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Year 2018, Volume: 47 Issue: 6, 1605 - 1624, 12.12.2018

Abstract

References

  • Celmins, A., Least-squares model fitting to fuzzy vector data, Fuzzy sets and systems 22 (3), 245-269, 1987.
  • Cheng, C.-B., Lee, E. S., Fuzzy linear regression with spreads unrestricted in sign, Computers and Mathematics with Applications 28(4), 61-70, 1994.
  • Cheng, C.-B., Lee, E. S., Applying Fuzzy Adoptive Network to Fuzzy Regression Analysis, Computers and Mathematics with Applications 38 (2), 123-140, 1999.
  • Cheng, C.-B., Lee, E. S., Nonparametric fuzzy regression k-NN and kernel smoothing techniques, Computers and Mathematics with Applications 38 (3-4), 239-251, 1999.
  • Cheng, C.-B., Lee, E. S., Fuzzy regression with radial basis function networks, Fuzzy Sets and Systems 119 (3), 291-301, 2001.
  • Cheng, M. Y., An improved estimator of the finite population mean in simple random sampling, Model Assisted Statistics and Applications 6 (1), 47-55, 2011.
  • Dalkilic, T. E., Apaydin, T., 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 (1), 36-45, 2009.
  • Dalkilic, T. E., Kula, K. S., Apaydin, T., Parameter estimation by ANFIS Where dependent variable has outlier, Hacettepe Journal of Mathematics and Statistics, 43 (2), 315-329, 2014.
  • Danesh, S., Farnoosh, R., Razzaghnia, T., Fuzzy nonparametric regression based on adaptive neuro-fuzzy inference system, Neurocomputing 173, 1450-1460, 2016.
  • Dewan, M. W., Huggett, D. J., Liao, T. W., Wahab, M. A., Okeil, A. M., Prediction of tensile strength of friction stir weld joints with adaptive neuro-fuzzy inference system (ANFIS) and neural network, Materials and Design 92, 288-299, 2016.
  • Diamond, P., Fuzzy least squares, Information Sciences 46 (3), 141-157, 1988.
  • Donoso, S., Marin N., Amparo Vila, M., Quadratic programming models for fuzzy regression, International Conference on Mathematical and Statistical Modeling in Honor of Enrique Castillo, 2006.
  • Fang, M. C., Lee, Zi. Y. Application of neuro-fuzzy algorithm to portable dynamic positioning control system for ships, International Journal of Naval Architecture and Ocean Engineering 8, 38-52, 2016.
  • Farnoosh, R., Ghasemian, J., Solaymani fard, O., A modification on ridge estimation for fuzzy nonparametric regression, Iranian Journal of Fuzzy System 9 (2), 75-88, 2012.
  • Gaxiola, F., Melin, P., Valdez, F., Castro, J. R., Castillo, O., Optimization of type-2 fuzzy weights in back propagation learning for neural networks using GAs and PSO, Applied Soft Computing 38, 860–871, 2016.
  • Ishibuchi, H., Kwon, K., Tanaka, H., A learning algorithm of fuzzy neural networks with triangular fuzzy weights, Fuzzy Sets and Systems 71 (3), 277-293, 1995.
  • Ishibushi, H., Tanaka, H., Fuzzy regression analysis using neural networks, Fuzzy Sets and systems 50 (3), 257-265, 1992.
  • Ishibushi, H., Tanaka, H., Okado, H., An architecture of neural networks with interval weights and its application to fuzzy regression analysis, Fuzzy Sets and Systems 57 (1),27-39, 1993.
  • Jang, J.S.R., Self-learning fuzzy controllers based on temporal back-propagation, IEEE Transactions on Neural Network, IEEE Transactions on Neural Network 3, 714-723, 1992.
  • Jang, J.S.R., ANFIS: adaptive-network-based fuzzy inference system, IEEE Trans Syst Man Cyber 23 (3), 665-685, 1993.
  • Kayacan, E., Khanesar, M. A., Chapter 8 – Hybrid Training Method for type-2 fuzzy Neural networks using particle swarm optimization, Fuzzy Neural Networks for Real Time Control Applications, 133–160, 2016.
  • Kim, B., Bishu, R. R., Evaluation of fuzzy linear regression models by comparing membership functions, Fuzzy Sets and Systems 100 (1-3), 343-351, 1998.
  • Kiraly, A., Fogarassy, A. V., Abonyi, J., Geodesic distance based fuzzy c-medoid clustering - searching for central points in graphs and high dimensional data, Fuzzy Sets and Systems 286, 157–172, 2016.
  • Ming, M., Friedman, M., Kandel, A., General fuzzy least squares, Fuzzy Sets and Systems 88 (1), 107–118, 1997.
  • Mosleh, M., Fuzzy neural network for solving a system of fuzzy differential equations, Applied Soft Computing 13, 3597-3607, 2013.
  • Mosleh, M., Otadi, M., Abbasbandy, S., Evaluation of fuzzy regression model by fuzzy neural networks, Journal of Computational and Applied Mathematics 234 (1), 825- 834, 2010.
  • Nasrabadi, M. M., Nasrabadi, E. A., mathematical-programming approach to fuzzy linear regression analysis, Applied Mathematics and Computation 155 (3), 873-881, 2004.
  • Pasha, E., Razzaghnia, T., Allahviranloo, T., Yari, Gh., Mostafaei, H. R., A new mathematical programming approach in fuzzy linear regression models, Applied Mathematical Sciences 35, 1715, 2007.
  • Razzaghnia, T., Danesh, S., Nonparametric Regression with Trapezoidal Fuzzy Data, International Journal on Recent and Innovation Trends in Computing and Communication (IJRITCC) 3 (6), 3826 - 3831, 2015.
  • Razzaghnia, T., Danesh, S., Maleki, A., Hybrid fuzzy regression with trapezoidal fuzzy data, Proc. SPIE 8349 (834921), 2011.
  • Sarhadi, P., Rezaie, B., Rahmani, Z., Adaptive predictive control based on adaptive neuro-fuzzy inference system for a class of nonlinear industrial processes, Journal of the Taiwan Institute of Chemical Engineers 61, 132-137, 2016.
  • Shapiro, A., The merge of neural networks, fuzzy logic, and genetic algorithms, Insurance: Mathematics and Economics 31 (1), 115-131, 2002.
  • Sridevi, S., Nirmal, S., ANFIS based decision support system for prenatal detection of Truncus Arteriosus congenital heart defect, Applied Soft Computing 46, 577–587, 2016.
  • Stone, M., Cross validation choice and assessment of statistical predictions, Journal of the Royal Statistical Society 36 (series B), 111-147, 1974.
  • Takagi, T., Sugeno, M. Fuzzy identification of systems and its application to modelling and control, IEEE Transactions on Systems, Man and Cybernetics 15, 116-132, 1985.
  • Tanaka, H., Fuzzy data analysis by possibilistic linear models, Fuzzy Sets and Systems 24 (3), 363-375, 1987.
  • Tanaka, H., Hayashi, I., Watada, J., Possibilistic linear regression analysis for fuzzy data, European Journal of Operational Research 40 (3), 389-396, 1989.
  • Tanaka, H., Uejima, S. K., Asia, K., Linear regression analysis with fuzzy model, IEEE Transactions on Systems, Man and Cybernetics 12, 903-907, 1982.
  • Tanaka, H., Watada, J., Possibilistic linear systems and their application to the linear regression model, Fuzzy Sets and Systems 27 (3), 275-289, 1988.
  • Wang, N., Zhang, W. X., Mei, C. L., Fuzzy nonparametric regression based on local linear smoothing technique, Information Sciences 177 (18), 3882-3900, 2007.
  • Zhang, P., Model selection via multifold cross validation, Annals of Statistics 21 (1), 299-313, 1993.

Fuzzy parameters estimation via hybrid methods

Year 2018, Volume: 47 Issue: 6, 1605 - 1624, 12.12.2018

Abstract

Fuzzy regression analysis is one of the most widely used statistical techniques which represents the relation between variables. In this paper, the crisp inputs and the symmetrical triangular fuzzy output are considered. Two hybrid algorithms are considered to fit the fuzzy regression model. In this study, algorithms are based on adaptive neuro-fuzzy inference system. The results are derived based on the $V$-fold cross validation, so that the validity and quality of the suggested methods can be guaranteed. Finally, using the numerical examples, the performance of the suggested methods are compared with the other ones, such as linear programming (LP) and quadratic programming (QP). Based on examples, hybrid methods are verified for the prediction.

References

  • Celmins, A., Least-squares model fitting to fuzzy vector data, Fuzzy sets and systems 22 (3), 245-269, 1987.
  • Cheng, C.-B., Lee, E. S., Fuzzy linear regression with spreads unrestricted in sign, Computers and Mathematics with Applications 28(4), 61-70, 1994.
  • Cheng, C.-B., Lee, E. S., Applying Fuzzy Adoptive Network to Fuzzy Regression Analysis, Computers and Mathematics with Applications 38 (2), 123-140, 1999.
  • Cheng, C.-B., Lee, E. S., Nonparametric fuzzy regression k-NN and kernel smoothing techniques, Computers and Mathematics with Applications 38 (3-4), 239-251, 1999.
  • Cheng, C.-B., Lee, E. S., Fuzzy regression with radial basis function networks, Fuzzy Sets and Systems 119 (3), 291-301, 2001.
  • Cheng, M. Y., An improved estimator of the finite population mean in simple random sampling, Model Assisted Statistics and Applications 6 (1), 47-55, 2011.
  • Dalkilic, T. E., Apaydin, T., 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 (1), 36-45, 2009.
  • Dalkilic, T. E., Kula, K. S., Apaydin, T., Parameter estimation by ANFIS Where dependent variable has outlier, Hacettepe Journal of Mathematics and Statistics, 43 (2), 315-329, 2014.
  • Danesh, S., Farnoosh, R., Razzaghnia, T., Fuzzy nonparametric regression based on adaptive neuro-fuzzy inference system, Neurocomputing 173, 1450-1460, 2016.
  • Dewan, M. W., Huggett, D. J., Liao, T. W., Wahab, M. A., Okeil, A. M., Prediction of tensile strength of friction stir weld joints with adaptive neuro-fuzzy inference system (ANFIS) and neural network, Materials and Design 92, 288-299, 2016.
  • Diamond, P., Fuzzy least squares, Information Sciences 46 (3), 141-157, 1988.
  • Donoso, S., Marin N., Amparo Vila, M., Quadratic programming models for fuzzy regression, International Conference on Mathematical and Statistical Modeling in Honor of Enrique Castillo, 2006.
  • Fang, M. C., Lee, Zi. Y. Application of neuro-fuzzy algorithm to portable dynamic positioning control system for ships, International Journal of Naval Architecture and Ocean Engineering 8, 38-52, 2016.
  • Farnoosh, R., Ghasemian, J., Solaymani fard, O., A modification on ridge estimation for fuzzy nonparametric regression, Iranian Journal of Fuzzy System 9 (2), 75-88, 2012.
  • Gaxiola, F., Melin, P., Valdez, F., Castro, J. R., Castillo, O., Optimization of type-2 fuzzy weights in back propagation learning for neural networks using GAs and PSO, Applied Soft Computing 38, 860–871, 2016.
  • Ishibuchi, H., Kwon, K., Tanaka, H., A learning algorithm of fuzzy neural networks with triangular fuzzy weights, Fuzzy Sets and Systems 71 (3), 277-293, 1995.
  • Ishibushi, H., Tanaka, H., Fuzzy regression analysis using neural networks, Fuzzy Sets and systems 50 (3), 257-265, 1992.
  • Ishibushi, H., Tanaka, H., Okado, H., An architecture of neural networks with interval weights and its application to fuzzy regression analysis, Fuzzy Sets and Systems 57 (1),27-39, 1993.
  • Jang, J.S.R., Self-learning fuzzy controllers based on temporal back-propagation, IEEE Transactions on Neural Network, IEEE Transactions on Neural Network 3, 714-723, 1992.
  • Jang, J.S.R., ANFIS: adaptive-network-based fuzzy inference system, IEEE Trans Syst Man Cyber 23 (3), 665-685, 1993.
  • Kayacan, E., Khanesar, M. A., Chapter 8 – Hybrid Training Method for type-2 fuzzy Neural networks using particle swarm optimization, Fuzzy Neural Networks for Real Time Control Applications, 133–160, 2016.
  • Kim, B., Bishu, R. R., Evaluation of fuzzy linear regression models by comparing membership functions, Fuzzy Sets and Systems 100 (1-3), 343-351, 1998.
  • Kiraly, A., Fogarassy, A. V., Abonyi, J., Geodesic distance based fuzzy c-medoid clustering - searching for central points in graphs and high dimensional data, Fuzzy Sets and Systems 286, 157–172, 2016.
  • Ming, M., Friedman, M., Kandel, A., General fuzzy least squares, Fuzzy Sets and Systems 88 (1), 107–118, 1997.
  • Mosleh, M., Fuzzy neural network for solving a system of fuzzy differential equations, Applied Soft Computing 13, 3597-3607, 2013.
  • Mosleh, M., Otadi, M., Abbasbandy, S., Evaluation of fuzzy regression model by fuzzy neural networks, Journal of Computational and Applied Mathematics 234 (1), 825- 834, 2010.
  • Nasrabadi, M. M., Nasrabadi, E. A., mathematical-programming approach to fuzzy linear regression analysis, Applied Mathematics and Computation 155 (3), 873-881, 2004.
  • Pasha, E., Razzaghnia, T., Allahviranloo, T., Yari, Gh., Mostafaei, H. R., A new mathematical programming approach in fuzzy linear regression models, Applied Mathematical Sciences 35, 1715, 2007.
  • Razzaghnia, T., Danesh, S., Nonparametric Regression with Trapezoidal Fuzzy Data, International Journal on Recent and Innovation Trends in Computing and Communication (IJRITCC) 3 (6), 3826 - 3831, 2015.
  • Razzaghnia, T., Danesh, S., Maleki, A., Hybrid fuzzy regression with trapezoidal fuzzy data, Proc. SPIE 8349 (834921), 2011.
  • Sarhadi, P., Rezaie, B., Rahmani, Z., Adaptive predictive control based on adaptive neuro-fuzzy inference system for a class of nonlinear industrial processes, Journal of the Taiwan Institute of Chemical Engineers 61, 132-137, 2016.
  • Shapiro, A., The merge of neural networks, fuzzy logic, and genetic algorithms, Insurance: Mathematics and Economics 31 (1), 115-131, 2002.
  • Sridevi, S., Nirmal, S., ANFIS based decision support system for prenatal detection of Truncus Arteriosus congenital heart defect, Applied Soft Computing 46, 577–587, 2016.
  • Stone, M., Cross validation choice and assessment of statistical predictions, Journal of the Royal Statistical Society 36 (series B), 111-147, 1974.
  • Takagi, T., Sugeno, M. Fuzzy identification of systems and its application to modelling and control, IEEE Transactions on Systems, Man and Cybernetics 15, 116-132, 1985.
  • Tanaka, H., Fuzzy data analysis by possibilistic linear models, Fuzzy Sets and Systems 24 (3), 363-375, 1987.
  • Tanaka, H., Hayashi, I., Watada, J., Possibilistic linear regression analysis for fuzzy data, European Journal of Operational Research 40 (3), 389-396, 1989.
  • Tanaka, H., Uejima, S. K., Asia, K., Linear regression analysis with fuzzy model, IEEE Transactions on Systems, Man and Cybernetics 12, 903-907, 1982.
  • Tanaka, H., Watada, J., Possibilistic linear systems and their application to the linear regression model, Fuzzy Sets and Systems 27 (3), 275-289, 1988.
  • Wang, N., Zhang, W. X., Mei, C. L., Fuzzy nonparametric regression based on local linear smoothing technique, Information Sciences 177 (18), 3882-3900, 2007.
  • Zhang, P., Model selection via multifold cross validation, Annals of Statistics 21 (1), 299-313, 1993.
There are 41 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Statistics
Authors

Sedigheh Danesh This is me

Publication Date December 12, 2018
Published in Issue Year 2018 Volume: 47 Issue: 6

Cite

APA Danesh, S. (2018). Fuzzy parameters estimation via hybrid methods. Hacettepe Journal of Mathematics and Statistics, 47(6), 1605-1624.
AMA Danesh S. Fuzzy parameters estimation via hybrid methods. Hacettepe Journal of Mathematics and Statistics. December 2018;47(6):1605-1624.
Chicago Danesh, Sedigheh. “Fuzzy Parameters Estimation via Hybrid Methods”. Hacettepe Journal of Mathematics and Statistics 47, no. 6 (December 2018): 1605-24.
EndNote Danesh S (December 1, 2018) Fuzzy parameters estimation via hybrid methods. Hacettepe Journal of Mathematics and Statistics 47 6 1605–1624.
IEEE S. Danesh, “Fuzzy parameters estimation via hybrid methods”, Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 6, pp. 1605–1624, 2018.
ISNAD Danesh, Sedigheh. “Fuzzy Parameters Estimation via Hybrid Methods”. Hacettepe Journal of Mathematics and Statistics 47/6 (December 2018), 1605-1624.
JAMA Danesh S. Fuzzy parameters estimation via hybrid methods. Hacettepe Journal of Mathematics and Statistics. 2018;47:1605–1624.
MLA Danesh, Sedigheh. “Fuzzy Parameters Estimation via Hybrid Methods”. Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 6, 2018, pp. 1605-24.
Vancouver Danesh S. Fuzzy parameters estimation via hybrid methods. Hacettepe Journal of Mathematics and Statistics. 2018;47(6):1605-24.