Geometric clustering fuzzy regression based on c-means clustering

Document Type : Research Paper

Author

University of Birjand

Abstract

In this paper, we present an approach to fit some clustering fuzzy linear regression models based on the fuzzy response variables and fuzzy parameters. In this approach, we first introduce a method for clustering crisp/fuzzy data based on fuzzy c-means clustering, and then, we fit some clustering fuzzy regression models based on the geometric mean. The optimal clustering fuzzy regression models are evaluated under two indices of goodness of fit. The applications of the proposed approach are studied in modeling some real data sets.

Keywords

Main Subjects

References

[1] M. Gh. Akbari, G. Hesamian, Linear model with exact inputs and interval-valued fuzzy outputs, IEEE Transactions
on Fuzzy Systems, 26 (2018), 518-530. https://doi.org/10.1109/TFUZZ.2017.2686356
[2] M. Arefi, Clustering regression based on interval-valued fuzzy outputs and interval-valued fuzzy parameters, Journal
of Intelligent and Fuzzy Systems, 30 (2016), 1339-1351. https://doi.org/10.3233/IFS-152048
[3] M. Arefi, Quantile fuzzy regression based on fuzzy outputs and fuzzy parameters, Soft Computing, 24 (2020), 311-320.
https://doi.org/10.1007/s00500-019-04424-2
[4] M. Arefi, A. H. Khammar, Nonlinear prediction of fuzzy regression model based on quantile loss function, Soft
Computing, 28(6) (2024), 4861-4871. https://doi.org/10.1007/s00500-023-09190-w
[5] M. Arefi, S. M. Taheri, Weighted similarity measure on interval-valued fuzzy sets and its application to pattern
recognition, Iranian Journal of Fuzzy Systems, 11 (2014), 67-79. https://doi.org/10.22111/ijfs.2014.1723
[6] M. Arefi, S. M. Taheri, Least squares regression based on Atanassov’s intuitionistic fuzzy inputs-outputs and
Atanassov’s intuitionistic fuzzy parameters, IEEE Transactions on Fuzzy Systems, 23 (2015), 1142-1154. https:
//doi.org/10.1109/TFUZZ.2014.2346246
[7] M. Asadolahi, M. Gh. Akbari, G. Hesamian, M. Arefi, A robust support vector regression with exact predictors
and fuzzy responses, International Journal of Approximate Reasoning, 132 (2021), 206-225. https://doi.org/10.
1016/j.ijar.2021.02.006
[8] E. Bas, E. Egrioglu, A fuzzy regression functions approach based on Gustafson-Kessel clustering algorithm, Information
Sciences, 592 (2022), 206-214. https://doi.org/10.1016/j.ins.2022.01.057
[9] J. Chachi, A weighted least-squares fuzzy regression for crisp input-fuzzy output data, IEEE Transactions on Fuzzy
Systems, 27 (2019), 739-748. https://doi.org/10.1109/TFUZZ.2018.2868554
[10] J. Chachi, A. Kazemifard, M. Jalalvand, A multi-attribute assessment of fuzzy regression models, Iranian Journal
of Fuzzy Systems, 18 (2021), 131-148. https://doi.org/10.22111/ijfs.2021.6181
[11] J. Chachi, M. Roozbeh, A fuzzy robust regression approach applied to bedload transport data, Communications
in Statistics - Simulation and Computation, 46 (2017), 1703-1714. https://doi.org/10.1080/03610918.2015.
1010002
[12] J. Chachi, S. M. Taheri, Multiple fuzzy regression model for fuzzy input-output data, Iranian Journal of Fuzzy
Systems, 13 (2016), 63-78. https://doi.org/10.22111/ijfs.2016.2596
[13] L. H. Chen, S. H. Nien, A new approach to formulate fuzzy regression models, Applied Soft Computing, 86 (2020),
Article No.: 105915. https://doi.org/10.1016/j.asoc.2019.105915
[14] F. Dotto, A. Farcomeni, L. A. Garcia-Escudero, A. Mayo-Iscar, A fuzzy approach to robust regression clustering,
Advances in Data Analysis and Classification, 11 (2017), 691-710. https://doi.org/10.1007/s11634-016-0271-9
[15] D. E. Gustafson, W. C. Kessel, Fuzzy clustering with a fuzzy covariance matrix, Proceedings of the IEEE Conference
on Decision and Control, San Diego, (1978), 761-766. https://doi.org/10.1109/CDC.1978.268028
[16] G. Hesamian, M. Gh. Akbari, Fuzzy quantile linear regression model adopted with a semi-parametric technique
based on fuzzy predictors and fuzzy responses, Expert Systems With Applications, 118 (2019), 585-597. https:
//doi.org/10.1016/j.eswa.2018.10.026
[17] G. Hesamian, M. Gh. Akbari, A fuzzy additive regression model with exact predictors and fuzzy responses, Applied
Soft Computing, 95 (2020), Article No.: 106507. https://doi.org/10.1016/j.asoc.2020.106507
[18] E. Hosseinzadeh, H. Hassanpour, M. Arefi, A weighted goal programming approach to fuzzy linear regression
with crisp inputs and type-2 fuzzy outputs, Soft Computing, 19 (2015), 1143-1151. https://doi.org/10.1007/
s00500-014-1328-3
[19] E. Hosseinzadeh, H. Hassanpour, M. Arefi, A weighted goal programming approach to estimate the linear regression
model in full quasi type-2 fuzzy environment, Journal of Intelligent and Fuzzy Systems, 30 (2016), 1319-1330.
https://doi.org/10.3233/IFS-152046
[20] H. Y. Jung, J. H. Yoon, S. H. Choi, Fuzzy linear regression using rank transform method, Fuzzy Sets and Systems,
274 (2015), 97-108. https://doi.org/10.1016/j.fss.2014.11.004
[21] M. Kelkinnama, S. M. Taheri, Fuzzy least-absolutes regression using shape preserving operations, Information
Sciences, 214 (2012), 105-120. https://doi.org/10.1016/j.ins.2012.04.017
[22] A. H. Khammar, M. Arefi, M. Gh. Akbari, A robust least squares fuzzy regression model based on kernel function,
Iranian Journal of Fuzzy Systems, 17(4) (2020), 105-119. https://doi.org/10.22111/ijfs.2020.5409
[23] A. H. Khammar, M. Arefi, M. Gh. Akbari, A general approach to fuzzy regression models based on different loss
functions, Soft Computing, 25 (2021), 835-849. https://doi.org/10.1007/s00500-020-05441-2
[24] A. H. Khammar, M. Arefi, M. Gh. Akbari, Quantile fuzzy varying coefficient regression based on kernel function,
Applied Soft Computing, 107 (2021), Article No.: 107313. https://doi.org/10.1016/j.asoc.2021.107313
[25] J. Mohammadi, S. M. Taheri, Pedomodels fitting with fuzzy least squares regression, Iranian Journal of Fuzzy
Systems, 1 (2004), 45-61. https://doi.org/10.22111/ijfs.2004.505
[26] E. N. Nasibov, Fuzzy least squares regression model based of weighted distance between fuzzy numbers, Automatic
Control and Computer Sciences, 41 (2007), 10-17. https://doi.org/10.3103/S0146411607010026
[27] S. M. Taheri, M. Kelkinnama, Fuzzy linear regression based on least absolute deviations, Iranian Journal of Fuzzy
Systems, 9 (2012), 121-140. https://doi.org/10.22111/ijfs.2012.230
[28] R. N. Xu, C. L. Li, Multidimensional least-squares fitting with a fuzzy model, Fuzzy Sets and Systems, 119 (2001),
215-223. https://doi.org/10.1016/S0165-0114(98)00350-9
[29] M. S. Yang, C. H. Ko, On cluster-wise fuzzy regression analysis, IEEE Transactions on Systems, Man, and Cybernetics,
Part B: Cybernetics, 27 (1997), 1-13. https://doi.org/10.1109/3477.552181
[30] M. S. Yang, T. S. Lin, Fuzzy least-squares linear regression analysis for fuzzy input-output data, Fuzzy Sets and
Systems, 126 (2002), 389-399. https://doi.org/10.1016/S0165-0114(01)00066-5
[31] W. Zeng, Q. Feng, J. Lia, Fuzzy least absolute linear regression, Applied Soft Computing, 52 (2016), 1009-1019.
https://doi.org/10.1016/j.asoc.2016.09.029
[32] H. J. Zimmermann, Fuzzy sets theory and its applications, Third Eds., Kluwer, Boston, 1996. hhttps://doi.org/
10.1007/978-94-010-0646-0
Iranian Journal of Fuzzy Systems
Volume 22, Issue 3
May and June 2025
Pages 87-101

Files

Share

How to cite

Statistics