New Multicriteria Method: AHPGaussian
ahpgaussian.RdAnalytic Hierarchy Process (AHP) is a method allowing individuals or groups to make complex decisions. The core concept of AHP is that alternatives are always compared pairwise (and not, say, by giving a score, or sorting alternatives). AHP is used in many fields, from finance to criminal investigation.
The AHP Gaussian is a modification of the AHP that uses a Gaussian function to model the pairwise comparisons between criteria and alternatives. In the traditional AHP, pairwise comparisons are made using numerical values on a scale from 1 to 9, which can be subjective and lead to inconsistencies. The AHP Gaussian addresses this issue by using a continuous function that allows for more precise and consistent comparisons.
The function is defined by a mean value and a standard deviation, which can be estimated from the pairwise comparison data. The resulting weights for the criteria and alternatives are obtained by solving a system of linear equations. The Gaussian AHP has been shown to be effective in various applications, including military decision-making and environmental management.
Author
Cid Edson Povoas (cidedson@gmail.com)
References
dos Santos, M, Costa, I. P. de A., & Gomes, C. F. S. (2021) Multicriteria decision-making in the selection of warships: a new approach to the ahp method. International Journal of the Analytic Hierarchy Process, 13(1). <doi:10.13033/ijahp.v13i1.833>
Examples
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## Example 1
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ws <- ahpgaussian(warships)
summary(ws)
#> Table1 :
#> criteria min_max variable value sum norm
#> 1 Action Radius max model_1 4.000000e+03 2.399000e+04 0.1667361
#> 2 Fuel Endurance max model_1 1.100000e+01 6.700000e+01 0.1641791
#> 3 Autonomy max model_1 3.000000e+01 9.000000e+01 0.3333333
#> 4 Primary Cannon max model_1 2.500000e+01 1.700000e+02 0.1470588
#> 5 Secondary Cannon max model_1 1.000000e+00 5.000000e+00 0.2000000
#> 6 AAW Missiles max model_1 0.000000e+00 2.000000e+00 0.0000000
#> 7 Initial Cost min model_1 3.448276e-03 9.899889e-03 0.3483146
#> 8 Life Cycle Cost min model_1 1.689189e-03 4.848747e-03 0.3483764
#> 9 Construction Time min model_1 1.666667e-01 4.166667e-01 0.4000000
#> 10 Action Radius max model_2 9.330000e+03 2.399000e+04 0.3889120
#> 11 Fuel Endurance max model_2 2.600000e+01 6.700000e+01 0.3880597
#> 12 Autonomy max model_2 2.500000e+01 9.000000e+01 0.2777778
#> 13 Primary Cannon max model_2 2.500000e+01 1.700000e+02 0.1470588
#> 14 Secondary Cannon max model_2 2.000000e+00 5.000000e+00 0.4000000
#> 15 AAW Missiles max model_2 1.000000e+00 2.000000e+00 0.5000000
#> 16 Initial Cost min model_2 3.225806e-03 9.899889e-03 0.3258427
#> 17 Life Cycle Cost min model_2 1.579779e-03 4.848747e-03 0.3258118
#> 18 Construction Time min model_2 1.250000e-01 4.166667e-01 0.3000000
#> 19 Action Radius max model_3 1.066000e+04 2.399000e+04 0.4443518
#> 20 Fuel Endurance max model_3 3.000000e+01 6.700000e+01 0.4477612
#> 21 Autonomy max model_3 3.500000e+01 9.000000e+01 0.3888889
#> 22 Primary Cannon max model_3 1.200000e+02 1.700000e+02 0.7058824
#> 23 Secondary Cannon max model_3 2.000000e+00 5.000000e+00 0.4000000
#> 24 AAW Missiles max model_3 1.000000e+00 2.000000e+00 0.5000000
#> 25 Initial Cost min model_3 3.225806e-03 9.899889e-03 0.3258427
#> 26 Life Cycle Cost min model_3 1.579779e-03 4.848747e-03 0.3258118
#> 27 Construction Time min model_3 1.250000e-01 4.166667e-01 0.3000000
#> mean sd factor
#> 1 0.3333333 0.14691617 0.44074851
#> 2 0.3333333 0.14950228 0.44850684
#> 3 0.3333333 0.05555556 0.16666667
#> 4 0.3333333 0.32263692 0.96791075
#> 5 0.3333333 0.11547005 0.34641016
#> 6 0.3333333 0.28867513 0.86602540
#> 7 0.3333333 0.01297416 0.03892249
#> 8 0.3333333 0.01302772 0.03908315
#> 9 0.3333333 0.05773503 0.17320508
#> 10 0.3333333 0.14691617 0.44074851
#> 11 0.3333333 0.14950228 0.44850684
#> 12 0.3333333 0.05555556 0.16666667
#> 13 0.3333333 0.32263692 0.96791075
#> 14 0.3333333 0.11547005 0.34641016
#> 15 0.3333333 0.28867513 0.86602540
#> 16 0.3333333 0.01297416 0.03892249
#> 17 0.3333333 0.01302772 0.03908315
#> 18 0.3333333 0.05773503 0.17320508
#> 19 0.3333333 0.14691617 0.44074851
#> 20 0.3333333 0.14950228 0.44850684
#> 21 0.3333333 0.05555556 0.16666667
#> 22 0.3333333 0.32263692 0.96791075
#> 23 0.3333333 0.11547005 0.34641016
#> 24 0.3333333 0.28867513 0.86602540
#> 25 0.3333333 0.01297416 0.03892249
#> 26 0.3333333 0.01302772 0.03908315
#> 27 0.3333333 0.05773503 0.17320508
#>
#> Table2 :
#> criteria factor
#> 1 Action Radius 0.12638026
#> 2 Fuel Endurance 0.12860489
#> 3 Autonomy 0.04779001
#> 4 Primary Cannon 0.27753880
#> 5 Secondary Cannon 0.09932968
#> 6 AAW Missiles 0.24832419
#> 7 Initial Cost 0.01116064
#> 8 Life Cycle Cost 0.01120671
#> 9 Construction Time 0.04966484
#>
#> Table3 :
#> variable punctuation rank
#> 1 model_3 0.5143176 1
#> 2 model_2 0.3392280 2
#> 3 model_1 0.1464544 3
#>
plot(ws)
