ANP: Analytic Network Process (AHP with feedback and interdependences)

Overview

Weight_Subjective (pairwise comparison, supermatrix, network structure). Output typically weight (higher value = preferred).

Strengths

• •Method-specific: Weight_Subjective (pairwise comparison, supermatrix, network structure)
• •Native group-decision support (multi-DM aggregation built into the pipeline)

Limitations

• •Rank reversal known on alternative-set changes (ref: Wang & Luo 2009 (AHP-inherited))
• •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

• •ties from W^∞ rows in the alternatives cluster.
• •ties.

Common pitfalls

• •Hatalı: 'ANP bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Domain experts available
• •Hatalı: 'ANP bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Experts can express consistent comparisons
• •Hatalı: ANP'yi 'No experts available → use objective weighting' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: ANP'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: Construct unweighted supermatrix W from cluster/criterion pairwise comparisons. Formül: W = [w_{ij}]_{N\times N},\ N=\sum_{c} n_{c} Anchor: Saaty 1996, p.137 Eq.(1)
2. 2.Adım 2 (F2): Step 2: Weighted supermatrix W' = W · C where C is the cluster weight matrix; columns stochastic. Formül: W' = W \cdot C,\quad \sum_{i} W'_{ij} = 1\ \forall j Anchor: Saaty 1996, p.139 Eq.(2)
3. 3.Adım 3 (F3): Step 3: Limit supermatrix W^∞ = lim_{k→∞} (W')^k (powers converge to steady state). Formül: W^{\infty} = \lim_{k\to\infty} (W')^{k} Anchor: Saaty 1996, p.140 Eq.(3)
4. 4.Adım 4 (F4): Step 4: Read alternative priorities from W^∞ rows in the alternatives cluster. Formül: p_{i} = W^{\infty}_{i,\text{any col in alt cluster}} Anchor: Saaty 1996, p.141
5. 5.Adım 5 (F5): Step 5: Descending ranking by priorities. Formül: \text{rank}(A_{i})\propto -p_{i} Anchor: Saaty 1996, Ch.4

Commonly paired with

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

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