LOPCOW: LOgarithmic Percentage Change-driven Objective Weighting

Overview

Logarithmic percentage change variance-based objective weighting. Output typically weight (higher value = preferred).

Strengths

• •Method-specific: Logarithmic percentage change variance-based objective weighting

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

Common pitfalls

• •Hatalı: 'LOPCOW bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix exists with measurable criteria
• •Hatalı: 'LOPCOW bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Sufficient inter-alternative variation per criterion
• •Hatalı: LOPCOW'yi 'No data variation (constant criterion) → weight degenerates' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: LOPCOW'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: Construct the initial decision matrix X = [x_ij]_{m×n}. Formül: X = \big[x_{ij}\big]_{m\times n} Anchor: Ecer-Pamucar 2022, p.4 Eq.(1); Çemrek 2025, Eq.(1)
2. 2.Adım 2 (F2): Step 2: Min-max normalisation per direction. Benefit: r_ij = (x_ij − x_min)/(x_max − x_min). Cost: r_ij = (x_max − x_ij)/(x_max − x_min). Formül: r_{ij} = \begin{cases} \dfrac{x_{ij} - x_{j}^{\min}}{x_{j}^{\max} - x_{j}^{\min}} & j\in J^{+}\\ \dfrac{x_{j}^{\max} - x_{ij}}{x_{j}^{\max} - x_{j}^{\min}} & j\in J^{-}\end{cases} Anchor: Ecer-Pamucar 2022, p.5 Eqs.(2)-(3); Çemrek 2025, Eqs.(2)-(3)
3. 3.Adım 3 (F3): Step 3: Percentage value PV_j: logarithm of ratio between root-mean-square of normalised values across m alternatives and their standard deviation, scaled by 100. Formül: PV_{j} = \Bigg|\ln\Bigg(\dfrac{\sqrt{\sum_{i=1}^{m} r_{ij}^{2}/m}}{\sigma_{j}}\Bigg)\Bigg| \cdot 100 Anchor: Ecer-Pamucar 2022, Eq.(4); Saraç-Karamaşa 2025 Eq.(4), p.94
4. 4.Adım 4 (F4): Step 4: Normalised LOPCOW weights w_j = PV_j / Σ PV_k; Σ w_j = 1. Formül: w_{j} = \dfrac{PV_{j}}{\sum_{k=1}^{n} PV_{k}},\quad \sum_{j=1}^{n} w_{j} = 1 Anchor: Ecer-Pamucar 2022, p.5 Eq.(5); Çemrek 2025, Eq.(5)

Commonly paired with

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

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