ROV: Range of Value method

Overview

Interval utility (optimistic-pessimistic bounds). Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Interval utility (optimistic-pessimistic bounds)

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

Common pitfalls

• •Hatalı: 'ROV bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Criteria preferences are independent (no synergistic interactions)
• •Hatalı: 'ROV bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Compensation is acceptable: high score on one criterion can offset low on another
• •Hatalı: 'ROV bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix is complete (no missing values)
• •Hatalı: ROV'yi 'Criteria strongly correlated → consider DEMATEL/ANP for interdependence' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: ROV'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: Min-max normalisation per criterion direction. Formül: r_{ij} = \begin{cases} (x_{ij}-\min_{i} x_{ij})/(\max_{i} x_{ij}-\min_{i} x_{ij}) & j\in J^{+} \\ (\max_{i} x_{ij}-x_{ij})/(\max_{i} x_{ij}-\min_{i} x_{ij}) & j\in J^{-} \end{cases} Anchor: Yakowitz 1993, p.1604 Eq.(1)
2. 2.Adım 2 (F2): Step 2: Best-case u^+_i = Σ_{j∈J+} w_j r_ij + Σ_{j∈J−} w_j (1−r_ij). Formül: u^{+}_{i} = \sum_{j\in J^{+}} w_{j}\,r_{ij} Anchor: Yakowitz 1993, p.1605 Eq.(2)
3. 3.Adım 3 (F3): Step 3: Worst-case u^−_i. Formül: u^{-}_{i} = \sum_{j\in J^{-}} w_{j}\,r_{ij} Anchor: Yakowitz 1993, p.1605 Eq.(3)
4. 4.Adım 4 (F4): Step 4: Range of Value u_i = (u^+_i + u^−_i)/2 and descending ranking. Formül: u_{i} = \dfrac{u^{+}_{i} + u^{-}_{i}}{2} Anchor: Yakowitz 1993, p.1605 Eq.(4)

Commonly paired with

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

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