N-VIKOR - VIKOR yönteminin Neutrosophic uzantısı

Formül adımları

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

1. SVN decision matrix; cost complement.

   $$𝐃=(⟨T_{ij},I_{ij},F_{ij}⟩{)}_{m\times n};\text{cost: }⟨F_{ij},1-I_{ij},T_{ij}⟩$$
   LaTeX

   \mathbf{D}=(\langle T_{ij},I_{ij},F_{ij}\rangle)_{m\times n};\quad\text{cost: }\langle F_{ij},1-I_{ij},T_{ij}\rangle

2. Best and worst SVN values per criterion.

   $${\tilde{f}}_j^{*}=⟨{max}_i{T}_{ij},{min}_i{I}_{ij},{min}_i{F}_{ij}⟩;{\tilde{f}}_j^{-}=⟨{min}_i{T}_{ij},{max}_i{I}_{ij},{max}_i{F}_{ij}⟩$$
   LaTeX

   \tilde{f}_j^*=\langle\max_i T_{ij},\min_i I_{ij},\min_i F_{ij}\rangle;\quad\tilde{f}_j^-=\langle\min_i T_{ij},\max_i I_{ij},\max_i F_{ij}\rangle

3. Normalised neutrosophic gap ratio.

   $$d({\alpha }_1,{\alpha }_2)=\sqrt{\frac{(T_1-T_2{)}^2+(I_1-I_2{)}^2+(F_1-F_2{)}^2}{3}};f_{ij}=\frac{d({\tilde{f}}_j^{*},{\tilde{a}}_{ij})}{d({\tilde{f}}_j^{*},{\tilde{f}}_j^{-})}$$
   LaTeX

   d(\alpha_1,\alpha_2)=\sqrt{\tfrac{(T_1-T_2)^2+(I_1-I_2)^2+(F_1-F_2)^2}{3}};\quad f_{ij}=\frac{d(\tilde{f}_j^*,\tilde{a}_{ij})}{d(\tilde{f}_j^*,\tilde{f}_j^-)}

4. Utility S_i and regret R_i measures.

   $$S_i=\sum _{j=1}^n{w}_j{f}_{ij};R_i={max}_j{w}_j{f}_{ij}$$
   LaTeX

   S_i=\sum_{j=1}^n w_j f_{ij};\quad R_i=\max_j\;w_j f_{ij}

5. Compromise index Q_i; rank ascending. Check acceptability conditions.

   $$Q_i=v\frac{S_i-S^{*}}{S^{-}-S^{*}}+(1-v)\frac{R_i-R^{*}}{R^{-}-R^{*}},v=0.5;\text{rank ascending by }{Q}_i;𝒞=\{A^{(1)}\}\text{ if C1 and C2; }\{A^{(1)},A^{(2)}\}\text{ if only C2 fails; otherwise include ordered }{A}^{(k)}\text{ while }Q(A^{(k)})-Q(A^{(1)})<DQ$$
   LaTeX

   Q_i=v\frac{S_i-S^*}{S^--S^*}+(1-v)\frac{R_i-R^*}{R^--R^*},\;v=0.5;\quad\text{rank ascending by }Q_i;\quad \mathcal{C}=\{A^{(1)}\}\text{ if C1 and C2; }\{A^{(1)},A^{(2)}\}\text{ if only C2 fails; otherwise include ordered }A^{(k)}\text{ while }Q(A^{(k)})-Q(A^{(1)})<DQ

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-vikor extends VIKOR 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 VIKOR 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.