N-MOORA - MOORA yönteminin Neutrosophic uzantısı

Formül adımları

Analiz motorunun yöntem bildirimindeki (manifest F.steps) adımlar; raporlardaki formüllerle aynı kaynaktır.

1. SVN score extraction and vector normalisation.

   $$s_{ij}=\frac{1+T_{ij}-2I_{ij}-F_{ij}}{2};{\overline{s}}_{ij}=\frac{s_{ij}}{\sqrt{{\sum }_{i=1}^m{s}_{ij}^2}}$$
   LaTeX

   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}}

2. Ratio system: net score subtracting cost-criteria contributions.

   $$y_i^{*}=\sum _{j\in {\Omega }_b}{w}_j{\overline{s}}_{ij}-\sum _{j\in {\Omega }_c}{w}_j{\overline{s}}_{ij};\text{rank descending}$$
   LaTeX

   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}

3. Reference point approach (optional Chebyshev minimax).

   $$r_j^{*}={max}_i{\overline{s}}_{ij}(j\in {\Omega }_b),{min}_i{\overline{s}}_{ij}(j\in {\Omega }_c);y_i^{**}={max}_j{w}_j|r_j^{*}-{\overline{s}}_{ij}|;\text{rank ascending}$$
   LaTeX

   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}

4. Final ranking from Ratio System (primary); Reference Point for cross-check.

   $$\text{Final rank by }{y}_i^{*}\text{ (descending). Cross-check with }{y}_i^{**}\text{ (ascending).}$$
   LaTeX

   \text{Final rank by }y_i^*\text{ (descending). Cross-check with }y_i^{**}\text{ (ascending).}

Sezgi

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).

Sonucu okuma: n-moora extends MOORA to handle Neutrosophic uncertainty. All arithmetic operations (normalisation, weighting, distance computation) are performed using Single-Valued Neutrosophic Set (SVNS: T, I, F; T,I,F ∈ [0,1], T+I+F ≤ 3) algebra. The final scores are defuzzified via score function S = (T − F + 1)/2 before ranking.

Varsayımlar

• 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

Ne zaman kullanılmaz

• Classical data sufficient - use base MOORA directly (avoid unnecessary uncertainty layer)
• Aggregation operator (PFWA/PFOWA/etc.) not specified - output ambiguous

Sınırlılıklar

• 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

Sık yapılan hatalar

• Değer-uzayı ihlali: hesaplamadan önce tüm girişlerin SVNS: T,I,F ∈ [0,1]; 0 ≤ T+I+F ≤ 3 koşulunu sağladığından emin olun.
• Defuzzifikasyon yöntemi sıralamayı etkiler: score function S = (T − F + 1)/2 kanonik seçimdir.