AHP steps and Consistensy
1
Analytic Hierarchy Process AHP is a multi-criteria decision-making method developed by Saaty. AHP aims at quantifying relative weights for a given set of criteria on a ratio scale. Two features of AHP differentiate it from other decision- making approaches. One, it provides a comprehensive structure to combine the intuitive rational and irrational values during the decision making process. The other is its ability to judge the consistency in decision-making process. The steps in AHP include the following: 1. Construct a pairwise comparison matrix using a scale of relative importance. Assuming n criteria, the pairwise comparison of criterion i with criterion j yields a square matrix A1 nxn where, a ij denotes the comparative importance of criterion i with respect to criterion j. In the matrix, a ij = 1, when i = j and a ji = 1/ a ij . a 11 a 12 ............. a 1n A1 nxn = a 21 a 22 ................a 2n ................................ a n1 a n2 ................a nn 2. Find the relative normalized weight (W j ) of each criterion by (a) calculating the geometric mean of i th row (GM i ) and (b) normalizing the geometric means of rows in the comparative matrix. n 1/n n GM i = ∏ a ij and W j = GM i / ∑ GM i j = 1 i = 1 3. Calculate matrix A3 and A4, such that A3 = A1 * A2 and A4 = A3 / A2, where, A2 = [W 1 , W 2 , .........W n ] T 4. Find out the maximum λ max , which is the average of matrix A4. 5. Calculate the consistency index (CI) = (λ max - n) / (n-1) 6. Obtain the random index (RI), for the number of criteria used in decision-making. 7. Finally, calculate the consistency ratio (CR) = CI / RI. Usually, a CR of 0.10 or less is considered acceptable. Scale of relative importance Intensity Definition 1 Equal Importance 3 Moderate Importance 5 Strong Importance 7 Very Strong Importance 9 Extreme Importance 2, 4, 6, 8 Intermediate Values Random consistency index Order of Matrix 1 2 3 4 5 6 7 Random Index (RI) 0.00 0.00 0.52 0.89 1.11 1.25 1.35
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Transcript of AHP steps and Consistensy
Analytic Hierarchy Process
AHP is a multi-criteria decision-making method developed by Saaty. AHP aims at quantifying relative
weights for a given set of criteria on a ratio scale. Two features of AHP differentiate it from other decision-
making approaches. One, it provides a comprehensive structure to combine the intuitive rational and
irrational values during the decision making process. The other is its ability to judge the consistency in
decision-making process. The steps in AHP include the following:
1. Construct a pairwise comparison matrix using a scale of relative importance. Assuming n
criteria, the pairwise comparison of criterion i with criterion j yields a square matrix A1nxn
where, aij denotes the comparative importance of criterion i with respect to criterion j. In the
matrix, aij = 1, when i = j and aji = 1/ aij .
a11 a12 ............. a1n
A1 nxn = a21 a22 ................a2n
................................
an1 an2 ................ann
2. Find the relative normalized weight (Wj) of each criterion by (a) calculating the geometric
mean of ith row (GMi) and (b) normalizing the geometric means of rows in the comparative
matrix.
n 1/n
n
GMi = ∏ aij and Wj = GMi / ∑ GMi j = 1 i = 1
3. Calculate matrix A3 and A4, such that A3 = A1 * A2 and A4 = A3 / A2,
where, A2 = [W1 , W2 , .........Wn ]T
4. Find out the maximum λmax, which is the average of matrix A4.
5. Calculate the consistency index (CI) = (λmax - n) / (n-1)
6. Obtain the random index (RI), for the number of criteria used in decision-making.
7. Finally, calculate the consistency ratio (CR) = CI / RI. Usually, a CR of 0.10 or less is
considered acceptable.
Scale of relative importance
Intensity Definition
1 Equal Importance
3 Moderate Importance
5 Strong Importance
7 Very Strong Importance
9 Extreme Importance
2, 4, 6, 8 Intermediate Values
Random consistency index
Order of Matrix 1 2 3 4 5 6 7
Random Index (RI) 0.00 0.00 0.52 0.89 1.11 1.25 1.35
