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Analytical Hierarchy Process. Hyman Chapter 9.3. Relative Preferences (Pairwise Comparison). Can be used in the pairwise comparison for a specific criterion but with a finer relative scale as shown in the following table. Relative Scale for Preference in Pairwise Comparison.

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Analytical hierarchy process

Analytical Hierarchy Process

Hyman Chapter 9.3


Relative preferences pairwise comparison
Relative Preferences (Pairwise Comparison)

  • Can be used in the pairwise comparison for a specific criterion but with a finer relative scale as shown in the following table

Relative Scale for Preference in Pairwise Comparison


Pairwise comparison torque criterion
Pairwise Comparison (Torque criterion)

  • Three options A, B, and C

    • A is strongly preferred over B (scale of 5)

    • A is very strongly preferred over C (scale of 7)

    • B is strongly/moderately preferred over C (4)

1/3(0.106+0.04+0.084)=0.077


Relative importance pairwise comparison
Relative Importance (Pairwise Comparison)

  • Similar scale can also be used in the relative comparison between criteria (ex. how important in considering torque vs. bearing loads in design; it is the “k” factor in Hyman chapter 9, figure 9.2)

Relative Scale for importance in Comparison of Criteria


Pairwise comparison between criteria
Pairwise Comparison Between Criteria

  • Three criteria slippage (S), bearing loads (BL), and torque (T)

    • BL is moderately more important than S (scale of 3)

    • BL is moderately/equally important than T (scale of 2)

    • S is equally important then T (1)

1/3(0.2+0.273+0.25)=0.241


Overall weighed scale
Overall Weighed Scale

Different design weighed scale

Criteria weighed scale importance to overall design

Inferior design

A = (0.211)(0.379) + (0.549)(0.319) + (0.241)(0.709) = 0.426

B = (0.211)(0.425) + (0.549)(0.074) + (0.241)(0.214) = 0.182

C = (0.211)(0.196) + (0.549)(0.607) + (0.241)(0.077) = 0.393


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