AHP Detail Step 2.Construct the pairwise comparison matrix for each layer For one layer,construct the comparison matrix A for pari-wise comparison.If there are n elements in the layer,the matrix A is in dimension n x n. The matrix A={has the following properties: ay>0,a5=1,4i=1. i Give the value of each aij according to the following table. CLGO System Engineering by J.J.Gao 11
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AHP Detail Intensity Definition Explanation of importance 1 Equal importance Two factors contribute equally to the objective 3 Somewhat more Experience and judgement slightly favour one over important the other. 5 Much more Experience and judgement strongly favour one over important the other. 7 Very much more Experience and judgement very strongly favour one important over the other.Its importance is demonstrated in practice. 9 Absolutely more The evidence favouing one over the other is of the important. highest possible validity. 2,4,6,8 Intermediate When compromise is needed values CLGO System Engineering by J.J.Gao 12
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AHP Detail Step 3.Compute the weight for one layer Compute the weight of each elements.Suppose there are n elements.Let w=(wi,w2,··,wn)'be the weight vector.. There are two ways to compute w Method 1:Vector w is the correspondent eigenvector of the maximum eigenvalue of matrix A,i.e., Aw=入marX, where Amax is the largest eigenvalue of A.Thus,we can compute w directly.(by hand or by computer)Do you still remember how to compute the eigenvector of a matrix? System Engineering by J.J.Gao CLGO 13
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AHP Detail Method 2:Since the structure of the A is special.We can use a simple way to compute w. 1 Normalize A by column summation: aij aij三 ∑=1a% Let A {au 2 Compute the row summation of A for each row,which is denoted by M:=∑1a: 3 Find w by normalization: Mi Wi ∑=M: CLGO System Engineering by J.J.Gao 14
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