N-WPM - WPM yönteminin Neutrosophic uzantısı

Formül adımları

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

1. SVN matrix; cost complement for cost criteria.

   $$𝐃=(⟨T_{ij},I_{ij},F_{ij}⟩);\text{cost: }{\widehat{a}}_{ij}=⟨F_{ij},1-I_{ij},T_{ij}⟩;\text{benefit: }{\widehat{a}}_{ij}={\tilde{a}}_{ij}$$
   LaTeX

   \mathbf{D}=(\langle T_{ij},I_{ij},F_{ij}\rangle);\quad\text{cost: }\hat{a}_{ij}=\langle F_{ij},1-I_{ij},T_{ij}\rangle;\quad\text{benefit: }\hat{a}_{ij}=\tilde{a}_{ij}

2. SVNWG operator: neutrosophic weighted geometric product.

   $${\tilde{P}}_i={\mathrm{S}\mathrm{V}\mathrm{N}\mathrm{W}\mathrm{G}}_w({\widehat{a}}_{i1},\dots ,{\widehat{a}}_{in})=\backslash langle\prod _{j=1}^n{\widehat{T}}_{ij}^{w_j},1-\prod _{j=1}^n(1-{\widehat{I}}_{ij}{)}^{w_j},1-\prod _{j=1}^n(1-{\widehat{F}}_{ij}{)}^{w_j}\backslash rangle$$
   LaTeX

   \tilde{P}_i=\mathrm{SVNWG}_w(\hat{a}_{i1},\ldots,\hat{a}_{in})=\Bigl\langle\prod_{j=1}^n\hat{T}_{ij}^{w_j},\;1-\prod_{j=1}^n(1-\hat{I}_{ij})^{w_j},\;1-\prod_{j=1}^n(1-\hat{F}_{ij})^{w_j}\Bigr\rangle

3. Score and rank descending; tiebreaker accuracy a(α)=T-F.

   $$s_i=\frac{1+{\tilde{T}}_i^P-2{\tilde{I}}_i^P-{\tilde{F}}_i^P}{2};a_i={\tilde{T}}_i^P-{\tilde{F}}_i^P;\text{rank descending by }{s}_i$$
   LaTeX

   s_i=\tfrac{1+\tilde{T}_i^P-2\tilde{I}_i^P-\tilde{F}_i^P}{2};\quad a_i=\tilde{T}_i^P-\tilde{F}_i^P;\quad\text{rank descending by }s_i

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-wpm extends WPM 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 WPM 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.