| تعداد نشریات | 31 |
| تعداد شمارهها | 834 |
| تعداد مقالات | 8,015 |
| تعداد مشاهده مقاله | 14,852,495 |
| تعداد دریافت فایل اصل مقاله | 9,586,515 |
Multiple Fuzzy Regression Model for Fuzzy Input-Output Data | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 6، دوره 13، شماره 4، آبان 2016، صفحه 63-78 اصل مقاله (410.75 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2016.2596 | ||
| نویسندگان | ||
| Jalal Chachi* 1؛ S. Mahmoud Taheri2 | ||
| 1Department of Mathematics, Statistics and Computer Sciences, Sem- nan University, Semnan, Semnan 35195-363, Iran | ||
| 2Faculty of Engineering Science, College of Engineering, University of Tehran, Tehran, P.O. Box 11365-4563, Iran | ||
| چکیده | ||
| A novel approach to the problem of regression modeling for fuzzy input-output data is introduced. In order to estimate the parameters of the model, a distance on the space of interval-valued quantities is employed. By minimizing the sum of squared errors, a class of regression models is derived based on the interval-valued data obtained from the $\alpha$-level sets of fuzzy input-output data. Then, by integrating the obtained parameters of the interval-valued regression models, the optimal values of parameters for the main fuzzy regression model are estimated. Numerical examples and comparison studies are given to clarify the proposed procedure, and to show the performance of the proposed procedure with respect to some common methods. | ||
| کلیدواژهها | ||
| Fuzzy regression؛ Interval-valued regression؛ Least squares method؛ $LR$-Fuzzy number؛ Multiple regression؛ Predictive ability | ||
| مراجع | ||
|
[1] A. R. Arabpour and M. Tata, Estimating the parameters of a fuzzy linear regression model, Iranian Journal of Fuzzy Systms, 5(2) (2008), 1-19. [2] M. Are and S. M. Taheri, Least-squares regression based on Atanassov's intuitionistic fuzzy inputs-outputs and Atanassov's intuitionistic fuzzy parameters, IEEE Trans. on Fuzzy Syst., 23 (2015), 1142-1154. [3] A. Bargiela, W. Pedrycz and T. Nakashima, Multiple regression with fuzzy data, Fuzzy Sets Syst., 158 (2007), 2169-2188. [4] A. Bisserier, R. Boukezzoula and S. Galichet, A revisited approach to linear fuzzy regression using trapezoidal fuzzy intervals, Inf. Sci., 180 (2010), 3653-3673. [5] J. Chachi and M. Roozbeh, A fuzzy robust regression approach applied to bed- load transport data, Communications in Statistics-Simulation and Computation, DOI: 10.1080/03610918.2015.1010002, 2015. [6] J. Chachi and S. M. Taheri, A least-absolutes approach to multiple fuzzy regression, in: Proc. 58th ISI Congress, Dublin, Ireland, CPS077-01, 2011. [7] J. Chachi and S. M. Taheri, A least-absolutes regression model for imprecise response based on the generalized Hausdor-metric, J. Uncertain Syst., 7 (2013), 265-276. [8] J. Chachi, S. M. Taheri and N. R. Arghami, A hybrid fuzzy regression model and its appli- cation in hydrology engineering, Applied Soft Comput., 25 (2014), 149{158. [9] J. Chachi, S. M. Taheri and H. Rezaei Pazhand, Suspended load estimation using L1-Fuzzy regression, L2-Fuzzy regression and MARS-Fuzzy regression models, Hydrological Sciences J., 61(8) (2016), 1489-1502. [10] J. Chachi, S. M. Taheri and R. H. Rezaei Pazhand, An interval-based approach to fuzzy regression for fuzzy input-output data, in: Proc. IEEE Int. Conf. Fuzzy Syst., Taipei, Taiwan, (2011), 2859-2863. [11] S. P. Chen and J. F. Dang, A variable spread fuzzy linear regression model with higher explanatory power and forecasting accuracy, Inf. Sci., 178 (2008), 3973-3988. [12] R. Coppi, P. D'Urso, P. Giordani and A. Santoro, Least squares estimation of a linear re- gression model with LR fuzzy response, Comp. Stat. Data Anal., 51 (2006), 267-286. [13] P. D'Urso, Linear regression analysis for fuzzy/crisp input and fuzzy/crisp output data, Comp. Stat. Data Anal., 42 (2003), 47-72. [14] P. D'Urso and Gastaldi T., An orderwise polynomial regression procedure for fuzzy data, Fuzzy Set Syst., 130 (2002), 1-19. [15] P. D'Urso, R. Massari and A. Santoro, A class of fuzzy clusterwise regression models, Inf. Sci., 180 (2010), 4737-4762. [16] P. D'Urso, R. Massari and A. Santoro, Robust fuzzy regression analysis, Inf. Sci., 181 (2011), 4154-4174. [17] P. D'Urso and A. Santoro, Fuzzy clusterwise regression analysis with symmetrical fuzzy output variable, Comp. Stat. Data Anal., 51 (2006), 287-313. [18] M. B. Ferraro, R. Coppi, G. Gonzalez Rodrguez and A. Colubi, A linear regression model for imprecise response, Int. J. Approx. Reason., 51 (2010), 759-770. [19] H. Hassanpour, H. R. Maleki and M. A. Yaghoobi, Fuzzy linear regression model with crisp coecients: A programming approach, Iranian J. Fuzzy Syst., 7 (2010), 19-39. [20] H. Hassanpour, H. R. Maleki and M. A. Yaghoobi, A goal programming approach to fuzzy linear regression with fuzzy input-output data, Soft Comput., 15 (2011), 1569-1580. [21] Y. C. Hu, Functional-link nets with genetic-algorithm-based learning for robust nonlinear interval regression analysis, Neurocomputin, 72 (2009), 1808-1816. [22] C. Kao and C. L. Chyu, A fuzzy linear regression model with better explanatory power, Fuzzy Sets Syst., 126 (2002), 401-409. [23] C. Kao and C. L. Chyu, Least-squares estimates in fuzzy regression analysis, European J. Oper. Res., 148 (2003), 426-435. [24] M. Kelkinnama and S. M. Taheri, Fuzzy least-absolutes regression using shape preserving operations, Inf. Sci., 214 (2012), 105-120. [25] B. Kim and R. R. Bishu, Evaluation of fuzzy linear regression models by comparison mem- bership function, Fuzzy Sets Syst., 100 (1998), 343-352. [26] K. S. Kula and A. Apaydin, Fuzzy robust regression analysis based on the ranking of fuzzy sets, Int. J. Uncertain., Fuzziness Knowledge-Based Syst., 16 (2008), 663-681. [27] J. Lu and R. Wang, An enhanced fuzzy linear regression model with more exible spreads, Fuzzy Sets Syst., 160 (2009), 2505-2523. [28] M. H. Mashinchi, M. A. Orgun, M. Mashinchi and W. Pedrycz, A tabu-harmony search-based approach to fuzzy linear regression, IEEE Trans. Fuzzy Syst., 19 (2011), 432-448. [29] MATLAB, The Language of Technical Computing, The MathWorks Inc., MA, 2009. [30] M. Modarres, E. Nasrabadi and M. M. Nasrabadi, Fuzzy linear regression analysis from the point of view risk, Int. J. Uncertain., Fuzziness Knowledge-Based Syst., 12 (2004), 635-649. [31] M. Modarres, E. Nasrabadi and M. M. Nasrabadi, Fuzzy linear regression with least squares errors, Appl. Math. Comput., 163 (2005), 977-989. [32] R. E. Moore, R. B. Kearfott and M. J. Cloud, Introduction to Interval Analysis, Society for Industrial and Applied Mathematics, Philadelphia, PA, 2009. [33] M. Namdari, J. H. Yoon, A. Abadi, S. M. Taheri and S. H. Choi, Fuzzy logistic regression with least absolute deviations estimators, Soft Comput., 19 (2015), 909-917. [34] E. Nasrabadi and S. M. Hashemi, Robust fuzzy regression analysis using neural networks, Int. J. Uncertain., Fuzziness Knowledge-Based Syst., 16 (2008), 579-598. [35] E. Nasrabadi, S. M. Hashemi and M. Ghatee, An LP-based approach to outliers detection in fuzzy regression analysis, Int. J. Uncertain., Fuzziness Knowledge-Based Syst., 15 (2007), 441-456. [36] M. M. Nasrabadi and E. Nasrabadi, A mathematical-programming approach to fuzzy linear regression analysis, Appl. Math. Comput., 155 (2004), 873-881. [37] M. M. Nasrabadi, E. Nasrabadi and A. R. Nasrabadi, Fuzzy linear regression analysis: a multi-objective programming approach, Appl. Math. Comput., 163 (2005), 245-251. [38] S. Pourahmad, S. M. T. Ayatollahi and S. M. Taheri, Fuzzy logistic regression: A new possibilistic model and its application in clinical vague status, Iranian J. Fuzzy Syst., 8 (2011), 1-17. [39] S. Pourahmad, S. M. T. Ayatollahi, S. M. Taheri and Z. Habib Agahi, Fuzzy logistic regression based on the least squares approach with application in clinical studies, Comput. Math. Appl., 62 (2011), 3353-3365. [40] M. R. Rabiei, N. R. Arghami, S. M. Taheri and B. Sadeghpour Gildeh, Least-squares approach to regression modeling in full interval-valued fuzzy environment, Soft Comput., 18 (2014), 2043-2059. [41] M. Sakawa and H. Yano, Multiobjective fuzzy linear regression analysis for fuzzy input-output data, Fuzzy Sets Syst., 157 (1992), 173-181. [42] H. Shakouri and R. Nadimi, A novel fuzzy linear regression model based on a non-equality possibility index and optimum uncertainty, Appl. Soft Comput., 9 (2009), 590-598. [43] S. M. Taheri and M. Kelkinnama, Fuzzy linear regression based on least absolute deviations, Irannian Journal of Fuzzy Systems, 9(1) (2012), 121-140. [44] H. Tanaka, I. Hayashi and J. Watada, Possibilistic linear regression analysis for fuzzy data, European J. Oper. Res., 40 (1989), 389-396. [45] H. Tanaka, S. Vejima and K. Asai, Linear regression analysis with fuzzy model, IEEE Trans. Syst., Man, Cybernetics, 12 (1982), 903-907. [46] H. J. Zimmermann, Fuzzy set theory and its applications, 4th ed., Kluwer Niho, Boston, 2001. | ||
|
آمار تعداد مشاهده مقاله: 2,370 تعداد دریافت فایل اصل مقاله: 5,467 |
||