IF-EDAS: Intuitionistic Fuzzy EDAS

Overview

Distance-from-average ranking under Intuitionistic Fuzzy uncertainty. Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Distance-from-average ranking under Intuitionistic Fuzzy uncertainty
• •Preserves intuitionistic uncertainty through the pipeline rather than premature crispification at elicitation
• •Native group-decision support (multi-DM aggregation built into the pipeline)

Limitations

• •Rank reversal known on alternative-set changes (ref: Inherited from crisp EDAS base (Keshavarz Ghorabaee et al. 2015): removing/adding alternatives changes the per-criterion Average solution AV and therefore PDA/NDA: the appraisal scores rebase against a different reference.)
• •Assumes: Decision matrix entries are valid IFN tuples (μ, ν) with μ+ν ≤ 1
• •Assumes: All decision-makers use the same linguistic-to-IFN scale
• •Assumes: Criterion directions (benefit/cost) are explicitly labelled
• •Assumes: Criterion weights form a simplex

Assumptions to verify

• •Decision matrix entries are valid IFN tuples (μ, ν) with μ+ν ≤ 1
• •All decision-makers use the same linguistic-to-IFN scale
• •Criterion directions (benefit/cost) are explicitly labelled
• •Criterion weights form a simplex

When not to use

• •Crisp data sufficient: use base EDAS directly (avoid unnecessary uncertainty layer)
• •Utility-ratio ranking is preferred (use IF-ARAS instead)
• •Hesitation degree π must be modelled explicitly with μ+ν > 1 raw judgements: consider Pythagorean Fuzzy EDAS or q-ROF EDAS

Edge cases

• •IF decision matrix R = (r_ij) where r_ij = (μ_ij, ν_ij) is the IFN rating of alternative A_i on criterion C_j. For group-decision settings (K≥2 DMs), collect K such matrices and aggregate cell-wise vi
• •default Chen-Tan 1994: s(α) = μ − ν ∈ [−1, 1]). This produces a crisp m×n score matrix that drives the PDA/NDA computation.

Common pitfalls

• •Hatalı: 'IF-EDAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix entries are valid IFN tuples (μ, ν) with μ+ν ≤ 1
• •Hatalı: 'IF-EDAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: All decision-makers use the same linguistic-to-IFN scale
• •Hatalı: 'IF-EDAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Criterion directions (benefit/cost) are explicitly labelled
• •Hatalı: 'IF-EDAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Criterion weights form a simplex
• •Hatalı: IF-EDAS'yi 'Crisp data sufficient' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: IF-EDAS'yi 'Utility-ratio ranking is preferred (use IF-ARAS instead)' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: IF-EDAS'yi 'Hesitation degree π must be modelled explicitly with μ+ν > 1 raw judgements' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1. 1.Adım 1 (F1): Step 1: Construct the IF decision matrix R = (r_ij) where r_ij = (μ_ij, ν_ij) is the IFN rating of alternative A_i on criterion C_j. For group-decision settings (K≥2 DMs), collect K such matrices and aggregate cell-wise via IFWA with DM weights λ_k before entering F2: r_ij = (1 − Π(1−μ_ij^{(k)})^{λ_k}, Π (ν_ij^{(k)})^{λ_k}). Formül: R = (r_{ij})_{m \times n},\ r_{ij} = (\mu_{ij}, \nu_{ij}),\ \mu_{ij}+\nu_{ij} \le 1;\quad \text{IFWA aggregation if } K \ge 2 Anchor: Yıldırım-Meydan 2021 Steps 1-2; Dumrul 2024 Steps 1-2; Xu 2007 IFWA
2. 2.Adım 2 (F2): Step 2: Defuzzify each cell via the IF score function (default Chen-Tan 1994: s(α) = μ − ν ∈ [−1, 1]). This produces a crisp m×n score matrix that drives the PDA/NDA computation. Formül: s_{ij} = \mu_{ij} - \nu_{ij},\quad s_{ij} \in [-1, 1] Anchor: Yıldırım-Meydan 2021 Step 3; Dumrul 2024 Step 3; Chen-Tan 1994 score
3. 3.Adım 3 (F3): Step 3: Compute the Average Solution AV per criterion as the mean of crisp scores: AV_j = (1/m) Σ_i s_ij. Formül: AV_j = \frac{1}{m} \sum_{i=1}^{m} s_{ij} Anchor: Yıldırım-Meydan 2021 Step 4; Dumrul 2024 Step 4; Keshavarz Ghorabaee 2015 Eq. (3) [crisp skeleton]
4. 4.Adım 4 (F4): Step 4: Direction-aware Positive and Negative Distance from Average (PDA, NDA). For benefit criteria j ∈ J_b: PDA_ij = max(0, s_ij − AV_j) / |AV_j|, NDA_ij = max(0, AV_j − s_ij) / |AV_j|. For cost criteria j ∈ J_c the branches swap: PDA_ij = max(0, AV_j − s_ij) / |AV_j|, NDA_ij = max(0, s_ij − AV_j) / |AV_j|. Formül: j \in J_b: PDA_{ij} = \frac{\max(0,\ s_{ij} - AV_j)}{|AV_j|},\ NDA_{ij} = \frac{\max(0,\ AV_j - s_{ij})}{|AV_j|};\quad j \in J_c: \text{swap branches} Anchor: Yıldırım-Meydan 2021 Step 5; Dumrul 2024 Step 4; Keshavarz Ghorabaee 2015 Eqs. (4)-(5)
5. 5.Adım 5 (F5): Step 5: Weighted Sums SP_i = Σ_j w_j · PDA_ij and SN_i = Σ_j w_j · NDA_ij across criteria. Formül: SP_i = \sum_{j=1}^{n} w_j \cdot PDA_{ij};\quad SN_i = \sum_{j=1}^{n} w_j \cdot NDA_{ij} Anchor: Yıldırım-Meydan 2021 Step 6; Dumrul 2024 Step 5; Keshavarz Ghorabaee 2015 Eqs. (6)-(7)
6. 6.Adım 6 (F6): Step 6: Normalise SP and SN by their respective maxima: NSP_i = SP_i / max_k SP_k and NSN_i = 1 − SN_i / max_k SN_k. NSP rewards positive deviation; NSN rewards low negative deviation. Both lie in [0, 1]. Formül: NSP_i = \frac{SP_i}{\max_k SP_k};\quad NSN_i = 1 - \frac{SN_i}{\max_k SN_k} Anchor: Yıldırım-Meydan 2021 Step 7; Dumrul 2024 Step 6; Keshavarz Ghorabaee 2015 Eqs. (8)-(9)
7. 7.Adım 7 (F7): Step 7: Appraisal Score AS_i = (NSP_i + NSN_i) / 2 ∈ [0, 1]. Formül: AS_i = \frac{1}{2}\,(NSP_i + NSN_i),\quad AS_i \in [0, 1] Anchor: Yıldırım-Meydan 2021 Step 8; Dumrul 2024 Step 7; Keshavarz Ghorabaee 2015 Eq. (10)
8. 8.Adım 8 (F8): Step 8: Rank alternatives in descending order of AS_i; the alternative with the largest AS_i is the best. Formül: \text{rank}(A_i) = \text{argsort}_{\downarrow}(AS_i) Anchor: Yıldırım-Meydan 2021 Step 8; Dumrul 2024 Step 8

Commonly paired with

• •IF-AHP + IF-EDAS (common)
• •IF-SWARA + IF-EDAS (common)
• •IF-MEREC + IF-EDAS (emerging)

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