Taxonomy Method: Wrocław Taxonomic Development Measure

Overview

Taxonomic distance composite index (z-score + Euclidean ideal). Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Taxonomic distance composite index (z-score + Euclidean ideal)

Limitations

• •Assumes: Criteria preferences are independent (no synergistic interactions)
• •Assumes: Compensation is acceptable: high score on one criterion can offset low on another
• •Assumes: Decision matrix is complete (no missing values)

Assumptions to verify

• •Criteria preferences are independent (no synergistic interactions)
• •Compensation is acceptable: high score on one criterion can offset low on another
• •Decision matrix is complete (no missing values)

When not to use

• •Criteria strongly correlated → consider DEMATEL/ANP for interdependence
• •Non-compensatory preferences → consider outranking (ELECTRE/PROMETHEE)

Edge cases

• •See F.steps and D.parameters for TAXONOMY-specific edge handling. recommendation_metadata.assumptions_to_verify also lists boundary conditions.

Common pitfalls

• •Hatalı: 'TAXONOMY bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Criteria preferences are independent (no synergistic interactions)
• •Hatalı: 'TAXONOMY bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Compensation is acceptable: high score on one criterion can offset low on another
• •Hatalı: 'TAXONOMY bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix is complete (no missing values)
• •Hatalı: TAXONOMY'yi 'Criteria strongly correlated → consider DEMATEL/ANP for interdependence' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: TAXONOMY'yi 'Non-compensatory preferences → consider outranking (ELECTRE/PROMETHEE)' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1. 1.Adım 1 (F1): Step 1: Z-score standardisation. Cost criteria are negated after standardisation so higher z always means better. Formül: z_{ij} = \frac{x_{ij} - \bar{x}_{j}}{s_{j}} \text{ (benefit)};\quad z_{ij} = -\frac{x_{ij} - \bar{x}_{j}}{s_{j}} \text{ (cost)} Anchor: Hellwig 1968, p.310 (extension of Wrocław taxonomy)
2. 2.Adım 2 (F2): Step 2: Define reference object (ideal) z⁺_j = max_i z_ij for all j (after negation of cost). Formül: z_{j}^{+} = \max_{i}\,z_{ij} \quad \forall j Anchor: Hellwig 1968, p.311
3. 3.Adım 3 (F3): Step 3: Compute Euclidean distance c_i from each alternative to the ideal. Formül: c_{i} = \sqrt{\sum_{j=1}^{n}(z_{ij} - z_{j}^{+})^{2}} Anchor: Hellwig 1968, p.311
4. 4.Adım 4 (F4): Step 4: Compute development measure d_i = 1 − c_i / c⁰ where c⁰ = c̄ + 2s_c. Rank descending. Formül: \bar{c}=\frac{1}{m}\sum_{i}c_{i},\;s_{c}=\sqrt{\frac{1}{m}\sum_{i}(c_{i}-\bar{c})^{2}},\;c^{0}=\bar{c}+2s_{c};\quad d_{i}=1-\frac{c_{i}}{c^{0}} Anchor: Hellwig 1968, p.312

Commonly paired with

• •AHP + TAXONOMY (high)
• •BWM + TAXONOMY (high)
• •ENTROPY + TAXONOMY (high)
• •CRITIC + TAXONOMY (high)
• •SWARA + TAXONOMY (high)

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