N-AROMAN: Neutrosophic extension of AROMAN

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

Edge cases

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

Common pitfalls

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

Worked example

1. 1.Adım 1 (F1): Compute SVN score for each rating. Formül: s_{ij}=s(\tilde{a}_{ij})=\frac{1+T_{ij}-2I_{ij}-F_{ij}}{2} Anchor: Bošković et al. 2023, Sec.3 Step1; Biswas 2016 score
2. 2.Adım 2 (F2): Step-1 linear normalisation of SVN scores. Formül: r_{ij}=\begin{cases}s_{ij}/s_j^{\max}&j\in\Omega_b\\s_j^{\min}/s_{ij}&j\in\Omega_c\end{cases} Anchor: Bošković et al. 2023, Sec.3 Step2
3. 3.Adım 3 (F3): Step-2 vector normalisation of linearly-normalised scores. Formül: z_{ij}=\frac{r_{ij}}{\sqrt{\sum_{i=1}^m r_{ij}^2}} Anchor: Bošković et al. 2023, Sec.3 Step3
4. 4.Adım 4 (F4): Combined two-step normalised value. Formül: t_{ij}=\frac{r_{ij}+z_{ij}}{2} Anchor: Bošković et al. 2023, Sec.3 Step4
5. 5.Adım 5 (F5): AROMAN composite score; rank descending. Formül: AROMAN_i=\sum_{j=1}^n w_j\,t_{ij};\quad\text{rank descending} Anchor: Bošković et al. 2023, Sec.3 Step5-6

Commonly paired with

• •n_a + N-AROMAN (common)

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