FUCOM-F: Fuzzy Full Consistency Method (TFN)

Overview

Triangular-fuzzy pairwise priority weighting with full-consistency NLP. Output typically weight (higher value = preferred).

Strengths

• •Method-specific: Triangular-fuzzy pairwise priority weighting with full-consistency NLP
• •Preserves triangular_fuzzy uncertainty through the pipeline rather than premature crispification at elicitation

Limitations

• •Assumes: Experts can rank criteria
• •Assumes: Each consecutive ratio φ̃_{j,j+1} expressible on the linguistic scale
• •Assumes: TFN shape (l ≤ m ≤ u) preserved

Assumptions to verify

• •Experts can rank criteria
• •Each consecutive ratio φ̃_{j,j+1} expressible on the linguistic scale
• •TFN shape (l ≤ m ≤ u) preserved

When not to use

• •Only crisp ratio available → use FUCOM (crisp)
• •Interactions between criteria expected → use ANP/DEMATEL

Edge cases

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

Common pitfalls

• •Hatalı: 'FUCOM-F bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Experts can rank criteria
• •Hatalı: 'FUCOM-F bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Each consecutive ratio φ̃_{j,j+1} expressible on the linguistic scale
• •Hatalı: 'FUCOM-F bu varsayımı kontrol etmeden uygulamak'. Doğrusu: TFN shape (l ≤ m ≤ u) preserved
• •Hatalı: FUCOM-F'yi 'Only crisp ratio available → use FUCOM (crisp)' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: FUCOM-F'yi 'Interactions between criteria expected → use ANP/DEMATEL' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1. 1.Adım 1 (F1): Step 1: Rank criteria by importance C_(1) ≻ C_(2) ≻ … ≻ C_(n). Formül: C_{(1)} \succeq C_{(2)} \succeq \cdots \succeq C_{(n)} Anchor: Pamucar-Ecer 2020 Step 1; Keleş 2025 Bölüm 4 Adım 1
2. 2.Adım 2 (F2): Step 2: For each consecutive pair, elicit the fuzzy comparative significance φ̃_{j,j+1} = (l_j, m_j, u_j) from the linguistic scale (n−1 TFNs). Formül: \tilde{\varphi}_{j,j+1} = (l_{j}, m_{j}, u_{j}),\quad j=1,\ldots,n-1 Anchor: Pamucar-Ecer 2020 Eq.(8); Keleş 2025 Bölüm 4 Adım 2
3. 3.Adım 3 (F3): Step 3: Solve the FUCOM-F nonlinear program for fuzzy weights w̃_j = (l_j^w, m_j^w, u_j^w) and deviation χ̃ = (l_χ, m_χ, u_χ): minimise S(χ̃) subject to (a) ratio constraints |w̃_(j)/w̃_(j+1) − φ̃_{j,j+1}| ≤ χ̃ componentwise; (b) transitivity |w̃_(j)/w̃_(j+2) − φ̃_{j,j+1}⊗φ̃_{j+1,j+2}| ≤ χ̃; (c) Σ_j S(w̃_j) = 1; (d) l_j^w ≤ m_j^w ≤ u_j^w; (e) l_j^w ≥ 0. Formül: \min\ S(\tilde{\chi})\quad \text{s.t.}\quad \left|\dfrac{\tilde{w}_{(j)}}{\tilde{w}_{(j+1)}} - \tilde{\varphi}_{j,j+1}\right| \le \tilde{\chi},\ \left|\dfrac{\tilde{w}_{(j)}}{\tilde{w}_{(j+2)}} - \tilde{\varphi}_{j,j+1}\otimes\tilde{\varphi}_{j+1,j+2}\right| \le \tilde{\chi},\ \sum_{j} S(\tilde{w}_{j}) = 1,\ l_{j}^{w} \le m_{j}^{w} \le u_{j}^{w},\ l_{j}^{w} \ge 0 Anchor: Pamucar-Ecer 2020 Eq.(9); Keleş 2025 Bölüm 4 Adım 3
4. 4.Adım 4 (F4): Step 4: Defuzzify w̃_j → w_j with graded mean: w_j = (l_j^w + 4 m_j^w + u_j^w)/6. Final output: crisp weights and crisp deviation S(χ̃). Formül: w_{j} = \dfrac{l_{j}^{w} + 4 m_{j}^{w} + u_{j}^{w}}{6} Anchor: Pamucar-Ecer 2020 Step 4; Keleş 2025 Bölüm 4 Adım 4

Commonly paired with

• •FUCOM-F + FUZZY-TOPSIS (high)
• •FUCOM-F + FUZZY-MARCOS (high)
• •FUCOM-F + FUZZY-WASPAS (medium)

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