Document Type : Original/Review Paper


1 Buein Zahra Technical University, Buein Zahra, Ghazvin, Iran.

2 Young Researchers and Elite Club, East Tehran Branch, Islamic Azad University, Tehran, Iran.



This paper presents a new method for regression model prediction in an uncertain environment. In practical engineering problems, in order to develop regression or ANN model for making predictions, the average of set of repeated observed values are introduced to the model as an input variable. Therefore, the estimated response of the process is also the average of a set of output values where the variation around the mean is not determinate. However, to provide unbiased and precise estimations, the predictions are required to be correct on average and the spread of date be specified. To address this issue, we proposed a method based on the fuzzy inference system, and genetic and linear programming algorithms. We consider the crisp inputs and the symmetrical triangular fuzzy output. The proposed algorithm is applied to fit the fuzzy regression model. In addition, we apply a simulation example and a practical example in the field of machining process to assess the performance of the proposed method in dealing with practical problems in which the output variables have the nature of uncertainty and impression. Finally, we compare the performance of the suggested method with other methods. Based on the examples, the proposed method is verified for prediction. The results show that the proposed method reduces the error values to a minimum level and is more accurate than the Linear Programming (LP) and fuzzy weights with linear programming (FWLP) methods.


[1] Zhang, C. & Guo, P. (2018). FLFP: A fuzzy linear fractional programming approach with double-sided fuzziness for optimal irrigation water allocation. Agricultural Water Management, vol. 199, pp.105–119.

[2] Tanaka, H., Uejima, S. & Asia, K. (1982). Linear regression analysis with fuzzy model, IEEE Transactions on Systems. Man and Cybernetics, vol. 12, pp. 903-907.

[3] Kumar, A.,  Kaur, J. & Singh P. (2011). A new method for solving fully fuzzy linear programming problems. Applied Mathematical Modelling, vol. 35, no. 2, pp. 817-823.

[4] Lotfi, F. H. T., Allahviranloo, M., Jondabeh, A. & Alizadeh, L. (2009). Solving a full fuzzy linear programming using lexicography method and fuzzy approximate solution. Applied Mathematical Modelling, vol. 33, pp.3151–3156.

[5] Goudarzi, F. K., Nasseri, S. H.& Taghnezhad, N. A. (2020). A new interactive approach for solving fully fuzzy mixed integer linear programming problems. Yugoslav Journal of Operations Research, vol. 30, no. 1, pp.71-89.

[6] Diamond, P. (1988). Fuzzy least squares. Information Sciences, vol. 46, no. 3, pp.141-157.

[7] Tanaka, H. (1987). Fuzzy data analysis by possibilistic linear models. Fuzzy Sets and Systems, vol. 24, no. 3, pp.363-375.

[8] Tanaka, H., Hayashi, I. & Watada, J. (1989). Possibilistic linear regression analysis for fuzzy data. European Journal of Operational Research, vol. 40, no. 3, pp. 389-396.

[9] Danesh, S., Farnoosh, R., Razzaghnia & T. (2016). Fuzzy nonparametric regression based on adaptive neuro-fuzzy inference system. Neurocomputing. vol. 173, pp. 1450-1460.

[10] Razzaghnia, T., Danesh, S. & Maleki, A. (2011). Hybrid fuzzy regression with trapezoidal fuzzy data. Proc. Fourth International Conference on Machine Vision (ICMV 2011): Machine Vision, Image Processing, and Pattern Analysis, Singapore, 2011.

[11] Razzaghnia, T. & Danesh, S. (2015). Nonparametric Regression with Trapezoidal Fuzzy Data. International Journal on Recent and Innovation Trends in Computing and Communication (IJRITCC), vol. 3, no. 6, pp. 3826 – 3831.

[12] Danesh, S. (2018). Fuzzy Parameters Estimation via Hybrid Methods. Hacettepe Journal of Mathematics and Statistics,  vol. 47, no. 6, pp. 1605 – 16244.

[13] Razzaghnia T. & Pasha, E. (2009). A new mathematical programming approach in fuzzy linear regression models. Applied Mathematical Sciences, vol. 18, no. 70, pp50-59.

[14] AL-Othman, A.K. (2009). A fuzzy state estimator based on uncertain measurements. Measurement, vol. 42, no. 4, pp. 628-637.

[15] Ali, M.,   Deo, R. C., Downs, N. J. & Maraseni T., An ensemble-ANFIS based uncertainty assessment model for forecasting multi-scalar standardized precipitation index. Atmospheric Research, vol. 207, no. 15, 2018, pp. 155-180.

[16] Danesh, M., Danesh, S. & Khalili K. (2019). Multi-Sensory Data Fusion System for Tool Condition Monitoring Using Optimized Artificial Fuzzy Inference System. Mechanics Aaerospace Journal, vol. 15, no. 2, pp. 103-118.

[17] Fogel, D.B. (1995). Evolutionary computation: toward a new philosophy of machine intelligence. New York, IEEE Press, pp. 87-121.

[18] DeJong, K. (1988). Learning with genetic algorithms: an overview. Mach Learn 3, pp. 121–138.

[19] Goldberg, DE. (1989). Genetic algorithms in search, optimization, and machine learning, Addison-Wesley, pp.1-15.

[20] Jang, J. S. R. (1992). Self-learning fuzzy controllers based on temporal back-propagation. IEEE Transactions on Neural Network, vol. 3, pp. 714-723.

[21] Jang, J. S. R. (1993). ANFIS: adaptive-network-based fuzzy inference system. IEEE Trans Syst Man Cyber, vvol. 23, no. 3, pp. 665-685.

[22] Takagi, T. & Sugeno, M. (1985) Fuzzy identification of systems and its application to modelling and control. IEEE Transactions on Systems, Man and Cybernetics, vol. 15, pp. 116-132.

[23] Benardos, P. G., Mosialos, S. & Vosniakos, G.C. (2006). Prediction of workpiece elastic deflections under cutting forces in turning. Robotics and Computer-Integrated Manufacturing, vol. 22, pp. 505–514.

[24] Danesh, M. & Khalili, K. (2015). Determination of Tool Wear in Turning Process Using Undecimated Wavelet Transform and Textural Features. Procedia Technology, vol.19, pp. 98-105.

[25] Khalili, K. & Danesh, M. (2015). Identification of vibration level in metal cutting using undecimated wavelet transform and gray-level co-occurrence matrix texture features, Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, vol. 229, pp. 205-213.

[26] Qiang, L.Z. (2000). Finite difference calculations of the deformations of multi-diameter workpieces during turning. Journal of Materials Processing Technology, vol. 98, pp. 310–316.

[27] Phan, A.V., Baron, L., Mayer, J.R.R. & Cloutier, G. (2003). Finite element and experimental studies of diametral errors in cantilever bar turning. Applied Mathematical Modelling, vol. 27, pp. 221–232.