RAT: Reference Alternative based Aggregation Technique

Overview

Rank aggregation (signum-weighted Euclidean-square-difference). Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Rank aggregation (signum-weighted Euclidean-square-difference)

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

• •zero.
• •if reference ranks better than alternative k in column j.

Common pitfalls

• •Hatalı: 'RAT bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Criteria preferences are independent (no synergistic interactions)
• •Hatalı: 'RAT bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Compensation is acceptable: high score on one criterion can offset low on another
• •Hatalı: 'RAT bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix is complete (no missing values)
• •Hatalı: RAT'yi 'Criteria strongly correlated → consider DEMATEL/ANP for interdependence' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: RAT'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: Build ranking matrix A = [r_ij]_{m×n} where rows are alternatives and columns are rankings from n different MCDM techniques. Formül: A = \begin{bmatrix} r_{11} & r_{12} & \cdots & r_{1n} \\ r_{21} & r_{22} & \cdots & r_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ r_{m1} & r_{m2} & \cdots & r_{mn} \end{bmatrix} Anchor: Orakçı 2024, p.41 Eq.(22)
2. 2.Adım 2 (F2): Step 2: Select the first alternative as reference (A_1); its aggregated value is defined as zero. Formül: A_{1} = 0\ \text{(referans alternatif)} Anchor: Orakçı 2024, p.41 Sec.2.1 Step 2
3. 3.Adım 3 (F3): Step 3: Compute aggregated value A_k for k = 1..m via the signum-weighted Euclidean-square-difference sum: positive sign if reference ranks better than alternative k in column j. Formül: A_{k} = \sum_{i=1}^{n} \sum_{j=1}^{n} \operatorname{sgn}(r_{1j} - r_{kj}) \cdot \sqrt{\big|r_{1j}^{2} - r_{kj}^{2}\big|},\quad k=1,2,\ldots,m Anchor: Orakçı 2024, p.41 Eq.(23)
4. 4.Adım 4 (F4): Step 4: Sort A_k values in descending order; the alternative with the highest A_k receives rank 1. Formül: \text{Rank}(A_{i}) \propto -A_{i},\quad i=1,\ldots,m Anchor: Orakçı 2024, p.42 Step 4

Commonly paired with

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

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