Fuzzy Delphi: Expert consensus with triangular fuzzy opinions and defuzzification

Overview

Fuzzy expert elicitation: TFN Delphi with centroid defuzzification. Output typically weight (higher value = preferred).

Strengths

• •Method-specific: Fuzzy expert elicitation: TFN Delphi with centroid defuzzification

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 Δj ≤ T (threshold), consensus reached; otherwise iterate.

Common pitfalls

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

Worked example

1. 1.Adım 1 (F1): Collect K expert TFN assessments ẽjk=(ejkα, ejkβ, ejkγ) for each criterion j=1..n. Formül: \tilde{e}_{jk}=(e_{jk}^{\alpha},e_{jk}^{\beta},e_{jk}^{\gamma}),\quad k=1,\ldots,K,\quad j=1,\ldots,n
2. 2.Adım 2 (F2): Aggregate K expert TFNs per criterion: lower bound = min, middle = arithmetic mean, upper = max. Formül: \tilde{E}_j=\left(\min_k e_{jk}^{\alpha},\;\frac{1}{K}\sum_{k=1}^{K}e_{jk}^{\beta},\;\max_k e_{jk}^{\gamma}\right)
3. 3.Adım 3 (F3): Consensus check: compute spread Δj = max_k(ejkγ) − min_k(ejkα); if Δj ≤ T (threshold), consensus reached; otherwise iterate. Formül: \Delta_j=\max_k e_{jk}^{\gamma}-\min_k e_{jk}^{\alpha};\quad\text{if }\Delta_j\leq T\Rightarrow\text{consensus, else iterate}
4. 4.Adım 4 (F4): Defuzzify consensus TFN via COA: Cj = (Ejα + Ejβ + Ejγ) / 3; normalise weights wj = Cj / Σj Cj. Formül: C_j=\frac{E_j^{\alpha}+E_j^{\beta}+E_j^{\gamma}}{3};\quad w_j=\frac{C_j}{\sum_{j=1}^{n}C_j}

Commonly paired with

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

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