N-MULTIMOORA - MULTIMOORA yönteminin Neutrosophic uzantısı

Formül adımları

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

1. SVN matrix; cost complement; score + vector normalisation.

   $${\widehat{a}}_{ij}=⟨F_{ij},1-I_{ij},T_{ij}⟩(j\in {\Omega }_c);s_{ij}=\frac{1+{\widehat{T}}_{ij}-2{\widehat{I}}_{ij}-{\widehat{F}}_{ij}}{2};{\overline{s}}_{ij}=s_{ij}/\sqrt{{\sum }_i{s}_{ij}^2}$$
   LaTeX

   \hat{a}_{ij}=\langle F_{ij},1-I_{ij},T_{ij}\rangle\;(j\in\Omega_c);\quad s_{ij}=\tfrac{1+\hat{T}_{ij}-2\hat{I}_{ij}-\hat{F}_{ij}}{2};\quad\bar{s}_{ij}=s_{ij}/\sqrt{\sum_i s_{ij}^2}

2. Sub-method 1: Ratio System score.

   $$y_i^{\mathrm{R}\mathrm{S}}=\sum _{j=1}^n{w}_j{\overline{s}}_{ij};\text{rank descending}$$
   LaTeX

   y_i^{\mathrm{RS}}=\sum_{j=1}^n w_j\bar{s}_{ij};\quad\text{rank descending}

3. Sub-method 2: Reference Point Chebyshev score.

   $$r_j^{*}={max}_i{\overline{s}}_{ij};y_i^{\mathrm{R}\mathrm{P}}={max}_j{w}_j|r_j^{*}-{\overline{s}}_{ij}|;\text{rank ascending}$$
   LaTeX

   r_j^*=\max_i\bar{s}_{ij};\quad y_i^{\mathrm{RP}}=\max_j\;w_j|r_j^*-\bar{s}_{ij}|;\quad\text{rank ascending}

4. Sub-method 3: Full Multiplicative Form via SVNWG operator.

   $${\tilde{U}}_i={\mathrm{S}\mathrm{V}\mathrm{N}\mathrm{W}\mathrm{G}}_w({\widehat{a}}_{i1},\dots ,{\widehat{a}}_{in})=\backslash langle\prod _j{\widehat{T}}_{ij}^{w_j},1-\prod _j(1-{\widehat{I}}_{ij}{)}^{w_j},1-\prod _j(1-{\widehat{F}}_{ij}{)}^{w_j}\backslash rangle;y_i^{\mathrm{F}\mathrm{M}\mathrm{F}}=s({\tilde{U}}_i);\text{rank descending}$$
   LaTeX

   \tilde{U}_i=\mathrm{SVNWG}_w(\hat{a}_{i1},\ldots,\hat{a}_{in})=\Bigl\langle\prod_j\hat{T}_{ij}^{w_j},\;1-\prod_j(1-\hat{I}_{ij})^{w_j},\;1-\prod_j(1-\hat{F}_{ij})^{w_j}\Bigr\rangle;\quad y_i^{\mathrm{FMF}}=s(\tilde{U}_i);\quad\text{rank descending}

5. Theory of Dominance: final rank from pairwise dominance across RS, RP, FMF.

   $$A_i\succ A_k⟺A_i\text{ ranks better in }\ge 2\text{ of }\{RS,RP,FMF\};\text{count dominances for final order}$$
   LaTeX

   A_i\succ A_k\iff A_i\text{ ranks better in }\geq 2\text{ of }\{RS,RP,FMF\};\quad\text{count dominances for final order}

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-multimoora extends MULTIMOORA 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 MULTIMOORA directly (avoid unnecessary uncertainty layer)
• Aggregation operator (PFWA/PFOWA/etc.) not specified - output ambiguous

Sınırlılıklar

• 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.