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Table 5 Pairwise comparison matrix, factor weights, the largest eigenvalues and CRs of the different layers

From: An evaluation system for the development of scaling off at earthen sites in arid areas in NW China

Criterion and index layers Pairwise comparison matrix Weights
[1] [2] [3]    
Criterion layer
 [1] Advantage area 1       0.6301
 [2] Thickness of crusted layers 1/4 1      0.2184
 [3] Thickness of loose layers 1/3 1/2 1     0.1515
 λmax=  3.1079, CR = 0.0930 < 0.1
Index layer
 Advantage area (B1) [1] [2]      
 [1] Porosity (C1) 1       0.6667
 [2] Shrinkage limit (C2) 2 1      0.3333
Thickness of crusted layers (B2) [1] [2] [3] [4] [5] [6]  
[1] Porosity (C3) 1       0.1596
[2] Shrinkage limit (C4) 3 1      0.3825
[3] Clay content (C5) 1/4 1/6 1     0.0428
[4] Coarse silt content (C6) 1/3 1/5 2 1    0.0641
[5] Annual rainfall (C7) 2 1/2 5 4 1   0.2504
[6] Annual evaporation (C8) 1/2 1/4 3 2 1/3 1 0.1006
λmax=  6.1225, CR = 0.0198 < 0.1
Thickness of crusted layers (B3) [1] [2] [3] [4] [5]   
[1] Porosity (C9) 1       0.0531
[2] Shrinkage limit (C10) 4 1      0.2242
[3] Coarse silt content (C11) 2 1/3 1     0.0858
[4] Annual rainfall (C12) 7 3 5 1    0.4978
[5] Annual evaporation (C13) 3 1/2 2 1/4 1   0.1392
λmax=  5.0778, CR = 0.0174 < 0.1
  1. When n = 2, CI = 0, RI = 0 and the eigenvalue of the matrix is a constant (λmax= 2). However, CR is undefined in this case, therefore the consistency of the matrix cannot be assessed. Due to practical reasons, it is claimed that the consistency of the matrix cannot be assessed and has to be used as it is to make this matrix work