Table 3 Weight of third-level evaluation index.

First-level index	Second-level index	Third-level index	Weight	Ranking	Model type
Financial performance evaluation of listed firms	Profitability	Return on equity (ROE)	0.016	2nd	Swallowtail model
		Return on assets (ROA)	0.005	3rd
		Return on invested capital (ROIC)	0.017	1st
	Operational capability	Accounts receivable turnover	0.393	1st	Swallowtail model
		Inventory turnover	0.180	3rd
		Total asset turnover	0.232	2nd
	Growth capability	Total asset growth rate	0.054	1st	Swallowtail model
		Revenue growth rate	0.045	2nd
		Sustainable growth rate	0.011	3rd
	Debt repayment capability	Current ratio	0.020	1st	Swallowtail model
		Quick ratio	0.018	2nd
		Debt-to-assets ratio	0.002	3rd

Note: According to the classification theorem, there are two catastrophe models: cusp-like catastrophe and umbilical catastrophe (Arnold et al., 1986). This article, based on related research, chose cusp-like mutations (including four types: Fold model (including one type of singular lines), Cusp model (including two types of singular lines), Swallowtail model (including three types of singular lines), Butterfly model (including four types of singular lines) (Anthony et al., 2019; Guastello et al., 2019).

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