LODECI: LOgarithmic DEcomposition of Criteria Importance

Overview

Objective weighting via logarithmic decomposition. Output typically weight (higher value = preferred).

Strengths

• •Method-specific: Objective weighting via logarithmic decomposition

Limitations

• •Assumes: Decision matrix exists with measurable criteria
• •Assumes: Sufficient inter-alternative variation per criterion

Assumptions to verify

• •Decision matrix exists with measurable criteria
• •Sufficient inter-alternative variation per criterion

When not to use

• •No data variation (constant criterion) → weight degenerates
• •Expert judgment is the actual driver → use subjective weighting

Edge cases

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

Common pitfalls

• •Hatalı: 'LODECI bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix exists with measurable criteria
• •Hatalı: 'LODECI bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Sufficient inter-alternative variation per criterion
• •Hatalı: LODECI'yi 'No data variation (constant criterion) → weight degenerates' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: LODECI'yi 'Expert judgment is the actual driver → use subjective weighting' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1. 1.Adım 1 (F1): Step 1: Decision matrix H = [h_ij]_{m×n}. Formül: H = \big[h_{ij}\big]_{m\times n} Anchor: Pala 2024, Eq.(1); Yürüyen-Ulutaş 2025 Eq.(1), p.6
2. 2.Adım 2 (F2): Step 2: Linear normalisation per direction. Benefit: p_ij = h_ij/max(h_ij). Cost: p_ij = 1 − min(h_ij)/h_ij. Formül: p_{ij} = \begin{cases} \dfrac{h_{ij}}{\max(h_{ij})} & j\in J^{+} \\ 1 - \dfrac{\min(h_{ij})}{h_{ij}} & j\in J^{-} \end{cases} Anchor: Pala 2024, Eqs.(2)-(3); Yürüyen-Ulutaş 2025 Eqs.(2)-(3)
3. 3.Adım 3 (F3): Step 3: Decomposition Value AD_ij = max_r|p_ij − p_rj| for r ≠ i (max absolute deviation from any other alternative on criterion j). Formül: AD_{ij} = \max_{r\neq i}\big\{\big|p_{ij} - p_{rj}\big|\big\} Anchor: Pala 2024, Eq.(4); Yürüyen-Ulutaş 2025 Eq.(4)
4. 4.Adım 4 (F4): Step 4: Logarithmic Decomposition Value LAD_j = ln(1 + Σ_i AD_ij / m). Formül: LAD_{j} = \ln\!\Bigg(1 + \dfrac{\sum_{i=1}^{m} AD_{ij}}{m}\Bigg) Anchor: Pala 2024, Eq.(5); Yürüyen-Ulutaş 2025 Eq.(5)
5. 5.Adım 5 (F5): Step 5: LODECI weights w_j = LAD_j / Σ LAD_k. Formül: w_{j,\text{LODECI}} = \dfrac{LAD_{j}}{\sum_{k=1}^{n} LAD_{k}} Anchor: Pala 2024, Eq.(6); Yürüyen-Ulutaş 2025 Eq.(6)

Commonly paired with

• •LODECI + TOPSIS (high)
• •LODECI + VIKOR (high)
• •LODECI + EDAS (high)
• •LODECI + WASPAS (high)
• •LODECI + MARCOS (high)

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