N-MOORA: Neutrosophic extension of MOORA

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

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

Edge cases

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

Common pitfalls

• •Hatalı: 'N-MOORA bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix entries are valid Single-Valued Neutrosophic numbers/tuples
• •Hatalı: 'N-MOORA bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Underlying crisp method's compensation assumption holds in uncertain space
• •Hatalı: 'N-MOORA bu varsayımı kontrol etmeden uygulamak'. Doğrusu: All decision-maker(s) and experts use the same linguistic/uncertainty scale
• •Hatalı: N-MOORA'yi 'Crisp data sufficient' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: N-MOORA'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 and vector normalisation. Formül: s_{ij}=\tfrac{1+T_{ij}-2I_{ij}-F_{ij}}{2};\quad\bar{s}_{ij}=\frac{s_{ij}}{\sqrt{\sum_{i=1}^m s_{ij}^2}} Anchor: Brauers & Zavadskas 2006, Eq.(1); SVN score: Ye 2014
2. 2.Adım 2 (F2): Ratio system: net score subtracting cost-criteria contributions. Formül: y_i^*=\sum_{j\in\Omega_b}w_j\bar{s}_{ij}-\sum_{j\in\Omega_c}w_j\bar{s}_{ij};\quad\text{rank descending} Anchor: Brauers & Zavadskas 2006, Sec.3
3. 3.Adım 3 (F3): Reference point approach (optional Chebyshev minimax). Formül: r_j^*=\max_i\bar{s}_{ij}\;(j\in\Omega_b),\;\min_i\bar{s}_{ij}\;(j\in\Omega_c);\quad y_i^{**}=\max_j\;w_j|r_j^*-\bar{s}_{ij}|;\quad\text{rank ascending} Anchor: Brauers & Zavadskas 2006, Sec.4
4. 4.Adım 4 (F4): Final ranking from Ratio System (primary); Reference Point for cross-check. Formül: \text{Final rank by }y_i^*\text{ (descending). Cross-check with }y_i^{**}\text{ (ascending).} Anchor: Brauers & Zavadskas 2006, Sec.5

Commonly paired with

• •n_a + N-MOORA (common)

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