Fuzzy Regression Analysis with a proposed model
Article Sidebar
Main Article Content
Abstract
Regression analysis refers to methods by which estimates are made for the model parameters from the knowledge of the values of a given input-output data set. The aim of this research this research is to find a suitable model and determine the ‘best’ values of the parameters of the model from the given data. In the statistical regression analysis, deviations between the observed output values and corresponding values predicted by the model are attributed to random errors. It is often assumed that the distribution of these random errors is Gaussian. On the other hand, in fuzzy regression analysis the deviations (errors) are attributed to the imprecision or the vagueness of the system structure or data. The research proposed a new fuzzy linear programming model. The new proposed model is compared with the models used in the literature which are Tanaka, Hojati and Tansu regression models. The results are presented and comparison has been done for each model. Eleven different applications have been mentioned. Then the comparison of results of all the application regarding each similarity measure of goodness of fit is stated in the paper.
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
Wong, Y. J., Arumugasamy, S. K., Chung, C. H., Selvarajoo, A., & Sethu, V. (2020). Comparative study of artificial neural network (ANN), adaptive neuro-fuzzy inference system (ANFIS) and multiple linear regression (MLR) for modeling of Cu (II) adsorption from aqueous solution using biochar derived from rambutan (Nephelium lappaceum) peel. Environmental monitoring and assessment, 192(7), 1-20.
Hosseinzadeh, E., & Hassanpour, H. (2021). Estimating the parameters of fuzzy linear regression model with crisp inputs and Gaussian fuzzy outputs: A goal programming approach. Soft Computing, 25(4), 2719-2728.
Kashani, M., Arashi, M., Rabiei, M. R., D’Urso, P., & De Giovanni, L. (2021). A fuzzy penalized regression model with variable selection. Expert Systems with Applications, 175, 114696.
TOPUZ, A. P. D. D. (2021). FUZZY LINEAR REGRESSION AND FUZZY PEARSON CORRELATION ANALYSIS. DIFFERENT STATISTICAL APPLICATIONS IN AGRICULTURE, 167.
Topuz, D. (2021). Jackknife Resampling Method for Estimation of Fuzzy Regression Parameters and Revised Tanaka Method. PROGRESS IN NUTRITION, 23.
Kayan, G., Türker, U., & Erten, E. (2022). A fuzzy logic framework to handle uncertainty in remote sensing‐based hydrological data for water budget improvement across mid‐and small‐scale basins. Hydrological Processes, 36(11), e14740.
Asai, H. T. S. U. K., Tanaka, S., & Uegima, K. (1982). Linear regression analysis with fuzzy model. IEEE Trans. Systems Man Cybern, 12, 903-907.
Medaglia, A. L., Fang, S. C., Nuttle, H. L., & Wilson, J. R. (2002). An efficient and flexible mechanism for constructing membership functions. European Journal of Operational Research, 139(1), 84-95.
Chen, J. E., & Otto, K. N. (1995). Constructing membership functions using interpolation and measurement theory. Fuzzy Sets and systems, 73(3), 313-327.
Yen, K. K., Ghoshray, S., & Roig, G. (1999). A linear regression model using triangular fuzzy number coefficients. Fuzzy sets and systems, 106(2), 167-177.
Tanaka, H., Hayashi, I., & Watada, J. (1989). Possibilistic linear regression analysis for fuzzy data. European Journal of Operational Research, 40(3), 389-396.
Luczynski, W., & Matloka, M. (1996). Fuzzy regression models and their applications. JOURNAL OF FUZZY MATHEMATICS, 4, 513-518.
Hojati, M., Bector, C. R., & Smimou, K. (2005). A simple method for computation of fuzzy linear regression. European Journal of Operational Research, 166(1), 172-184.
Kambo, N. S. (1984). Mathematical Programming Techniques, Affiliated East.
Ishibuchi, H., & Nii, M. (2001). Fuzzy regression using asymmetric fuzzy coefficients and fuzzified neural networks. Fuzzy Sets and Systems, 119(2), 273-290.