By Thomas L. Saaty
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Extra info for Analytical Planning. The Organization of System
CR. 173 1/4 1/5 6 1/7 1/3 3 1 6 Priority vector Financing 3 3 5 1 3 Consistency General condition and 6 7 Modern facilities for Level 2, Solution 5 Yard space Age Matrix 1/3 1 Neighborhood Buying a House: Pairwise Comparison Location 3-7. 1/5 Size EXHIBIT The Analytic Hierarchy Process 35 36 Analytical Planning it is often difficult to achieve a high level of consistency. However, the level of consistency should correspond to the risk associated with inconsistent results. If, for example we were comparing the effects of drugs we would want a very high level of consistency.
W 2 w 2 w 2 w 2 . If — χ — χ — χ — are multiplied out Wx w2 w3 w4 and the 4th root taken an estimate of the second component of the principal eigenvector has been developed from this row, and so on. 32 Analytical Planning So the eigenvector component row 1 = 4 / — χ — χ — x — V w W l 2 W 3 W3 7 eigenvector component row 2 = 4 / — χ — χ — χ — w4 v3 Once the η eigenvector components have been developed for all the rows, it becomes necessary to normalize them to do further computation. Αγ Ai The matrix A2 A3 A4 Wj Wx Wx Wj Wx wl w2 w w Wj w 2 w Wj w 2 w 2 w 3 2 w 3 w Normalize the result to get the estimate of vector of priorities Compute estimates of the eigenvector components from the rows 4 2 4 W3 W3 W3 W3 w x w 2 w 3 vv4 w 4 w 4 w 4 w 4 w x w 2 w 3 w 4 /w 4 / 2 - > λ/ Wi χ X Wj w χ 2 w 2 w 2 X Wj w w χ 3 2 X ννλ Wi w : w2 w 4 a Now + oAt 4 : b column and + normalize = w b T ol t a c Total = x 3 w.
35 Thus the process revealed the most likely outcome to be the relocation of the snail darter. The hierarchy of this example is incomplete. It is illustrated in Exhibit 3-12. This exercise was carried out in the 1970s and a decision has been made to construct the Dam. If our information is adequate it was thought that the snail darter is not, after all, endangered by the dam. C. Use of the ΑΗΡ with Objective Data Now we give an example of a comparison in linear utility. Let us show how the ΑΗΡ may used to solve an ordinary decision problem.
Analytical Planning. The Organization of System by Thomas L. Saaty