RAFSI: Ranking of Alternatives through Functional mapping of criterion sub-intervals into a Single Interval

Overview

Functional interval mapping (rank-reversal free). Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Functional interval mapping (rank-reversal free)

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

Common pitfalls

• •Hatalı: 'RAFSI bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Criteria preferences are independent (no synergistic interactions)
• •Hatalı: 'RAFSI bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Compensation is acceptable: high score on one criterion can offset low on another
• •Hatalı: 'RAFSI bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix is complete (no missing values)
• •Hatalı: RAFSI'yi 'Criteria strongly correlated → consider DEMATEL/ANP for interdependence' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: RAFSI'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: Define ideal n_{ij}^{I} and anti-ideal n_{ij}^{A} criteria endpoints. Formül: n_{i}^{I}\equiv \text{ideal value of criterion } j,\quad n_{i}^{A}\equiv \text{anti-ideal value} Anchor: Žižović 2020, p.4 Eq.(1)
2. 2.Adım 2 (F2): Step 2: Map decision values to [n_i, n_k] interval via linear scaling. Formül: a_{ij} = n_{i} + \dfrac{x_{ij} - n_{i}^{A}}{n_{i}^{I} - n_{i}^{A}}\,(n_{k} - n_{i}) Anchor: Žižović 2020, p.4 Eq.(2)
3. 3.Adım 3 (F3): Step 3: Weighted scaled matrix v_ij = w_j · a_ij. Formül: v_{ij} = w_{j}\,a_{ij} Anchor: Žižović 2020, p.5 Eq.(3)
4. 4.Adım 4 (F4): Step 4: Arithmetic mean A_i (benefit aspect) and harmonic mean H_i (cost aspect). Formül: A_{i} = \dfrac{1}{n^{+}} \sum_{j\in J^{+}} v_{ij},\quad H_{i} = \dfrac{n^{-}}{\sum_{j\in J^{-}} 1/v_{ij}} Anchor: Žižović 2020, p.5 Eq.(4)
5. 5.Adım 5 (F5): Step 5: Final score V_i = (A_i + H_i)/2 (rank-reversal-free) and descending ranking. Formül: V_{i} = \dfrac{A_{i} + H_{i}}{2} Anchor: Žižović 2020, p.5 Eq.(5)

Commonly paired with

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

How to cite