CODAS: Combinative Distance-Based Assessment

Overview

Distance from anti-ideal (Euclidean + Taxicab). Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Distance from anti-ideal (Euclidean + Taxicab)

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

Common pitfalls

• •Hatalı: 'CODAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Criteria preferences are independent (no synergistic interactions)
• •Hatalı: 'CODAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Compensation is acceptable: high score on one criterion can offset low on another
• •Hatalı: 'CODAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix is complete (no missing values)
• •Hatalı: CODAS'yi 'Criteria strongly correlated → consider DEMATEL/ANP for interdependence' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: CODAS'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: Linear normalisation (max for benefit, min/x for cost). Formül: n_{ij} = \begin{cases} \dfrac{x_{ij}}{\max_{i} x_{ij}} & j\in J^{+} \\ \dfrac{\min_{i} x_{ij}}{x_{ij}} & j\in J^{-} \end{cases} Anchor: Keshavarz-Ghorabaee 2016, p.31 Eq.(2)
2. 2.Adım 2 (F2): Step 2: Weighted normalised matrix r_ij = w_j · n_ij. Formül: r_{ij} = w_{j} \cdot n_{ij} Anchor: Keshavarz-Ghorabaee 2016, p.31 Eq.(3)
3. 3.Adım 3 (F3): Step 3: Negative-Ideal solution NI per criterion. Formül: NI_{j} = \min_{i} r_{ij} Anchor: Keshavarz-Ghorabaee 2016, p.31 Eq.(4)
4. 4.Adım 4 (F4): Step 4: Euclidean E_i and Taxicab T_i distances from NI. Formül: E_{i} = \sqrt{\sum_{j=1}^{n}(r_{ij}-NI_{j})^{2}},\quad T_{i} = \sum_{j=1}^{n}\lvert r_{ij}-NI_{j}\rvert Anchor: Keshavarz-Ghorabaee 2016, p.31 Eqs.(5)-(6)
5. 5.Adım 5 (F5): Step 5: Relative Assessment matrix h_ik with threshold function ψ. Formül: h_{ik} = (E_{i}-E_{k}) + \psi(E_{i}-E_{k})\cdot(T_{i}-T_{k}),\quad \psi(z) = \begin{cases}1 & |z|\ge\tau \\ 0 & |z|<\tau\end{cases} Anchor: Keshavarz-Ghorabaee 2016, p.32 Eq.(7)
6. 6.Adım 6 (F6): Step 6: Assessment score H_i and descending ranking. Formül: H_{i} = \sum_{k=1}^{m} h_{ik} Anchor: Keshavarz-Ghorabaee 2016, p.32 Eq.(8)

Commonly paired with

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

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