RAPS: Ranking of Alternatives based on Preference Strength

Overview

Preference-strength aggregation (rank-reversal resistant). Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Preference-strength aggregation (rank-reversal resistant)

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

Common pitfalls

• •Hatalı: 'RAPS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Criteria preferences are independent (no synergistic interactions)
• •Hatalı: 'RAPS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Compensation is acceptable: high score on one criterion can offset low on another
• •Hatalı: 'RAPS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix is complete (no missing values)
• •Hatalı: RAPS'yi 'Criteria strongly correlated → consider DEMATEL/ANP for interdependence' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: RAPS'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 normalise 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: Dezert & Tchamova 2021, p.15
2. 2.Adım 2 (F2): Step 2: For each pair (A_i, A_k), compute pairwise preference strength PS_ik = Σ_j w_j · max(0, r_ij − r_kj). Formül: PS_{ik} = \sum_{j=1}^{n}w_{j}\,\max(0,\,r_{ij}-r_{kj}) Anchor: Dezert & Tchamova 2021, p.15 Eq.(6)
3. 3.Adım 3 (F3): Step 3: Compute RAPS score R_i = Σ_{k≠i} PS_ik / Σ_{k≠i}(PS_ik + PS_ki). Rank descending. Formül: R_{i} = \frac{\sum_{k \neq i}PS_{ik}}{\sum_{k \neq i}(PS_{ik}+PS_{ki})} Anchor: Dezert & Tchamova 2021, p.16 Eq.(7)

Commonly paired with

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

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