DANP: DEMATEL-based ANP

Overview

Hybrid: DEMATEL total-relation + ANP supermatrix. Output typically weight (higher value = preferred).

Strengths

• •Method-specific: Hybrid: DEMATEL total-relation + ANP supermatrix

Limitations

• •Assumes: Domain experts available
• •Assumes: Experts can express consistent comparisons

Assumptions to verify

• •Domain experts available
• •Experts can express consistent comparisons

When not to use

• •No experts available → use objective weighting
• •High inconsistency → discard and re-elicit

Edge cases

• •if cyclic.

Common pitfalls

• •Hatalı: 'DANP bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Domain experts available
• •Hatalı: 'DANP bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Experts can express consistent comparisons
• •Hatalı: DANP'yi 'No experts available → use objective weighting' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: DANP'yi 'High inconsistency → discard and re-elicit' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1. 1.Adım 1 (F1): Step 1: Direct-influence matrix A from experts (criteria pairwise influence on 0-4 scale). Formül: A = [a_{ij}]_{n\times n},\ a_{ij}\in\{0,1,2,3,4\} Anchor: Tzeng-Huang 2011, Ch.7 Eq.(7.1)
2. 2.Adım 2 (F2): Step 2: Normalised direct relation X = A / max(row-sum, col-sum). Formül: X = \dfrac{A}{\max\big(\max_{i}\sum_{j} a_{ij},\ \max_{j}\sum_{i} a_{ij}\big)} Anchor: Tzeng-Huang 2011, p.140 Eq.(7.2)
3. 3.Adım 3 (F3): Step 3: Total relation matrix T = X(I − X)^{−1} (DEMATEL output). Formül: T = X(I - X)^{-1} Anchor: Tzeng-Huang 2011, p.140 Eq.(7.3)
4. 4.Adım 4 (F4): Step 4: Normalise T column-wise to form unweighted supermatrix W. Formül: w_{ij} = \dfrac{t_{ij}}{\sum_{i} t_{ij}}\ \text{(column-stochastic supermatrix)} Anchor: Tzeng-Huang 2011, p.141 Eq.(7.4)
5. 5.Adım 5 (F5): Step 5: Limit supermatrix W^∞ = lim_{k→∞} W^k (powers converge to steady state). Use Cesaro sum if cyclic. Formül: W^{\infty} = \lim_{k\to\infty} W^{k}\ \text{or}\ \lim_{N\to\infty} \dfrac{1}{N}\sum_{r=1}^{N} W^{r} Anchor: Tzeng-Huang 2011, p.141 Eq.(7.5)
6. 6.Adım 6 (F6): Step 6: Final criterion weights from any column of W^∞ (DEMATEL-derived dependency baked in). Formül: \mathbf{w} = W^{\infty}_{:,k}\ \text{(any column)} Anchor: Tzeng-Huang 2011, p.142 Sec.7.5

Commonly paired with

• •DANP + TOPSIS (high)
• •DANP + VIKOR (high)
• •DANP + EDAS (high)
• •DANP + PROMETHEE (high)
• •DANP + ELECTRE-III (high)

How to cite