TIF-CODAS: Triangular Intuitionistic Fuzzy Group CODAS (TIFN-CODAS)

Overview

Triangular Intuitionistic Fuzzy ranking: TIFN: {(a1,a2,a3);(a'1,a2,a'3)} with membership and non-membership triangles. Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Triangular Intuitionistic Fuzzy ranking: TIFN: {(a1,a2,a3);(a'1,a2,a'3)} with membership and non-membership triangles
• •Preserves triangular_intuitionistic uncertainty through the pipeline rather than premature crispification at elicitation
• •Native group-decision support (multi-DM aggregation built into the pipeline)

Limitations

• •Assumes: Decision matrix entries are valid Intuitionistic Fuzzy numbers/tuples
• •Assumes: Underlying crisp method's compensation assumption holds in uncertain space
• •Assumes: All decision-maker(s) and experts use the same linguistic/uncertainty scale

Assumptions to verify

• •Decision matrix entries are valid Intuitionistic Fuzzy numbers/tuples
• •Underlying crisp method's compensation assumption holds in uncertain space
• •All decision-maker(s) and experts use the same linguistic/uncertainty scale

When not to use

• •Crisp data sufficient: use base CODAS directly (avoid unnecessary uncertainty layer)
• •Aggregation operator (PFWA/PFOWA/etc.) not specified: output ambiguous

Edge cases

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

Common pitfalls

• •Hatalı: 'IF-CODAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix entries are valid Intuitionistic Fuzzy numbers/tuples
• •Hatalı: 'IF-CODAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Underlying crisp method's compensation assumption holds in uncertain space
• •Hatalı: 'IF-CODAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: All decision-maker(s) and experts use the same linguistic/uncertainty scale
• •Hatalı: IF-CODAS'yi 'Crisp data sufficient' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: IF-CODAS'yi 'Aggregation operator (PFWA/PFOWA/etc.) not specified' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1. 1.Adım 1 (F1): Step 1: Collect linguistic decision matrices from each DM and convert to TIFNs using a linguistic scale. Aggregate each DM's TIFN matrix using DM weights λ_l (Eq.9): TIFN weighted aggregation formula. Formül: f_w(I_1,...,I_n) = \{(1-\prod_{i=1}^n(1-a_{i1})^{w_i},\, 1-\prod_{i=1}^n(1-a_{i2})^{w_i},\, 1-\prod_{i=1}^n(1-a_{i3})^{w_i});\,(\prod_{i=1}^n(a'_{i1})^{w_i},\, \prod_{i=1}^n(a_{i2})^{w_i},\, \prod_{i=1}^n(a'_{i3})^{w_i})\} Anchor: Daami Remadi & Frikha 2020, Def.4, Eq.(9)
2. 2.Adım 2 (F2): Step 2: Normalize TIFN decision matrix by dividing each component by the maximum a_j+ = max_i a_{ij2} (Eq.10). Formül: \hat{a}_{ij} = \{(a_{ij1}/a_j^+,\, a_{ij2}/a_j^+,\, a_{ij3}/a_j^+);\,(a'_{ij1}/a_j^+,\, a_{ij2}/a_j^+,\, a'_{ij3}/a_j^+)\},\quad a_j^+ = \max_i a_{ij} Anchor: Daami Remadi & Frikha 2020, Def.5, Eq.(10)
3. 3.Adım 3 (F3): Step 3: Apply criterion weights to normalized TIFN matrix (element-wise TIFN multiplication with criterion weight w_j). Formül: r_{ij} = w_j \otimes \hat{a}_{ij} Anchor: Daami Remadi & Frikha 2020, §III
4. 4.Adım 4 (F4): Step 4: Determine TIFN negative-ideal solution (TNS_j) for each criterion: minimum-valued alternative across all alternatives. Formül: TNS_j = \min_i r_{ij} Anchor: Daami Remadi & Frikha 2020, §III (Table VII)
5. 5.Adım 5 (F5): Step 5: Defuzzify TIFNs and compute Euclidean distance E_i (Eq.11) and Taxicab distance T_i (Eq.12) from each alternative to the negative-ideal solution. Formül: E_i = \sqrt{\sum_{j=1}^m (r_{ij} - TNS_j)^2},\quad T_i = \sum_{j=1}^m |r_{ij} - TNS_j| Anchor: Daami Remadi & Frikha 2020, Eqs.(11)-(12)
6. 6.Adım 6 (F6): Step 6: Build relative assessment matrix Ra_{ik} = (E_i - E_k) + ψ(E_i - E_k)·(T_i - T_k) per DM (where ψ is threshold function with τ). Compute per-DM scores H_i = Σ_k Ra_{ik}. Aggregate across DMs using weights λ_l → group score HG_i. Rank descending by HG_i. Formül: Ra_{ik} = (E_i - E_k) + \psi(E_i - E_k)\cdot(T_i - T_k),\quad H_i = \sum_k Ra_{ik},\quad HG_i = \sum_l \lambda_l H_i^l Anchor: Daami Remadi & Frikha 2020, §III (Tables IX-X)

Commonly paired with

• •n_a + IF-CODAS (common)

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