ARAS: Additive Ratio Assessment

Overview

Additive utility ratio (optimal reference row). Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Additive utility ratio (optimal reference row)

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

Common pitfalls

• •Hatalı: 'ARAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Criteria preferences are independent (no synergistic interactions)
• •Hatalı: 'ARAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Compensation is acceptable: high score on one criterion can offset low on another
• •Hatalı: 'ARAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix is complete (no missing values)
• •Hatalı: ARAS'yi 'Criteria strongly correlated → consider DEMATEL/ANP for interdependence' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: ARAS'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: Augment matrix with optimal alternative A_0 (best per criterion). Formül: X_{0j} = \begin{cases}\max_{i} x_{ij} & j\in J^{+}\\\min_{i} x_{ij} & j\in J^{-}\end{cases} Anchor: Zavadskas-Turskis 2010, p.166 Eq.(1)
2. 2.Adım 2 (F2): Step 2: Linear-sum normalisation (cost criteria inverted first). Formül: \bar{x}_{ij} = \dfrac{x_{ij}}{\sum_{k=0}^{m} x_{kj}},\ j\in J^{+};\quad x_{ij}\leftarrow 1/x_{ij}\ \text{for}\ j\in J^{-} Anchor: Zavadskas-Turskis 2010, p.166 Eq.(2)
3. 3.Adım 3 (F3): Step 3: Weighted normalised matrix d_ij = w_j · x̄_ij. Formül: d_{ij} = w_{j}\,\bar{x}_{ij} Anchor: Zavadskas-Turskis 2010, p.167 Eq.(3)
4. 4.Adım 4 (F4): Step 4: Optimality function S_i = Σ d_ij (including S_0 row). Formül: S_{i} = \sum_{j=1}^{n} d_{ij},\quad i=0,1,\ldots,m Anchor: Zavadskas-Turskis 2010, p.167 Eq.(4)
5. 5.Adım 5 (F5): Step 5: Utility K_i = S_i / S_0 and descending ranking. Formül: K_{i} = \dfrac{S_{i}}{S_{0}},\quad 0\le K_{i}\le 1 Anchor: Zavadskas-Turskis 2010, p.167 Eq.(5)

Commonly paired with

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

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