Kübik sezgisel bulanık TOPSIS

Formül adımları

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

1. Yerel kübik sezgisel bulanık değerlendirmeleri doğrulayın

   $${\alpha }_{ij}^{(k)}=(([{\zeta }_{ij}^{Lk},{\zeta }_{ij}^{Uk}],[{\vartheta }_{ij}^{Lk},{\vartheta }_{ij}^{Uk}]),({\zeta }_{ij}^k,{\vartheta }_{ij}^k));0\le {\zeta }^{Lk}\le {\zeta }^{Uk}\le 1,0\le {\vartheta }^{Lk}\le {\vartheta }^{Uk}\le 1,{\zeta }^{Uk}+{\vartheta }^{Uk}\le 1,{\zeta }^k,{\vartheta }^k\ge 0,{\zeta }^k+{\vartheta }^k\le 1.$$
   LaTeX

   \alpha_{ij}^{(k)}=(( [\zeta_{ij}^{Lk},\zeta_{ij}^{Uk}],[\vartheta_{ij}^{Lk},\vartheta_{ij}^{Uk}] ),(\zeta_{ij}^{k},\vartheta_{ij}^{k}));\quad 0\le\zeta^{Lk}\le\zeta^{Uk}\le1,\quad0\le\vartheta^{Lk}\le\vartheta^{Uk}\le1,\quad\zeta^{Uk}+\vartheta^{Uk}\le1,\quad\zeta^{k},\vartheta^{k}\ge0,\quad\zeta^{k}+\vartheta^{k}\le1.

2. Uzman başına yerel ideal referansları seçin

   $$\begin{gathered} {\alpha }_j^{+(k)}\&=({max}_i{\zeta }_{ij}^{Lk},{max}_i{\zeta }_{ij}^{Uk},{min}_i{\vartheta }_{ij}^{Lk},{min}_i{\vartheta }_{ij}^{Uk},{min}_i{\zeta }_{ij}^k,{max}_i{\vartheta }_{ij}^k), \\ {\alpha }_j^{-(k)}\&=({min}_i{\zeta }_{ij}^{Lk},{min}_i{\zeta }_{ij}^{Uk},{max}_i{\vartheta }_{ij}^{Lk},{max}_i{\vartheta }_{ij}^{Uk},{max}_i{\zeta }_{ij}^k,{min}_i{\vartheta }_{ij}^k), \\ {\alpha }_{j,\mathrm{f}\mathrm{i}\mathrm{x}\mathrm{e}\mathrm{d}}^{+}\&=(1,1,0,0,0,1),{\alpha }_{j,\mathrm{f}\mathrm{i}\mathrm{x}\mathrm{e}\mathrm{d}}^{-}=(0,0,1,1,1,0). \end{gathered}$$
   LaTeX

   \begin{aligned}\alpha_j^{+(k)}&=(\max_i\zeta_{ij}^{Lk},\max_i\zeta_{ij}^{Uk},\min_i\vartheta_{ij}^{Lk},\min_i\vartheta_{ij}^{Uk},\min_i\zeta_{ij}^{k},\max_i\vartheta_{ij}^{k}),\\ \alpha_j^{-(k)}&=(\min_i\zeta_{ij}^{Lk},\min_i\zeta_{ij}^{Uk},\max_i\vartheta_{ij}^{Lk},\max_i\vartheta_{ij}^{Uk},\max_i\zeta_{ij}^{k},\min_i\vartheta_{ij}^{k}),\\ \alpha_{j,\mathrm{fixed}}^+&=(1,1,0,0,0,1),\quad\alpha_{j,\mathrm{fixed}}^-=(0,0,1,1,1,0).\end{aligned}

3. Ağırlıklı yerel mesafeleri hesaplayın

   $$d_i^{\pm (k)}={[\frac{1}{6}{\sum }_{j=1}^n{\omega }_j^{(k)}{\sum }_{c=1}^6|{\alpha }_{ijc}^{(k)}-{\alpha }_{jc}^{\pm (k)}{|}^q]}^{1/q},1\le q<\infty ,{\omega }_j^{(k)}>0,\sum _j{\omega }_j^{(k)}=1.$$
   LaTeX

   d_i^{\pm(k)}=\left[\frac{1}{6}\sum_{j=1}^{n}\omega_j^{(k)}\sum_{c=1}^{6}|\alpha_{ijc}^{(k)}-\alpha_{jc}^{\pm(k)}|^q\right]^{1/q},\quad1\le q<\infty,\quad\omega_j^{(k)}>0,\quad\sum_j\omega_j^{(k)}=1.

4. Uzman başına yakınlığı hesaplayın

   $$C_i^{(k)}=\frac{d_i^{-(k)}}{d_i^{+(k)}+d_i^{-(k)}},d_i^{+(k)}>0.$$
   LaTeX

   C_i^{(k)}=\frac{d_i^{-(k)}}{d_i^{+(k)}+d_i^{-(k)}},\qquad d_i^{+(k)}>0.

5. Uzman mesafelerini öncelik ağırlıklarıyla toplayın

   $$D_i^{+}=\sum _{k=1}^K{\lambda }_k{d}_i^{+(k)},D_i^{-}=\sum _{k=1}^K{\lambda }_k{d}_i^{-(k)},{\lambda }_k>0,\sum _k{\lambda }_k=1.$$
   LaTeX

   D_i^+=\sum_{k=1}^{K}\lambda_kd_i^{+(k)},\qquad D_i^-=\sum_{k=1}^{K}\lambda_kd_i^{-(k)},\quad\lambda_k>0,\quad\sum_k\lambda_k=1.

6. Genel yakınlığı hesapla

   $$C_i=\frac{D_i^{-}}{D_i^{+}+D_i^{-}},D_i^{+}>0,0\le C_i\le 1.$$
   LaTeX

   C_i=\frac{D_i^-}{D_i^++D_i^-},\qquad D_i^+>0,\qquad0\le C_i\le1.

7. Alternatifleri azalan yakınlığa göre sıralayın

   $$A_i\succ A_h⟺C_i>C_h,r_i=1+\#\{h:C_h>C_i\}.$$
   LaTeX

   A_i\succ A_h\iff C_i>C_h,\qquad r_i=1+\#\{h:C_h>C_i\}.

Sezgi

Sonucu okuma: Native interval membership and point nonmembership indicate satisfaction in this source. Point membership has the opposite preference direction to interval membership. Report q, ideal mode, every expert matrix, applied criterion weights and expert priorities. Higher overall closeness is better; no input defuzzification is used.

Varsayımlar

• All six native components are independently supplied and domain-valid.
• Ratings follow the source satisfaction semantics; raw cost directions are unsupported.
• Every expert matrix uses matching axes and positive criterion/priority coefficients.

Ne zaman kullanılmaz

• Only scalar or simpler fuzzy judgments are available; do not synthesize missing CIF components.
• The requested raw cost-criterion profile has no validated source implementation.

Sık yapılan hatalar

• Nokta çiftini aralık orta noktalarından türetmeyiniz veya skaler verilerden CIF hücresi sentezlemeyiniz.
• Her uzman farklı pozitif toplam birim kriter vektörü sağlayabilir; ortak bir vektör yalnızca ortak ağırlıklı özel durumdur.
• Yayımlanmış profil pozitif idealdan pozitif mesafe gerektirir; tanımsız veya hariç bırakılan durumlar hata üretir.
• Seçilen yayımlanmış profil tarafından ham maliyet yönü uygulanmaz; sessizce yeniden etiketlemeyin veya dönüştürmeyin.