TODIM: TOmada de Decisão Interativa e Multicritério (Interactive and Multicriteria Decision Making)

Overview

Prospect theory (loss aversion pairwise dominance). Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Prospect theory (loss aversion pairwise dominance)

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

Common pitfalls

• •Hatalı: 'TODIM bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Criteria preferences are independent (no synergistic interactions)
• •Hatalı: 'TODIM bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Compensation is acceptable: high score on one criterion can offset low on another
• •Hatalı: 'TODIM bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix is complete (no missing values)
• •Hatalı: TODIM'yi 'Criteria strongly correlated → consider DEMATEL/ANP for interdependence' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: TODIM'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-sum normalisation per criterion. Formül: p_{ij} = \dfrac{x_{ij}}{\sum_{k=1}^{m} x_{kj}} Anchor: Gomes-Lima 1992, p.116 Eq.(1)
2. 2.Adım 2 (F2): Step 2: Reference criterion (max weight) and relative weights w_jr = w_j / w_r. Formül: r = \arg\max_{j} w_{j},\quad w_{jr} = \dfrac{w_{j}}{w_{r}} Anchor: Gomes-Lima 1992, p.116 Eq.(2)
3. 3.Adım 3 (F3): Step 3: Pairwise dominance Φ_j(A_i,A_k) with prospect-theory loss aversion θ. Formül: \Phi_{j}(A_{i},A_{k}) = \begin{cases} \sqrt{\dfrac{w_{jr}(p_{ij}-p_{kj})}{\sum w_{kr}}} & p_{ij}>p_{kj}\\ 0 & p_{ij}=p_{kj}\\ -\dfrac{1}{\theta}\sqrt{\dfrac{(\sum w_{kr})(p_{kj}-p_{ij})}{w_{jr}}} & p_{ij}<p_{kj}\end{cases} Anchor: Gomes-Lima 1992, p.117 Eq.(3)
4. 4.Adım 4 (F4): Step 4: Aggregated dominance δ(A_i,A_k) = Σ_j Φ_j. Formül: \delta(A_{i},A_{k}) = \sum_{j=1}^{n} \Phi_{j}(A_{i},A_{k}) Anchor: Gomes-Lima 1992, p.117 Eq.(4)
5. 5.Adım 5 (F5): Step 5: Global value ξ_i normalised in [0,1] and descending ranking. Formül: \xi_{i} = \dfrac{\sum_{k} \delta(A_{i},A_{k}) - \min_{i'}\sum_{k}\delta(A_{i'},A_{k})}{\max_{i'}\sum_{k}\delta(A_{i'},A_{k}) - \min_{i'}\sum_{k}\delta(A_{i'},A_{k})} Anchor: Gomes-Lima 1992, p.117 Eq.(5)

Commonly paired with

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

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