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. 2026 Jun 19;16:28192. doi: 10.1038/s41598-026-59014-8

Table 2.

Indicator weight values and their rankings calculated by the CDFA and LTDM.

Specific indicators indicator LTDM weight CDFA weight
Financial Institutions’ Deposit-Loan Ratio X1 0.1468(14) 0.0644(5)
Public Finance Revenue-Expenditure Ratio X2 0.1648(9) 0.0401(12)
Agricultural Output Growth X3 0.1905(7) 0.0287(16)
Mean Nighttime Light Intensity X4 0.1223(16) 0.0318(15)
Consumption Rate X5 0.2111(5) 0.0477(8)
Per Capita Retail Sales of Consumer Goods X6 0.2595(4) 0.0717(4)
Industrial Structure Advancement Index X7 0.1602(10) 0.0255(18)
PM₂.₅ Index X8 0.1599(11) 0.0438(10)
CO₂ Emissions X9 0.1526(13) 0.0353(14)
Chemical Fertilizer Usage per Unit of Cultivated Area X10 0.1577(12) 0.0412(11)
Pesticide Usage per Unit of Cultivated Area X11 0.1014(19) 0.0729(3)
Urbanization Rate X12 0.1781(8) 0.0482(7)
Urban-Rural Income Coordination Index X13 0.1289(15) 0.0286(17)
Physicians per 1000 People X14 0.195(6) 0.0458(9)
Hospital beds per 1000 People X15 0.5106(1) 0.0381(13)
Social Welfare Recipients per 10,000 People X16 0.3609(3) 0.021(19)
Social Welfare Beds per 1000 People X17 0.4192(2) 0.0634(6)
Economic Association Intensity X18 0.1211(17) 0.1145(2)
County Association Intensity X19 0.1039(18) 0.1371(1)

The numbers in parentheses indicate the descending rank order of each indicator’s weight value in the corresponding method. Unlike conventional methods constrained by a linear sum of 1 (∑wi=1), the LTDM weights represent an eigenvector governed by the Euclidean norm constraint (Inline graphic); therefore, their simple mathematical sum naturally exceeds 1.