & Memmedli, M. (2021). COMPARATIVE ANALYSIS FOR FUZZY NONPARAMETRIC REGRESSION MODELS . Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering , 22 (4) , 353-365 . DOI: 10.18038/estubtda.1033350 MLA Yıldız, M. , Memmedli, M. "COMPARATIVE ANALYSIS FOR FUZZY NONPARAMETRIC REGRESSION MODELS" . Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering 22 (2021 ): 353-365 Chicago Yıldız, M. , Memmedli, M. "COMPARATIVE ANALYSIS FOR FUZZY NONPARAMETRIC REGRESSION MODELS". Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering 22 (2021 ): 353-365 RIS TY - JOUR T1 - COMPARATIVE ANALYSIS FOR FUZZY NONPARAMETRIC REGRESSION MODELS AU - Münevvere Yıldız , Memmedağa Memmedli Y1 - 2021 PY - 2021 N1 - doi: 10.18038/estubtda.1033350 DO - 10.18038/estubtda.1033350 T2 - Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering JF - Journal JO - JOR SP - 353 EP - 365 VL - 22 IS - 4 SN - 2667-4211- M3 - doi: 10.18038/estubtda.1033350 UR - https://doi.org/10.18038/estubtda.1033350 Y2 - 2021 ER - EndNote %0 Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering COMPARATIVE ANALYSIS FOR FUZZY NONPARAMETRIC REGRESSION MODELS %A Münevvere Yıldız , Memmedağa Memmedli %T COMPARATIVE ANALYSIS FOR FUZZY NONPARAMETRIC REGRESSION MODELS %D 2021 %J Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering %P 2667-4211- %V 22 %N 4 %R doi: 10.18038/estubtda.1033350 %U 10.18038/estubtda.1033350 ISNAD Yıldız, Münevvere , Memmedli, Memmedağa . "COMPARATIVE ANALYSIS FOR FUZZY NONPARAMETRIC REGRESSION MODELS". Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering 22 / 4 (Aralık 2021): 353-365 . https://doi.org/10.18038/estubtda.1033350 AMA Yıldız M. , Memmedli M. COMPARATIVE ANALYSIS FOR FUZZY NONPARAMETRIC REGRESSION MODELS. Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering. 2021; 22(4): 353-365. Vancouver Yıldız M. , Memmedli M. COMPARATIVE ANALYSIS FOR FUZZY NONPARAMETRIC REGRESSION MODELS. Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering. 2021; 22(4): 353-365. IEEE M. Yıldız ve M. Memmedli , "COMPARATIVE ANALYSIS FOR FUZZY NONPARAMETRIC REGRESSION MODELS", Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering, c. 22, sayı. 4, ss. 353-365, Ara. 2021, doi:10.18038/estubtda.1033350
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