N-GRA: Neutrosophic extension of GRA

Overview

Neutrosophic outranking/ranking: Single-Valued Neutrosophic Set (SVNS: T, I, F; T,I,F ∈ [0,1], T+I+F ≤ 3). Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Neutrosophic outranking/ranking: Single-Valued Neutrosophic Set (SVNS: T, I, F; T,I,F ∈ [0,1], T+I+F ≤ 3)
• •Preserves single_valued_neutrosophic 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 Single-Valued Neutrosophic 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 Single-Valued Neutrosophic 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 GRA directly (avoid unnecessary uncertainty layer)
• •Aggregation operator (PFWA/PFOWA/etc.) not specified: output ambiguous

Edge cases

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

Common pitfalls

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

Worked example

1. 1.Adım 1 (F1): SVN matrix; cost complement for cost criteria. Formül: \mathbf{D}=(\langle T_{ij},I_{ij},F_{ij}\rangle);\quad\text{cost: }\tilde{a}_{ij}^c=\langle F_{ij},1-I_{ij},T_{ij}\rangle Anchor: Biswas, Pramanik & Giri 2014, Sec.3 Step1
2. 2.Adım 2 (F2): Neutrosophic ideal reference sequence. Formül: \alpha_j^0=\langle\max_i T_{ij},\;\min_i I_{ij},\;\min_i F_{ij}\rangle,\quad j=1,\ldots,n Anchor: Biswas, Pramanik & Giri 2014, Sec.3 Step2
3. 3.Adım 3 (F3): Neutrosophic Euclidean distances to ideal; global extremes. Formül: \Delta_{ij}=\sqrt{\tfrac{(\max_k T_{kj}-T_{ij})^2+(\min_k I_{kj}-I_{ij})^2+(\min_k F_{kj}-F_{ij})^2}{3}};\quad\Delta_{\min}=\min_i\min_j\Delta_{ij};\quad\Delta_{\max}=\max_i\max_j\Delta_{ij} Anchor: Biswas, Pramanik & Giri 2014, Sec.3 Step3-4
4. 4.Adım 4 (F4): Grey Relational Coefficient with ρ=0.5. Formül: \xi_{ij}=\frac{\Delta_{\min}+\rho\Delta_{\max}}{\Delta_{ij}+\rho\Delta_{\max}},\quad\rho=0.5 Anchor: Deng 1989, Eq.(3); Biswas, Pramanik & Giri 2014, Sec.3 Step5
5. 5.Adım 5 (F5): Grey Relational Grade; rank descending. Formül: \Gamma_i=\sum_{j=1}^n w_j\xi_{ij};\quad\text{rank descending} Anchor: Biswas, Pramanik & Giri 2014, Sec.3 Step6-7

Commonly paired with

• •n_a + N-GRA (common)

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