VIKOR: VlseKriterijumska Optimizacija I Kompromisno Resenje (Multicriteria Optimisation and Compromise Solution)

Overview

Compromise / aggregation-function based. Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Compromise / aggregation-function based

Limitations

• •Rank reversal known on alternative-set changes (ref: Opricovic & Tzeng 2007 (Extended VIKOR); Mareschal-Brans 1988 (broader compromise-methods discussion))
• •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

• •If C1 fails, return the maximum prefix A^(1)..A^(M) for which Q(A^(M)) − Q(A^(1)) < DQ. If only C2 fails, return {A^(1), A^(2)}.

Common pitfalls

• •Hatalı: 'VIKOR bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Criteria preferences are independent (no synergistic interactions)
• •Hatalı: 'VIKOR bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Compensation is acceptable: high score on one criterion can offset low on another
• •Hatalı: 'VIKOR bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix is complete (no missing values)
• •Hatalı: VIKOR'yi 'Criteria strongly correlated → consider DEMATEL/ANP for interdependence' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: VIKOR'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: Determine the best f_j* and worst f_j^- value of every criterion across alternatives, respecting benefit/cost direction. Formül: f_{j}^{*} = \begin{cases}\max_{i} x_{ij} & j \in J \\ \min_{i} x_{ij} & j \in J'\end{cases},\quad f_{j}^{-} = \begin{cases}\min_{i} x_{ij} & j \in J \\ \max_{i} x_{ij} & j \in J'\end{cases} Anchor: Opricovic & Tzeng 2004, §2 Eq.(3)
2. 2.Adım 2 (F2): Step 2: Compute the group utility S_i and the individual regret R_i. S aggregates weighted normalised regret (L_1-metric); R is the maximum weighted regret (L_∞-metric). Formül: S_{i} = \sum_{j=1}^{n} w_{j}\,\dfrac{f_{j}^{*}-x_{ij}}{f_{j}^{*}-f_{j}^{-}},\quad R_{i} = \max_{j}\left[w_{j}\,\dfrac{f_{j}^{*}-x_{ij}}{f_{j}^{*}-f_{j}^{-}}\right] Anchor: Opricovic & Tzeng 2004, §2 Eq.(4)
3. 3.Adım 3 (F3): Step 3: Compute the VIKOR index Q_i as a convex combination of normalised S and R, weighted by the compromise coefficient v. Formül: Q_{i} = v\,\dfrac{S_{i}-S^{*}}{S^{-}-S^{*}} + (1-v)\,\dfrac{R_{i}-R^{*}}{R^{-}-R^{*}},\ S^{*}=\min_{i}S_{i},\ S^{-}=\max_{i}S_{i},\ R^{*}=\min_{i}R_{i},\ R^{-}=\max_{i}R_{i} Anchor: Opricovic & Tzeng 2004, §2 Eq.(5)
4. 4.Adım 4 (F4): Step 4: Propose A^(1) (the lowest-Q alternative) as compromise solution iff both C1 (acceptable advantage) and C2 (acceptable stability) hold. If C1 fails, return the maximum prefix A^(1)..A^(M) for which Q(A^(M)) − Q(A^(1)) < DQ. If only C2 fails, return {A^(1), A^(2)}. Formül: DQ = \dfrac{1}{m-1};\quad C1: Q(A^{(2)}) - Q(A^{(1)}) \ge DQ;\quad C2: A^{(1)} \text{ is best in } S \text{ or in } R Anchor: Opricovic & Tzeng 2004, §2 Eqs.(6)-(7)

Commonly paired with

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

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