WEBIRA: WEighted Bi-directional Ideal Ratio Analysis

Overview

Bidirectional ideal ratio scoring. Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Bidirectional ideal ratio scoring

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

Common pitfalls

• •Hatalı: 'WEBIRA bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Criteria preferences are independent (no synergistic interactions)
• •Hatalı: 'WEBIRA bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Compensation is acceptable: high score on one criterion can offset low on another
• •Hatalı: 'WEBIRA bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix is complete (no missing values)
• •Hatalı: WEBIRA'yi 'Criteria strongly correlated → consider DEMATEL/ANP for interdependence' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: WEBIRA'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 ideal x*_j and anti-ideal x°_j for each criterion. Formül: x_{j}^{*} = \max_{i}x_{ij} \text{ (benefit)},\;\min_{i}x_{ij} \text{ (cost)};\quad x_{j}^{\circ} = \min_{i}x_{ij} \text{ (benefit)},\;\max_{i}x_{ij} \text{ (cost)} Anchor: Krstović et al. 2022, p.42 Eqs.(1)-(2)
2. 2.Adım 2 (F2): Step 2: Compute positive ratio R⁺_ij (closeness to ideal) and negative ratio R⁻_ij (closeness to anti-ideal). Formül: R_{ij}^{+} = \frac{x_{ij}}{x_{j}^{*}},\qquad R_{ij}^{-} = \frac{x_{j}^{\circ}}{x_{ij}} Anchor: Krstović et al. 2022, p.43 Eqs.(3)-(4)
3. 3.Adım 3 (F3): Step 3: Compute WEBIRA score B_i = weighted sum of (R⁺_ij − R⁻_ij). Rank in descending order. Formül: B_{i} = \sum_{j=1}^{n}w_{j}\bigl(R_{ij}^{+} - R_{ij}^{-}\bigr) Anchor: Krstović et al. 2022, p.43 Eq.(5)

Commonly paired with

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

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