APLOCO: Automatic Pairwise Linear Order Combination

Overview

Pairwise dominance aggregation (automatic combination). Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Pairwise dominance aggregation (automatic combination)

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 APLOCO-specific edge handling. recommendation_metadata.assumptions_to_verify also lists boundary conditions.

Common pitfalls

• •Hatalı: 'APLOCO bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Criteria preferences are independent (no synergistic interactions)
• •Hatalı: 'APLOCO bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Compensation is acceptable: high score on one criterion can offset low on another
• •Hatalı: 'APLOCO bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix is complete (no missing values)
• •Hatalı: APLOCO'yi 'Criteria strongly correlated → consider DEMATEL/ANP for interdependence' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: APLOCO'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: Min-max normalisation to [0,1]. Formül: r_{ij} = \frac{x_{ij}-x_{j}^{\min}}{x_{j}^{\max}-x_{j}^{\min}} \text{ (benefit)};\quad r_{ij} = \frac{x_{j}^{\max}-x_{ij}}{x_{j}^{\max}-x_{j}^{\min}} \text{ (cost)} Anchor: Konstantinos et al. 2020, p.3726
2. 2.Adım 2 (F2): Step 2: Compute pairwise dominance score D(A_i, A_k) for each pair: weighted sum of positive normalised differences. Formül: D(A_{i},A_{k}) = \sum_{j=1}^{n}w_{j}\max\bigl(0,\,r_{ij}-r_{kj}\bigr) Anchor: Konstantinos et al. 2020, p.3727 Eq.(1)
3. 3.Adım 3 (F3): Step 3: Compute APLOCO score S_i = net dominance (sum of D(A_i,A_k) minus sum of D(A_k,A_i)). Rank in descending order. Formül: S_{i} = \sum_{k \neq i} D(A_{i},A_{k}) - \sum_{k \neq i} D(A_{k},A_{i}) Anchor: Konstantinos et al. 2020, p.3728 Eq.(2)

Commonly paired with

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

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