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Fuzzy Linear Regression Model Based on Adaptive Lasso Method

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Abstract

In this paper, we propose a fuzzy adaptive lasso (least absolute shrinkage and selection operator) estimate for fuzzy linear regression with crisp inputs and fuzzy outputs. The proposed estimate is obtained by imposing an \(L_1\) penalty on the least-squares error. Compared with fuzzy lasso estimate proposed by Hesamian and Akbari (Int J Approx Reason 115:290–300, 2019), the estimate we proposed assigns different weights to different coefficients, which is reasonable to significant covariates. Some numerical experiments are conducted to evaluate the performance of the proposed estimate. In most cases, fuzzy adaptive lasso estimate outperforms five commonly used estimates, especially when the variances of the error terms are small.

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Acknowledgements

Dr. Kong was supported by the National Natural Science Foundation of China (No. 11801317).

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  1. School of Statistics, Shandong University of Finance and Economics, Jinan, 250014, China

    Lingtao Kong

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  1. Lingtao Kong
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Correspondence to Lingtao Kong.

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Kong, L. Fuzzy Linear Regression Model Based on Adaptive Lasso Method. Int. J. Fuzzy Syst. 24, 508–518 (2022). https://doi.org/10.1007/s40815-021-01156-0

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