qR-EDAS: q-Rung Orthopair extension of EDAS

Overview

q-Rung Orthopair outranking/ranking: q-Rung Orthopair Fuzzy Number (q-ROFN: μ, ν; μ^q+ν^q ≤ 1, q ≥ 1). Output typically utility (higher value = preferred).

Strengths

• •Method-specific: q-Rung Orthopair outranking/ranking: q-Rung Orthopair Fuzzy Number (q-ROFN: μ, ν; μ^q+ν^q ≤ 1, q ≥ 1)
• •Preserves q_rung_orthopair 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 base; cf. Belton-Gear 1983, Wang-Luo 2009)
• •Assumes: Decision matrix entries are valid q-Rung Orthopair 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 q-Rung Orthopair 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 EDAS directly (avoid unnecessary uncertainty layer)
• •Aggregation operator (PFWA/PFOWA/etc.) not specified: output ambiguous

Edge cases

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

Common pitfalls

• •Hatalı: 'QR-EDAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix entries are valid q-Rung Orthopair Fuzzy numbers/tuples
• •Hatalı: 'QR-EDAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Underlying crisp method's compensation assumption holds in uncertain space
• •Hatalı: 'QR-EDAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: All decision-maker(s) and experts use the same linguistic/uncertainty scale
• •Hatalı: QR-EDAS'yi 'Crisp data sufficient' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: QR-EDAS'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: Liu-Wang score reduction on q-ROFN decision matrix: s_ij = μ_ij^q − ν_ij^q ∈ [−1, 1]. Cost criteria use q-ROFN complement α^c = (ν, μ) before scoring (equivalently, score sign flips). Formül: s_{ij}=\mu_{ij}^{q}-\nu_{ij}^{q};\quad (\mu_{ij},\nu_{ij})^{c}=(\nu_{ij},\mu_{ij})\ \text{for}\ j\in\Omega_c Anchor: Liu-Wang 2018, Def. 2.4 score function; QR-EDAS.tex §Algorithmic Steps, Step 1
2. 2.Adım 2 (F2): Step 2: Average solution per criterion on score values: AV_j = s̄_j = (1/m) Σ_i s_ij. Formül: AV_{j}=\bar{s}_{j}=\dfrac{1}{m}\sum_{i=1}^{m}s_{ij} Anchor: QR-EDAS.tex §Algorithmic Steps, Step 2; Keshavarz-Ghorabaee 2015 Eq.(3) adapted to score domain
3. 3.Adım 3 (F3): Step 3: Positive (PDA) and negative (NDA) distance from AV. Benefit criteria: PDA rewards above-average, NDA penalises below-average. Direction handled at F1 via complement so both branches use the benefit form here. Formül: PDA_{ij}=\dfrac{\max(0,\,s_{ij}-\bar{s}_{j})}{|\bar{s}_{j}|},\quad NDA_{ij}=\dfrac{\max(0,\,\bar{s}_{j}-s_{ij})}{|\bar{s}_{j}|} Anchor: QR-EDAS.tex §Algorithmic Steps, Step 3; Keshavarz-Ghorabaee 2015 Eqs.(4)-(5)
4. 4.Adım 4 (F4): Step 4: Weighted PDA and NDA sums across criteria. Formül: SP_{i}=\sum_{j=1}^{n}w_{j}\,PDA_{ij};\quad SN_{i}=\sum_{j=1}^{n}w_{j}\,NDA_{ij} Anchor: QR-EDAS.tex §Algorithmic Steps, Step 4; Keshavarz-Ghorabaee 2015 Eqs.(6)-(7)
5. 5.Adım 5 (F5): Step 5: Normalise SP and SN by their per-method maxima. Formül: NSP_{i}=\dfrac{SP_{i}}{\max_{k}SP_{k}};\quad NSN_{i}=1-\dfrac{SN_{i}}{\max_{k}SN_{k}} Anchor: QR-EDAS.tex §Algorithmic Steps, Step 4 (normalisation); Keshavarz-Ghorabaee 2015 Eqs.(8)-(9)
6. 6.Adım 6 (F6): Step 6: Appraisal score AS_i ∈ [0, 1] and descending ranking. Formül: AS_{i}=\tfrac{1}{2}(NSP_{i}+NSN_{i});\quad \text{rank}=\operatorname{argsort}_{\downarrow}(AS_{1},\ldots,AS_{m}) Anchor: QR-EDAS.tex §Algorithmic Steps, Step 4 (AS); Keshavarz-Ghorabaee 2015 Eq.(10)

Commonly paired with

• •n_a + QR-EDAS (common)

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