LMAW: Logarithm Methodology of Additive Weights

Overview

Logarithm-based additive weighting. Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Logarithm-based additive weighting

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

Common pitfalls

• •Hatalı: 'LMAW bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Criteria preferences are independent (no synergistic interactions)
• •Hatalı: 'LMAW bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Compensation is acceptable: high score on one criterion can offset low on another
• •Hatalı: 'LMAW bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix is complete (no missing values)
• •Hatalı: LMAW'yi 'Criteria strongly correlated → consider DEMATEL/ANP for interdependence' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: LMAW'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: Direction-aware standardisation ϑ_ij. Benefit: ϑ_ij = (x_ij + max_i x_ij)/max_i x_ij. Cost: ϑ_ij = (x_ij + min_i x_ij)/x_ij. Formül: \vartheta_{ij} = \begin{cases} \dfrac{x_{ij} + \max_{i} x_{ij}}{\max_{i} x_{ij}}, & j \in J^{+}\ (\text{benefit}) \\[6pt] \dfrac{x_{ij} + \min_{i} x_{ij}}{x_{ij}}, & j \in J^{-}\ (\text{cost}) \end{cases} Anchor: Pamucar et al. 2021 Facta Universitatis 19:361-380, Eq.(2)
2. 2.Adım 2 (F2): Step 2: Logarithmic transformation ϕ_ij = ln(ϑ_ij)/ln(Π_i ϑ_ij). Formül: \phi_{ij} = \dfrac{\ln(\vartheta_{ij})}{\ln\big(\prod_{i=1}^{m} \vartheta_{ij}\big)} Anchor: Pamucar et al. 2021 Facta Universitatis 19:361-380, Eq.(7)
3. 3.Adım 3 (F3): Step 3: Sigmoid-form weighted aggregation ξ_ij = 2·ϕ_ij^{w_j} / [(2−ϕ_ij)^{w_j} + ϕ_ij^{w_j}]. Formül: \xi_{ij} = \dfrac{2\,\phi_{ij}^{w_{j}}}{(2-\phi_{ij})^{w_{j}} + \phi_{ij}^{w_{j}}} Anchor: Pamucar et al. 2021 Facta Universitatis 19:361-380, Eq.(6)
4. 4.Adım 4 (F4): Step 4: Aggregation Q_i = Σ_j ξ_ij; descending ranking (higher Q = better). Formül: Q_{i} = \sum_{j=1}^{n} \xi_{ij} Anchor: Pamucar et al. 2021 Facta Universitatis 19:361-380, Eq.(8)

Commonly paired with

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

How to cite