fuzzy parameter estimation via fuzzy weights and linear programming

Document Type : Original Paper


1 Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran

2 School of Mathematics, Iran University of Science and Technology, Tehran, Iran

3 Department of Statistics, Roudehen Branch, Islamic Azad University, Roudehen, Iran


Fuzzy regression represents the relation between variables. Fuzzy regression analysis is one of the most widely used statistical techniques. In this study, fuzzy regression is considered with the crisp input and the fuzzy output. A hybrid algorithm based on fuzzy weights and linear programming is designed for the fuzzy nonparametric regression model prediction that function form is assumed unknown and in cases low data. In proposed method, the objective function minimizes the spread of outputs. Finally, the performance of the suggested method is compared with linear programming (LP) and quadratic programming (QP) methods using the numerical examples. The results demonstrate that the proposed method has more accurate than the LP and QP methods. Also, it is verified in cases of low data.


Main Subjects

[1].Zadeh, L.A. (1965). Fuzzy sets, Information and Control, 8, 338-353.
[2].Tanaka, H. Uejima, S. Asia, K. (1982). Linear regression analysis with fuzzy model, IEEE Transactions on Systems, Man and Cybernetics, 12, 903-907.
[3]. Diamond, P. (1988). Fuzzy least squares, Information Sciences, 46, 141-157.
[4].Farnoosh, R. Ghasemian, J. and Solaymani fard, O. (2012). A modification on ridge estimation for fuzzy nonparametric regression, Iranian Journal of Fuzzy System, 9, 75-88.
[5].Hong, D.H. Song, J.-K. Young, H. (2001). Fuzzy least-squares linear regression analysis using shape preserving operations, Information Sciences, 138, 185-193.
[6].Razzaghnia, T. Danesh S. and Maleki, A. (2011). Hybrid fuzzy regression with trapezoidal fuzzy data, Proc. SPIE 8349, 834921.
[7].Razzaghnia, T. Danesh, S. (2015). Nonparametric Regression with Trapezoidal Fuzzy Data, International Journal on Recent and Innovation Trends in Computing and Communication (IJRITCC), 3826 – 3831.
[8].Wang, N. Zhang, W. X. Mei, C. L. (2007). Fuzzy nonparametric regression based on local linear smoothing technique, Information Sciences, 177, 3882-3900.
[9].Tanaka, H. Ishibushi, H. (1991). Identification of possibilistic linear systems by quadratic membership functions of fuzzy parameters, Fuzzy Sets and Systems, 41, 145-160.
[10].Tanaka, H. Lee, H. (1998). Interval regression analysis by quadratic programming approach, IEEE Transactions on Fuzzy Systems, 6, 473-481.
 [11].Cheng, C.-B. Lee, E. S. (1999). Nonparametric fuzzy regression k-NN and kernel smoothing techniques, Computers and Mathematics with Applications, 38, 239-251.
[12].Donoso, S. Marin, N. and Amparo, V. (2006). M. Quadratic programming models for fuzzy regression, International Conference on Mathematical and Statistical Modeling in Honor of Enrique Castillo.
[13].Razzaghnia, T. Pasha, E. (2009). A new mathematical programming approach in fuzzy linear regression models, J. Sci. A. U, 18, 50-59.
[14].Ishibuchi, H. Kwon, K. Tanaka, H. (1995). A learning algorithm of fuzzy neural networks with triangular fuzzy weights, Fuzzy Sets and Systems, 71, 277-293.
[15].Ishibuchi, H. Tanaka, H. (1992). Fuzzy regression analysis using neural networks, Fuzzy Sets and Systems, 50,257-265.
[16].Jang. J.S.R. (1993). ANFIS: adaptive-network-based fuzzy inference system. IEEE Trans Syst Man Cyber, 23, 665-685.
[17].Cheng, C.-B. Lee, E. S. (1999). Applying Fuzzy Adoptive Network to Fuzzy Regression Analysis, Computers and Mathematics with Applications, 38,123-140.
[18].Dalkilic, T. E. Apaydin, T. (2009). A fuzzy adaptive network approach to parameter estimation in cases where independent variables come from an exponential distribution, Journal of Computational and Applied Mathematics, 233, 36-45.
[19].Dalkilic, T. E. Apaydin, T. (2014). Parameter Estimation by ANFIS in Cases Where Outputs are Non-Symmetric Fuzzy Numbers, International Journal of Applied Science and Technology, 92-103.
[20].Danesh, S. Farnoosh, R. Razzaghnia, T. (2016). Fuzzy nonparametric regression based on adaptive neuro fuzzy inference system, Neurocomputing, 173, 1450-1460.
[21].Jang, J.S.R. (1992). Self-learning fuzzy controllers based on temporal back-propagation, IEEE Transactions on Neural Network, 3, 714-723.
[22].Kim, B. and Bishu, R. R. (1998). Evaluation of fuzzy linear regression models by comparing membership functions, Fuzzy Sets and Systems, 100,343-351.
[23].Tanaka, H., Hayashi, I., Watada, J. (1989). Possibilistic linear regression analysis for fuzzy data. European Journal of Operational Research, 40, 389-396.
Volume 6, Issue 1
April 2016
Pages 61-80
  • Receive Date: 08 November 2015
  • Revise Date: 18 August 2016
  • Accept Date: 08 September 2016
  • First Publish Date: 08 September 2016