N-SPOTIS - SPOTIS yönteminin Neutrosophic uzantısı

Formül adımları

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

1. SVN scores; pre-specified bounds and ideal.

   $$s_{ij}=\frac{1+T_{ij}-2I_{ij}-F_{ij}}{2}\text{clipped to }[s_j^{min},s_j^{max}];s_j^{*}=s_j^{max}(j\in {\Omega }_b),s_j^{min}(j\in {\Omega }_c)$$
   LaTeX

   s_{ij}=\tfrac{1+T_{ij}-2I_{ij}-F_{ij}}{2}\;\text{clipped to }[s_j^{\min},s_j^{\max}];\quad s_j^*=s_j^{\max}\;(j\in\Omega_b),\;s_j^{\min}\;(j\in\Omega_c)

2. Normalised distance from ideal within fixed bounds.

   $$p_{ij}=\frac{|s_{ij}-s_j^{*}|}{s_j^{max}-s_j^{min}},p_{ij}\in [0,1]$$
   LaTeX

   p_{ij}=\frac{|s_{ij}-s_j^*|}{s_j^{\max}-s_j^{\min}},\quad p_{ij}\in[0,1]

3. SPOTIS score D_i; rank ascending (lower = better).

   $$D_i=\sum _{j=1}^n{w}_j{p}_{ij};\text{rank ascending}$$
   LaTeX

   D_i=\sum_{j=1}^n w_j\,p_{ij};\quad\text{rank 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-spotis extends SPOTIS 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 SPOTIS 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.