Weight_Subjective

AHP: Analytic Hierarchy Process

Saaty, T. L. · 1980

Overview

Pairwise comparison (eigenvalue). Output typically weight (higher value = preferred).

Strengths

•Method-specific: Pairwise comparison (eigenvalue)
•Native group-decision support (multi-DM aggregation built into the pipeline)

Limitations

•Rank reversal known on alternative-set changes (ref: Belton-Gear-1983; Saaty-1990)
•Assumes: Domain experts available
•Assumes: Experts can express consistent comparisons

Method assistant

Grounded explanations: it explains the method, it does not compute.

Assumptions to verify

•Domain experts available
•Experts can express consistent comparisons

When not to use

•No experts available → use objective weighting
•High inconsistency → discard and re-elicit

Edge cases

•See F.steps and D.parameters for AHP-specific edge handling. recommendation_metadata.assumptions_to_verify also lists boundary conditions.

Common pitfalls

•Hatalı: 'AHP bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Domain experts available
•Hatalı: 'AHP bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Experts can express consistent comparisons
•Hatalı: AHP'yi 'No experts available → use objective weighting' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
•Hatalı: AHP'yi 'High inconsistency → discard and re-elicit' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1.Adım 1 (F1): Step 1: Construct the pairwise comparison matrix A on Saaty's 1-9 fundamental scale; check reciprocity. Formül: A = [a_{ij}]_{n \times n},\quad a_{ij}>0,\ a_{ji}=1/a_{ij},\ a_{ii}=1 Anchor: Saaty 1980, Ch.1-3 (pairwise comparison construction; pending PDF page verification)
2.Adım 2 (F2): Step 2: Compute the principal eigenvalue λ_max and its right eigenvector; normalise so its entries sum to 1. Formül: A\,w = \lambda_{\max}\,w,\quad \sum_{i=1}^{n} w_{i}=1,\ w_{i}>0 Anchor: Saaty 1980, Ch.7 (principal-eigenvector priority extraction; pending PDF page verification)
3.Adım 3 (F3): Step 3: Compute the Consistency Index CI = (λ_max − n)/(n − 1). Formül: CI = \dfrac{\lambda_{\max} - n}{n - 1} Anchor: Saaty 1980, Ch.11 (Consistency Index definition; pending PDF page verification)
4.Adım 4 (F4): Step 4: Compute the Consistency Ratio CR = CI / RI(n), where RI(n) is Saaty's Random Index for matrix order n. Formül: CR = \dfrac{CI}{RI(n)},\ \text{accept if } CR \le 0.10 Anchor: Saaty 1980, Ch.11 (Random Index table; RI_3=0.58 pending PDF table verification)

Commonly paired with

•AHP + TOPSIS (high)
•AHP + VIKOR (high)
•AHP + EDAS (high)
•AHP + PROMETHEE (high)
•AHP + ELECTRE-III (high)

How to cite

Saaty, T. L. (1980). The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation. McGraw-Hill, New York.

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Common pitfalls

•Hatalı: 'AHP bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Domain experts available

•Hatalı: 'AHP bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Experts can express consistent comparisons

•Hatalı: AHP'yi 'No experts available → use objective weighting' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

•Hatalı: AHP'yi 'High inconsistency → discard and re-elicit' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1.Adım 1 (F1): Step 1: Construct the pairwise comparison matrix A on Saaty's 1-9 fundamental scale; check reciprocity. Formül: A = [a_{ij}]_{n \times n},\quad a_{ij}>0,\ a_{ji}=1/a_{ij},\ a_{ii}=1 Anchor: Saaty 1980, Ch.1-3 (pairwise comparison construction; pending PDF page verification)

2.Adım 2 (F2): Step 2: Compute the principal eigenvalue λ_max and its right eigenvector; normalise so its entries sum to 1. Formül: A\,w = \lambda_{\max}\,w,\quad \sum_{i=1}^{n} w_{i}=1,\ w_{i}>0 Anchor: Saaty 1980, Ch.7 (principal-eigenvector priority extraction; pending PDF page verification)

3.Adım 3 (F3): Step 3: Compute the Consistency Index CI = (λ_max − n)/(n − 1). Formül: CI = \dfrac{\lambda_{\max} - n}{n - 1} Anchor: Saaty 1980, Ch.11 (Consistency Index definition; pending PDF page verification)

4.Adım 4 (F4): Step 4: Compute the Consistency Ratio CR = CI / RI(n), where RI(n) is Saaty's Random Index for matrix order n. Formül: CR = \dfrac{CI}{RI(n)},\ \text{accept if } CR \le 0.10 Anchor: Saaty 1980, Ch.11 (Random Index table; RI_3=0.58 pending PDF table verification)