A Hybrid Method for Estimating ‎ Fuzzy Regression Parameters Data

Subject Areas : Computer Engineering

Ali Maleki ¹

1 -

Received: 2024-11-30 Accepted : 2025-01-06 Published : 2024-12-31

Keywords: Trapezoidal fuzzy numbers, hybrid fuzzy regression, reliability,

Abstract :

In this study, a hybrid fuzzy regression method for trapezoidal fuzzy data is proposed. Initially, a new definition of a weighted fuzzy arithmetic for trapezoidal fuzzy data is introduced. Subsequently, a method for hybrid fuzzy least squares linear regression based on this definition is developed. Additionally, methods for bivariate and multivariate regression models are obtained. Finally, reliability measures for the hybrid regression model using the new definition of weighted fuzzy arithmetic for trapezoidal fuzzy data are calculated.

References:

[1] H. Tanaka, S. Uejima, K. Asia, “Linear regression analysis with fuzzy model”, IEEE Transactions on Systems, Man, and Cybernetics, Vol. 12, pp. 903-907,(1982).
[2] H. Tanaka, J. Watada, “Possibility linear systems and their application to the linear regression model” , Fuzzy Sets and Systems Vol. 27, pp. 275-289(1988).
[3] H. Tanaka, I. Hayashi, J. Watada, “Possibility linear regression analysis for fuzzy data” , European Journal of Operational Research Vol. 40, pp. 389-396, (1989).
[4] D.T. Redden and W. H Woodall, “Properties of certain fuzzy linear regression methods”, Fuzzy Sets and Systems Vol. 64, pp. 361-375, (1994).
[5] Tanaka, H., Ishibuchi, H., “Identification of possibility linear sytsems by quadratic Membership functions of Fuzzy parmeters”, Fuzzy Sets and Systems, Vol. 69, pp. 305-318 , (1995). [6] P. Diamond, “Fuzzy least squares”, Inform.Sci, Vol. 46, pp. 669-690, (1988).
[7] M. Sakawa, H. Yano, “Multi objective fuzzy linear regression analysis for fuzzy input-output data” , Fuzzy Sets and Systems, Vol. 47, pp. 173-181, (1992).
[8] B., Kim, R.R., Bishu, “Evaluation of Fuzzy linear regression models by comparison membership function”, Fuzzy Sets and Systems, Vol. 100, pp. 343-352, (1998).
[9] D.Hun Hong, Ch.Hwang, Ch.Ahn, “Ridge estimation for regression models with crisp inputs and Gaussian fuzzy output”, Fuzzy Sets and Systems, Vol. 142, pp. 307-319, (2004)
[10] T. Razzaghnia, “Regression parameters Prediction in data set with outlier using neural network”, Hacettepe Journal of Mathematics and Statistics, Vol. 48, pp. 1170-1184, (2019).
[11] T. Razaghnia. ,R. Naderkhani, M. H. Behzad, R. Farnoosh, “Fuzzy Regression Analysis Based on Fuzzy Neural Networks Using Trapezoidal Data”, Int. J. Fuzzy Syst., Vol. 23, No. 5, pp. 1267-1280, (2021).
[12] T. Razzaghnia, S. Danesh, A. Maleki, M. Danesh, M, “An Adaptive Fuzzy Inference System Model to Analyze Fuzzy Regression with Quadratic Programming and Fuzzy Weights Incorporating Uncertainty in the Observed Data”, Fuzzy Information and Engineering, Vol. 15, No. 2, pp. 87-99, (2023).
[13] D. Dubois, H. Prade, “Fuzzy Sets and Systems: Theory and Application”, Academic Press, New York, (1980).
[14] Y. H.O. Chang, “Hybrid fuzzy least-squares regression analysis and its reliability measures”, Fuzzy Sets and Systems, Vol. 119, pp. 225-246, (2001).