Weight_Subjective

BWM: Best-Worst Method

Rezaei, J. · 2015

Overview

Pairwise comparison (best-to-others + others-to-worst vectors), LP. Output typically weight (higher value = preferred).

Strengths

•Method-specific: Pairwise comparison (best-to-others + others-to-worst vectors), LP
•Native group-decision support (multi-DM aggregation built into the pipeline)

Limitations

•Assumes: Domain experts available
•Assumes: Experts can express consistent comparisons

Method assistant

Grounded explanations: it explains the method, it does not compute.

Assumptions to verify

•Domain experts available
•Experts can express consistent comparisons

When not to use

•No experts available → use objective weighting
•High inconsistency → discard and re-elicit

Edge cases

•See F.steps and D.parameters for BWM-specific edge handling. recommendation_metadata.assumptions_to_verify also lists boundary conditions.

Common pitfalls

•Hatalı: 'BWM bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Domain experts available
•Hatalı: 'BWM bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Experts can express consistent comparisons
•Hatalı: BWM'yi 'No experts available → use objective weighting' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
•Hatalı: BWM'yi 'High inconsistency → discard and re-elicit' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1.Adım 1 (F1): Step 1: Identify Best (B) and Worst (W) criteria from expert. Formül: B \in \{c_{j}\},\ W \in \{c_{j}\},\ B\neq W Anchor: Rezaei 2015, p.51 Sec.2.1
2.Adım 2 (F2): Step 2: Pairwise vectors A_B = (a_{B1},…,a_{Bn}) and A_W = (a_{1W},…,a_{nW}) on 1-9 scale. Formül: A_{B} = (a_{B1},\ldots,a_{Bn}),\ A_{W} = (a_{1W},\ldots,a_{nW}),\ a_{ij}\in\{1,2,\ldots,9\} Anchor: Rezaei 2015, p.51 Eqs.(1)-(2)
3.Adım 3 (F3): Step 3: Min-max LP for optimal weights satisfying both vectors plus consistency. Formül: \min\ \xi \quad \text{s.t.}\ \Big|\dfrac{w_{B}}{w_{j}}-a_{Bj}\Big|\le\xi,\ \Big|\dfrac{w_{j}}{w_{W}}-a_{jW}\Big|\le\xi,\ \sum w_{j}=1,\ w_{j}\ge 0 Anchor: Rezaei 2015, p.52 Eqs.(3)-(4)

Commonly paired with

•BWM + TOPSIS (high)
•BWM + VIKOR (high)
•BWM + EDAS (high)
•BWM + PROMETHEE (high)
•BWM + ELECTRE-III (high)

How to cite

Rezaei, J. (2015). Best-worst multi-criteria decision-making method. Omega. https://doi.org/10.1016/j.omega.2014.11.009

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Common pitfalls

•Hatalı: 'BWM bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Domain experts available

•Hatalı: 'BWM bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Experts can express consistent comparisons

•Hatalı: BWM'yi 'No experts available → use objective weighting' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

•Hatalı: BWM'yi 'High inconsistency → discard and re-elicit' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1.Adım 1 (F1): Step 1: Identify Best (B) and Worst (W) criteria from expert. Formül: B \in \{c_{j}\},\ W \in \{c_{j}\},\ B\neq W Anchor: Rezaei 2015, p.51 Sec.2.1

2.Adım 2 (F2): Step 2: Pairwise vectors A_B = (a_{B1},…,a_{Bn}) and A_W = (a_{1W},…,a_{nW}) on 1-9 scale. Formül: A_{B} = (a_{B1},\ldots,a_{Bn}),\ A_{W} = (a_{1W},\ldots,a_{nW}),\ a_{ij}\in\{1,2,\ldots,9\} Anchor: Rezaei 2015, p.51 Eqs.(1)-(2)

3.Adım 3 (F3): Step 3: Min-max LP for optimal weights satisfying both vectors plus consistency. Formül: \min\ \xi \quad \text{s.t.}\ \Big|\dfrac{w_{B}}{w_{j}}-a_{Bj}\Big|\le\xi,\ \Big|\dfrac{w_{j}}{w_{W}}-a_{jW}\Big|\le\xi,\ \sum w_{j}=1,\ w_{j}\ge 0 Anchor: Rezaei 2015, p.52 Eqs.(3)-(4)