BibTex RIS Cite

Fuzzy Linear Regression for the Time Series Data which is Fuzzified with SMRGT Method

Year 2016, Volume: 20 Issue: 3, 405 - 413, 17.10.2016
https://doi.org/10.19113/sdufbed.49849

Abstract

Our work on regression and classification provides a new contribution to the analysis of time series used in many areas for years. Owing to the fact that convergence could not obtained with the methods used in autocorrelation fixing process faced with time series regression application, success is not met or fall into obligation of changing the models’ degree. Changing the models’ degree may not be desirable in every situation. In our study, recommended for these situations, time series data was fuzzified by using the simple membership function and fuzzy rule generation technique (SMRGT) and to estimate future an equation has created by applying fuzzy least square regression (FLSR) method which is a simple linear regression method to this data. Although SMRGT has success in determining the flow discharge in open channels and can be used confidently for flow discharge modeling in open canals, as well as in pipe flow with some modifications, there is no clue about that this technique is successful in fuzzy linear regression modeling. Therefore, in order to address the luck of such a modeling, a new hybrid model has been described within this study. In conclusion, to demonstrate our methods’ efficiency, classical linear regression for time series data and linear regression for fuzzy time series data were applied to two different data sets, and these two approaches performances were compared by using different measures.

References

  • [1] Zadeh, L.A., 1965. Fuzzy Sets, Inf. Control 8 (3) (1965), 338–353.
  • [2] Q. Song and B. S. Chissom, “Fuzzy time series and its models,” Fuzzy Sets and Systems, vol. 54, no. 3, pp. 269–277, 1993.
  • [3] S. M. Chen, “Forecasting enrollments based on fuzzy time series,”Fuzzy Sets and Systems, vol. 81, no. 3, pp. 311–319, 1996.
  • [4] K. Huarng, “Effective lengths of intervals to improve forecasting in fuzzy time series,” Fuzzy Sets and Systems, vol. 123, no. 3, pp. 387–394, 2001.
  • [5] S. Chen, “Forecasting enrollments based on high-order fuzzy time series,” Cybernetics and Systems, vol. 33, no. 1, pp. 1–16, 2002.
  • [6] R.-C. Tsaur, J. C. O. Yang, and H.-F. Wang, “Fuzzy relation analysis in fuzzy time series model,” Computers & Mathematics with Applications, vol. 49, no. 4, pp. 539–548, 2005.
  • [7] S. R. Singh, “A simple method of forecasting based on fuzzy time series,” Applied Mathematics and Computation, vol. 186, no. 1, pp. 330–339, 2007.
  • [8] Toprak, Z.F., 2009. Flow Discharge Modeling in Open Canals Using a New Fuzzy Modeling Technique (SMRGT), CLEAN-Soil. Air. Water 37 (9) (2009), 742–752.
  • [9] Toprak ZF, Songur M, Hamidi N, and Gulsever H, (2012), Determination of Losses in Water-Networks Using a New Fuzzy Technique (SMRGT), AWERProcedia Information Technology & Computer Science, Vol 03 (2013) 833-840.
  • [10] Toprak ZF, Songur M, Hamidi N, and Gulsever H, (2012), Determination of Losses in Water-Networks Using a New Fuzzy Technique (SMRGT), 3rd World Conference on Information Technology (WCIT 2012), 14-16 November 2012, Barcelona-Spain.
  • [11] Coşkun, C. (2014), Automated Fuzzy Model Generation and an Analysis of the Proposed Method, Int. J. Open Problems Compt. Math., Vol. 7, No. 2, June 2014 ISSN 1998-6262
  • [12] Yalaz S, A Atay, Toprak ZF (2015), SMRGT yöntemi ile bulanıklaştırılmış veriler için bulanık doğrusal regresyon, Erciyes Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 31(3), 152-158, ISSN: 1012-2354
  • [13] Toprak S, Atay A, Toprak ZF (2013), SMRGT yöntemi ile bulanıklaştırılmış veriler için bulanık doğrusal regresyon, XXVI. Ulusal Matematik Sempozyumu, Dicle Üniversitesi Kongre Merkezi, Diyarbakır.
  • [14] Toprak S, Atay A, Toprak ZF (2013), SMRGT yöntemi ile bulanıklaştırılmış zamana bağlı veriler için bulanık doğrusal regresyon, XXVI. Ulusal Matematik Sempozyumu, Dicle Üniversitesi Kongre Merkezi, Diyarbakır.
  • [15] Gujarati, D.N., 1995. Basic Econometrics, third edit. MC-Graw-Hill.Inc., USA, (1995), pp. 712-713.
  • [16] Toprak, S., 2011. Çok Değişkenli Uyarlamalı Regresyon Eğrileri ve Konik Programlama ile Zaman Serilerinin Modellenmesi, Dicle University, Science Institue, Master Dissertation, 107, Diyarbakır.
  • [17] Box, G.E.P., Jenkins, G.M., 1976. Time series analysis forecasting and control, California.
  • [18] Özmen, A., 1986. Zaman Serisi Analizinde Box-Jenkins Yöntemi ve Banka Mevduat Tahmininde Uygulama Denemesi, Anadolu University Press, 201, Eskişehir.
  • [19] Kayım, H., 1985. İstatistiksel Ön Tahmin Yöntemleri, Hacettepe University Faculty of Economics and Administrative Sciences Press, 160, Ankara.
  • [20] Tekin, V. N., 2006. SPSS Uygulamalı İstatistik Teknikleri, 296, Ankara.
  • [21] Department of Political Science and International Relations Posc/Uapp 816 2010. Time Series Regression. http://www.udel.edu/htr/Statistics/Notes816/class20.PDF, (23.10.2010).
  • [22] Evans, W., 2010. Durbin-Watson Significance Tables, http://www.nd.edu/~wevans1/econ30331/Durbin_Watson_tables.pdf, (24.10.2010).
  • [23] Hamit, A., 2010. Korelasyon Analizi, http://maden.karaelmas.edu.tr/hocalar/hamitaydin/Sunu_6ci_hafta.pdf, (18.05.2010).
  • [24] Kmenta, J., 1986. Elements of econometrics, second edition, Macmillan, 655, New York.
  • [25] People Emich, 2010, Autocorrelation, people.emich.edu/jthornton/text-files/Econ415_autocorrelation.doc, (13.03.2010).
  • [26] Aster, R., Borchers, B., Thurber, C., 2004. Parameter Estimation and Inverse Problems, Academic Press, 355.
  • [27] Kao, C., Chyu, C.L., 2003. Least-squares estimates in fuzzy regression analysis, Europen Journal of Operational Research, 148 (2003), 426-435.
  • [28] STATA, http://www.stata.com/, (28.12.2010).
  • [29] MATLAB, http://www.mathworks.com/products/matlab/tryit.html, (29.12.2010).
Year 2016, Volume: 20 Issue: 3, 405 - 413, 17.10.2016
https://doi.org/10.19113/sdufbed.49849

Abstract

References

  • [1] Zadeh, L.A., 1965. Fuzzy Sets, Inf. Control 8 (3) (1965), 338–353.
  • [2] Q. Song and B. S. Chissom, “Fuzzy time series and its models,” Fuzzy Sets and Systems, vol. 54, no. 3, pp. 269–277, 1993.
  • [3] S. M. Chen, “Forecasting enrollments based on fuzzy time series,”Fuzzy Sets and Systems, vol. 81, no. 3, pp. 311–319, 1996.
  • [4] K. Huarng, “Effective lengths of intervals to improve forecasting in fuzzy time series,” Fuzzy Sets and Systems, vol. 123, no. 3, pp. 387–394, 2001.
  • [5] S. Chen, “Forecasting enrollments based on high-order fuzzy time series,” Cybernetics and Systems, vol. 33, no. 1, pp. 1–16, 2002.
  • [6] R.-C. Tsaur, J. C. O. Yang, and H.-F. Wang, “Fuzzy relation analysis in fuzzy time series model,” Computers & Mathematics with Applications, vol. 49, no. 4, pp. 539–548, 2005.
  • [7] S. R. Singh, “A simple method of forecasting based on fuzzy time series,” Applied Mathematics and Computation, vol. 186, no. 1, pp. 330–339, 2007.
  • [8] Toprak, Z.F., 2009. Flow Discharge Modeling in Open Canals Using a New Fuzzy Modeling Technique (SMRGT), CLEAN-Soil. Air. Water 37 (9) (2009), 742–752.
  • [9] Toprak ZF, Songur M, Hamidi N, and Gulsever H, (2012), Determination of Losses in Water-Networks Using a New Fuzzy Technique (SMRGT), AWERProcedia Information Technology & Computer Science, Vol 03 (2013) 833-840.
  • [10] Toprak ZF, Songur M, Hamidi N, and Gulsever H, (2012), Determination of Losses in Water-Networks Using a New Fuzzy Technique (SMRGT), 3rd World Conference on Information Technology (WCIT 2012), 14-16 November 2012, Barcelona-Spain.
  • [11] Coşkun, C. (2014), Automated Fuzzy Model Generation and an Analysis of the Proposed Method, Int. J. Open Problems Compt. Math., Vol. 7, No. 2, June 2014 ISSN 1998-6262
  • [12] Yalaz S, A Atay, Toprak ZF (2015), SMRGT yöntemi ile bulanıklaştırılmış veriler için bulanık doğrusal regresyon, Erciyes Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 31(3), 152-158, ISSN: 1012-2354
  • [13] Toprak S, Atay A, Toprak ZF (2013), SMRGT yöntemi ile bulanıklaştırılmış veriler için bulanık doğrusal regresyon, XXVI. Ulusal Matematik Sempozyumu, Dicle Üniversitesi Kongre Merkezi, Diyarbakır.
  • [14] Toprak S, Atay A, Toprak ZF (2013), SMRGT yöntemi ile bulanıklaştırılmış zamana bağlı veriler için bulanık doğrusal regresyon, XXVI. Ulusal Matematik Sempozyumu, Dicle Üniversitesi Kongre Merkezi, Diyarbakır.
  • [15] Gujarati, D.N., 1995. Basic Econometrics, third edit. MC-Graw-Hill.Inc., USA, (1995), pp. 712-713.
  • [16] Toprak, S., 2011. Çok Değişkenli Uyarlamalı Regresyon Eğrileri ve Konik Programlama ile Zaman Serilerinin Modellenmesi, Dicle University, Science Institue, Master Dissertation, 107, Diyarbakır.
  • [17] Box, G.E.P., Jenkins, G.M., 1976. Time series analysis forecasting and control, California.
  • [18] Özmen, A., 1986. Zaman Serisi Analizinde Box-Jenkins Yöntemi ve Banka Mevduat Tahmininde Uygulama Denemesi, Anadolu University Press, 201, Eskişehir.
  • [19] Kayım, H., 1985. İstatistiksel Ön Tahmin Yöntemleri, Hacettepe University Faculty of Economics and Administrative Sciences Press, 160, Ankara.
  • [20] Tekin, V. N., 2006. SPSS Uygulamalı İstatistik Teknikleri, 296, Ankara.
  • [21] Department of Political Science and International Relations Posc/Uapp 816 2010. Time Series Regression. http://www.udel.edu/htr/Statistics/Notes816/class20.PDF, (23.10.2010).
  • [22] Evans, W., 2010. Durbin-Watson Significance Tables, http://www.nd.edu/~wevans1/econ30331/Durbin_Watson_tables.pdf, (24.10.2010).
  • [23] Hamit, A., 2010. Korelasyon Analizi, http://maden.karaelmas.edu.tr/hocalar/hamitaydin/Sunu_6ci_hafta.pdf, (18.05.2010).
  • [24] Kmenta, J., 1986. Elements of econometrics, second edition, Macmillan, 655, New York.
  • [25] People Emich, 2010, Autocorrelation, people.emich.edu/jthornton/text-files/Econ415_autocorrelation.doc, (13.03.2010).
  • [26] Aster, R., Borchers, B., Thurber, C., 2004. Parameter Estimation and Inverse Problems, Academic Press, 355.
  • [27] Kao, C., Chyu, C.L., 2003. Least-squares estimates in fuzzy regression analysis, Europen Journal of Operational Research, 148 (2003), 426-435.
  • [28] STATA, http://www.stata.com/, (28.12.2010).
  • [29] MATLAB, http://www.mathworks.com/products/matlab/tryit.html, (29.12.2010).
There are 29 citations in total.

Details

Journal Section Makaleler
Authors

Seçil Yalaz

Arife Atay

Publication Date October 17, 2016
Published in Issue Year 2016 Volume: 20 Issue: 3

Cite

APA Yalaz, S., & Atay, A. (2016). Fuzzy Linear Regression for the Time Series Data which is Fuzzified with SMRGT Method. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 20(3), 405-413. https://doi.org/10.19113/sdufbed.49849
AMA Yalaz S, Atay A. Fuzzy Linear Regression for the Time Series Data which is Fuzzified with SMRGT Method. J. Nat. Appl. Sci. December 2016;20(3):405-413. doi:10.19113/sdufbed.49849
Chicago Yalaz, Seçil, and Arife Atay. “Fuzzy Linear Regression for the Time Series Data Which Is Fuzzified With SMRGT Method”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 20, no. 3 (December 2016): 405-13. https://doi.org/10.19113/sdufbed.49849.
EndNote Yalaz S, Atay A (December 1, 2016) Fuzzy Linear Regression for the Time Series Data which is Fuzzified with SMRGT Method. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 20 3 405–413.
IEEE S. Yalaz and A. Atay, “Fuzzy Linear Regression for the Time Series Data which is Fuzzified with SMRGT Method”, J. Nat. Appl. Sci., vol. 20, no. 3, pp. 405–413, 2016, doi: 10.19113/sdufbed.49849.
ISNAD Yalaz, Seçil - Atay, Arife. “Fuzzy Linear Regression for the Time Series Data Which Is Fuzzified With SMRGT Method”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 20/3 (December 2016), 405-413. https://doi.org/10.19113/sdufbed.49849.
JAMA Yalaz S, Atay A. Fuzzy Linear Regression for the Time Series Data which is Fuzzified with SMRGT Method. J. Nat. Appl. Sci. 2016;20:405–413.
MLA Yalaz, Seçil and Arife Atay. “Fuzzy Linear Regression for the Time Series Data Which Is Fuzzified With SMRGT Method”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol. 20, no. 3, 2016, pp. 405-13, doi:10.19113/sdufbed.49849.
Vancouver Yalaz S, Atay A. Fuzzy Linear Regression for the Time Series Data which is Fuzzified with SMRGT Method. J. Nat. Appl. Sci. 2016;20(3):405-13.

e-ISSN :1308-6529
Linking ISSN (ISSN-L): 1300-7688

All published articles in the journal can be accessed free of charge and are open access under the Creative Commons CC BY-NC (Attribution-NonCommercial) license. All authors and other journal users are deemed to have accepted this situation. Click here to access detailed information about the CC BY-NC license.