WENSLO: WEight deNomination based on Slope coefficient for objective weighting

Overview

Weight_Objective (envelope/slope ratio of accumulation polyline). Output typically weight (higher value = preferred).

Strengths

• •Method-specific: Weight_Objective (envelope/slope ratio of accumulation polyline)

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

Common pitfalls

• •Hatalı: 'WENSLO bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix exists with measurable criteria
• •Hatalı: 'WENSLO bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Sufficient inter-alternative variation per criterion
• •Hatalı: WENSLO'yi 'No data variation (constant criterion) → weight degenerates' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: WENSLO'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: Column-sum normalisation. Each column j is divided by its column sum, producing a normalised matrix Z whose columns sum to 1. The procedure is direction-agnostic: cost/benefit orientation does not enter the algorithm (Pamucar et al. 2024, p.9510 Abstract; p.9513 §III-A). Formül: z_{ij} = \dfrac{\zeta_{ij}}{\sum_{i=1}^{m} \zeta_{ij}}\quad\forall j\in[1,n] Anchor: Pamucar et al. 2024, p.9512 Eq.(2)
2. 2.Adım 2 (F2): Step 2: Criterion class interval via Sturges' rule. Δz_j scales the (max - min) range of the j-th normalised column by 1 + 3.322·log10(m). Formül: \Delta z_j = \dfrac{\max_{i} z_{ij} - \min_{i} z_{ij}}{1 + 3.322\cdot\log_{10}(m)} Anchor: Pamucar et al. 2024, p.9513 Eq.(5)
3. 3.Adım 3 (F3): Step 3: Criterion slope tan(φ_j). The slope of the hypotenuse of the artificial right-angled triangle defined by ((m-1)·Δz_j, Σ_i z_ij). Since Σ_i z_ij = 1 by F1, this reduces to tan(φ_j) = 1/((m-1)·Δz_j). Formül: \tan\varphi_j = \dfrac{\sum_{i=1}^{m} z_{ij}}{(m-1)\cdot\Delta z_j} Anchor: Pamucar et al. 2024, p.9513 Eq.(7)
4. 4.Adım 4 (F4): Step 4: Criterion envelope E_j. Total Euclidean distance between successive normalised values along the j-th column, with the class interval Δz_j as the constant horizontal step. Captures the zig-zag length of the criterion's accumulation polyline. Formül: E_j = \sum_{i=1}^{m-1} \sqrt{(z_{i+1,j} - z_{i,j})^{2} + (\Delta z_j)^{2}} Anchor: Pamucar et al. 2024, p.9513 Eq.(8)
5. 5.Adım 5 (F5): Step 5: Envelope-slope ratio q_j = E_j / tan(φ_j). Larger q_j ⇒ longer accumulation envelope relative to the average slope ⇒ richer information about criterion variability ⇒ higher weight. Formül: q_j = \dfrac{E_j}{\tan\varphi_j} Anchor: Pamucar et al. 2024, p.9513 Eq.(9)
6. 6.Adım 6 (F6): Step 6: Additive normalisation of q_j yields the criterion weights. Formül: w_j = \dfrac{q_j}{\sum_{j'=1}^{n} q_{j'}}\quad\forall j\in[1,n] Anchor: Pamucar et al. 2024, p.9513 Eq.(10)

Commonly paired with

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

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