SMART: Simple Multi-Attribute Rating Technique

Overview

Direct rating, compensatory. Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Direct rating, compensatory

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

Common pitfalls

• •Hatalı: 'SMART bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Criteria preferences are independent (no synergistic interactions)
• •Hatalı: 'SMART bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Compensation is acceptable: high score on one criterion can offset low on another
• •Hatalı: 'SMART bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix is complete (no missing values)
• •Hatalı: SMART'yi 'Criteria strongly correlated → consider DEMATEL/ANP for interdependence' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: SMART'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: Identify per-criterion minimum P_min and maximum P_max bounds. The range is partitioned using the relation e_v = (1+e)^v · e_0 with P_max = e_v + P_min. Formül: e_{v} = (1+e)^{v}\cdot e_{0}, \qquad P_{\max} = e_{v} + P_{\min} Anchor: Edwards 1986, p.15 Sec.2
2. 2.Adım 2 (F2): Step 2: Effective rating g_ij per alternative-criterion. Positive (benefit) criteria use g_ij = 4 + log₂[(P_v − P_min)/(P_max − P_min)·64]; negative (cost) criteria use g_ij = 10 − log₂[(P_v − P_min)/(P_max − P_min)·64]. Formül: g_{ij} = \begin{cases} 4+\log_{2}\!\left(\dfrac{P_{v}-P_{\min}}{P_{\max}-P_{\min}}\cdot 64\right) & j\in J^{+} \\ 10-\log_{2}\!\left(\dfrac{P_{v}-P_{\min}}{P_{\max}-P_{\min}}\cdot 64\right) & j\in J^{-} \end{cases} Anchor: Edwards 1986, p.17 Eqs.(1)-(2)
3. 3.Adım 3 (F3): Step 3: Decision maker scores each criterion h_j ∈ [4,10]; unnormalised weight w_j = (√2)^h_j, then normalise. Formül: w_{j} = \dfrac{(\sqrt{2})^{h_{j}}}{\sum_{k=1}^{n}(\sqrt{2})^{h_{k}}},\quad h_{j}\in[4,10] Anchor: Edwards 1986, p.18 Eq.(3)
4. 4.Adım 4 (F4): Step 4: Final SMART score f_i = Σ w_j · g_ij and descending ranking. Formül: f_{i} = \sum_{j=1}^{n} w_{j}\cdot g_{ij},\quad i=1,\ldots,m Anchor: Edwards 1986, p.18 Eq.(4)

Commonly paired with

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

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