ENTROPY: Shannon Entropy Weighting Method

Overview

Information-theoretic objective weighting (Shannon entropy). Output typically weight (higher value = preferred).

Strengths

• •Method-specific: Information-theoretic objective weighting (Shannon entropy)

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

• •default min_j(x_kj)/x_ij). For j ∈ J⁺ leave unchanged.
• •when p = 0.

Common pitfalls

• •Hatalı: 'ENTROPY bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix exists with measurable criteria
• •Hatalı: 'ENTROPY bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Sufficient inter-alternative variation per criterion
• •Hatalı: ENTROPY'yi 'No data variation (constant criterion) → weight degenerates' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: ENTROPY'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 0: Cost-criterion inversion: for j ∈ J⁻ apply chosen strategy (default min_j(x_kj)/x_ij). For j ∈ J⁺ leave unchanged. Formül: r_{ij} = \begin{cases} x_{ij} & j \in J^{+} \\ \min_{k} x_{kj} / x_{ij} & j \in J^{-} \text{ (default)} \\ 1/x_{ij} & j \in J^{-} \text{ (reciprocal)} \\ \max_{k} x_{kj} - x_{ij} + \varepsilon & j \in J^{-} \text{ (max-minus)} \end{cases} Anchor: Hwang & Yoon 1981 §3.3 (cost inversion convention)
2. 2.Adım 2 (F2): Step 1: Column-sum probability normalisation: p_ij = r_ij / Σ_i r_ij. Formül: p_{ij} = \dfrac{r_{ij}}{\sum_{i=1}^{m} r_{ij}} Anchor: Hwang & Yoon 1981 §3.3 Eq.(3.3.1)
3. 3.Adım 3 (F3): Step 2: Shannon entropy per criterion: E_j = -k Σ_i p_ij ln(p_ij), k = 1/ln(m). Convention: p ln(p) = 0 when p = 0. Formül: E_{j} = -\dfrac{1}{\ln(m)} \sum_{i=1}^{m} p_{ij} \ln(p_{ij}),\quad E_{j} \in [0, 1] Anchor: Shannon 1948 (entropy definition); MCDM adaptation per Hwang & Yoon 1981 §3.3
4. 4.Adım 4 (F4): Step 3: Divergence (information variability) d_j = 1 − E_j. Formül: d_{j} = 1 - E_{j} Anchor: Hwang & Yoon 1981 §3.3
5. 5.Adım 5 (F5): Step 4: Normalised entropy weights w_j = d_j / Σ_k d_k; Σ w_j = 1. Formül: w_{j} = \dfrac{d_{j}}{\sum_{k=1}^{n} d_{k}},\quad \sum_{j=1}^{n} w_{j} = 1 Anchor: Hwang & Yoon 1981 §3.3

Commonly paired with

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

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