PAM: Polygons Area Method

Overview

Geometric aggregation via polygon area on equal-angle axes. Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Geometric aggregation via polygon area on equal-angle axes

Limitations

• •Assumes: Criteria preferences are independent (no synergistic interactions)
• •Assumes: Compensation is acceptable: high score on one criterion can offset low on another
• •Assumes: Decision matrix is complete (no missing values)

Assumptions to verify

• •Criteria preferences are independent (no synergistic interactions)
• •Compensation is acceptable: high score on one criterion can offset low on another
• •Decision matrix is complete (no missing values)

When not to use

• •Criteria strongly correlated → consider DEMATEL/ANP for interdependence
• •Non-compensatory preferences → consider outranking (ELECTRE/PROMETHEE)

Edge cases

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

Common pitfalls

• •Hatalı: 'PAM bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Criteria preferences are independent (no synergistic interactions)
• •Hatalı: 'PAM bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Compensation is acceptable: high score on one criterion can offset low on another
• •Hatalı: 'PAM bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix is complete (no missing values)
• •Hatalı: PAM'yi 'Criteria strongly correlated → consider DEMATEL/ANP for interdependence' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: PAM'yi 'Non-compensatory preferences → consider outranking (ELECTRE/PROMETHEE)' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1. 1.Adım 1 (F1): Step 1: Normalise matrix per criterion (direction-aware to [0,1]). Formül: r_{ij} = \begin{cases} (x_{ij}-\min)/(\max-\min) & j\in J^{+} \\ (\max-x_{ij})/(\max-\min) & j\in J^{-} \end{cases} Anchor: PAM literature, Eq.(1)
2. 2.Adım 2 (F2): Step 2: Weighted normalised polygon vertices p_ij = w_j · r_ij per criterion. Formül: p_{ij} = w_{j}\,r_{ij} Anchor: PAM literature, Eq.(2)
3. 3.Adım 3 (F3): Step 3: Polygon area for each alternative (radii arranged on n equal-angle axes 2π/n). Formül: \text{Area}_{i} = \dfrac{1}{2} \sin\!\left(\dfrac{2\pi}{n}\right) \sum_{j=1}^{n} p_{ij}\,p_{i,j+1},\ p_{i,n+1}=p_{i1} Anchor: PAM literature, Eq.(3)
4. 4.Adım 4 (F4): Step 4: Descending ranking by polygon area. Formül: \text{rank}(i) \propto -\text{Area}_{i} Anchor: PAM literature, Sec.4

Commonly paired with

• •AHP + PAM (high)
• •BWM + PAM (high)
• •ENTROPY + PAM (high)
• •CRITIC + PAM (high)
• •SWARA + PAM (high)

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