N-RAFSI: Neutrosophic extension of RAFSI

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 RAFSI directly (avoid unnecessary uncertainty layer)
• •Aggregation operator (PFWA/PFOWA/etc.) not specified: output ambiguous

Edge cases

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

Common pitfalls

• •Hatalı: 'N-RAFSI bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix entries are valid Single-Valued Neutrosophic numbers/tuples
• •Hatalı: 'N-RAFSI bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Underlying crisp method's compensation assumption holds in uncertain space
• •Hatalı: 'N-RAFSI bu varsayımı kontrol etmeden uygulamak'. Doğrusu: All decision-maker(s) and experts use the same linguistic/uncertainty scale
• •Hatalı: N-RAFSI'yi 'Crisp data sufficient' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: N-RAFSI'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 score extraction. Formül: s_{ij}=\frac{1+T_{ij}-2I_{ij}-F_{ij}}{2} Anchor: Žižović et al. 2020, Sec.2; SVN score Ye 2014
2. 2.Adım 2 (F2): Ideal and non-ideal scores per criterion. Formül: s_j^{\mathrm{id}}=\begin{cases}\max_i s_{ij}&j\in\Omega_b\\\min_i s_{ij}&j\in\Omega_c\end{cases};\quad s_j^{\mathrm{nid}}=\begin{cases}\min_i s_{ij}&j\in\Omega_b\\\max_i s_{ij}&j\in\Omega_c\end{cases} Anchor: Žižović et al. 2020, Sec.2 Step2
3. 3.Adım 3 (F3): Map scores to [1, n_CI] interval. Formül: \hat{x}_{ij}=1+(n_{\mathrm{CI}}-1)\cdot\frac{|s_{ij}-s_j^{\mathrm{nid}}|}{|s_j^{\mathrm{id}}-s_j^{\mathrm{nid}}|},\quad n_{\mathrm{CI}}\text{ user-defined} Anchor: Žižović et al. 2020, Sec.2 Step3
4. 4.Adım 4 (F4): RAFSI composite score. Formül: R_i=\sum_{j=1}^n w_j\,\frac{\hat{x}_{ij}}{n_{\mathrm{CI}}} Anchor: Žižović et al. 2020, Sec.2 Step4
5. 5.Adım 5 (F5): Rank descending by R_i. Formül: \text{rank descending by }R_i Anchor: Žižović et al. 2020, Sec.2 Step5

Commonly paired with

• •n_a + N-RAFSI (common)

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