Correction: A multi-stakeholder fuzzy best–worst method analysis of key factors in remanufacturing production processes

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Correction to: Scientific Reports 10.1038/s41598-025-31401-7, published online 02 February 2026

The original version of this Article contained errors in Equation 6.

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\mathop{\mathrm{min}\:\xi}\limits_{s.t.}\left\{\begin{array}{c}\left|\frac{{W}{b}}{{W}{b}+{W}{j}}-{a}{bj}\right|\:\leq\:\xi\:,\:\forall\:j,\\\:\left|\frac{{W}{j}}{{W}{w}+{W}{j}}-{a}{jw}\right|\:\leq\:\xi\:,\:\forall\:j,\\\:{\sum\:}{j=1}^{n}{W}{j}=1,\text{}\\\:{W}_{j}\in\:\left[\mathrm{0,1}\right],\:\forall\:j.\text{}\end{array}\right.$$\end{document}

now reads:

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\mathop{\mathrm{min}\:\xi}\limits_{s.t.}\left\{\begin{array}{l}\left|\frac{{W}_{b}}{{W}_{b}+{W}_{j}}-{a}_{bj}\right|\:\leq\:\xi,\:\forall j,\\\:\left|\frac{{W}_{j}}{{W}_{w}+{W}_{j}}-{a}_{jw}\right|\:\leq\:\xi,\:\forall j,\\\:{\sum}_{j=1}^{n}\:{W}_{j}=1,\text{}\\\:{W}_{j}\in\:\left[\mathrm{0,1}\right],\:\forall j.\text{}\end{array}\right.$$\end{document}

The original Article has been corrected.