LODECI - LOgarithmic DEcomposition of Criteria Importance

Overview

Apply F.steps in order.

Output

Weight, higher is better

Data

Crisp, complete numeric matrix

Weights

Derived internally, no weight source needed

Size

2+ alternatives, 3-12 criteria works best

Used for

Any (objective weighting)

How it works

1. 1

   Decision matrix H = [h_ij]_{m×n}.

   $$H=[h_{ij}{]}_{m\times n}$$

   Pala 2024, Eq.(1); Yürüyen-Ulutaş 2025 Eq.(1), p.6

2. 2

   Linear normalisation per direction. Benefit: p_ij = h_ij/max(h_ij). Cost: p_ij = 1 − min(h_ij)/h_ij.

   $$p_{ij}=\{\begin{array}{ll}\frac{h_{ij}}{\max (h_{ij})}& j\in J^{+}\\ 1-\frac{\min (h_{ij})}{h_{ij}}& j\in J^{-}\end{array}$$

   Pala 2024, Eqs.(2)-(3); Yürüyen-Ulutaş 2025 Eqs.(2)-(3)

3. 3

   Decomposition Value AD_ij = max_r|p_ij − p_rj| for r ≠ i (max absolute deviation from any other alternative on criterion j).

   $$A{D}_{ij}=\underset{r\ne i}{\max }\left\{\right|p_{ij}-p_{rj}\left|\right\}$$

   Pala 2024, Eq.(4); Yürüyen-Ulutaş 2025 Eq.(4)

4. 4

   Logarithmic Decomposition Value LAD_j = ln(1 + Σ_i AD_ij / m).

   $$LA{D}_j=\ln (1+\frac{{\sum }_{i=1}^{m}A{D}_{ij}}{m})$$

   Pala 2024, Eq.(5); Yürüyen-Ulutaş 2025 Eq.(5)

5. 5

   LODECI weights w_j = LAD_j / Σ LAD_k.

   $$w_{j,\text{LODECI}}=\frac{LA{D}_j}{{\sum }_{k=1}^{n}LA{D}_k}$$

   Pala 2024, Eq.(6); Yürüyen-Ulutaş 2025 Eq.(6)

Look elsewhere when

Assumptions to verify

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

Edge cases and pitfalls

• Applying LODECI without verifying this assumption.

  Requirement: Decision matrix exists with measurable criteria

• Applying LODECI without verifying this assumption.

  Requirement: Sufficient inter-alternative variation per criterion

• Using LODECI when: No data variation (constant criterion) → weight degenerates.

  An alternative method is recommended in this situation.

• Using LODECI when: Expert judgment is the actual driver → use subjective weighting.

  An alternative method is recommended in this situation.

Works with

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