IF-VIKOR

IF-VIKOR - VIKOR yönteminin Intuitionistic uzantısı

Intuitionistic üstünlük/sıralama - Sezgisel Bulanık Sayı (IFS: μ, ν; μ+ν ≤ 1)

Formül adımları

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

normalization

${\tilde{a}}_{i j}^{c} = (ν_{i j}, μ_{i j}) for cost criteria$

LaTeX
\tilde{a}_{ij}^c=(\nu_{ij},\mu_{ij})\quad\text{for cost criteria}
ranking_computation

$f_{j}^{*} = ({max}_{i} μ_{i j}, {min}_{i} ν_{i j}), f_{j}^{-} = ({min}_{i} μ_{i j}, {max}_{i} ν_{i j})$

LaTeX
f_j^*=\bigl(\max_i\mu_{ij},\min_i\nu_{ij}\bigr),\quad f_j^-=\bigl(\min_i\mu_{ij},\max_i\nu_{ij}\bigr)
ranking_computation

$f_{i j} = \frac{d (f_{j}^{*}, {\tilde{a}}_{i j})}{d (f_{j}^{*}, f_{j}^{-})}, d (α, β) = \sqrt{\frac{1}{2} [(μ_{α} - μ_{β})^{2} + (ν_{α} - ν_{β})^{2}]}$

LaTeX
f_{ij}=\frac{d(f_j^*,\tilde{a}_{ij})}{d(f_j^*,f_j^-)},\quad d(\alpha,\beta)=\sqrt{\tfrac{1}{2}\bigl[(\mu_\alpha-\mu_\beta)^2+(\nu_\alpha-\nu_\beta)^2\bigr]}
ranking_computation

$S_{i} = \sum_{j = 1}^{n} w_{j} f_{i j}, R_{i} = {max}_{j} (w_{j} f_{i j})$

LaTeX
S_i=\sum_{j=1}^n w_j f_{ij},\quad R_i=\max_j(w_j f_{ij})
ranking_computation

$Q_{i} = v \frac{S_{i} - S^{*}}{S^{-} - S^{*}} + (1 - v) \frac{R_{i} - R^{*}}{R^{-} - R^{*}}, v = 0.5, rank ascending; 𝒞 = {A^{(1)}} if C1 and C2; {A^{(1)}, A^{(2)}} if only C2 fails; otherwise include ordered A^{(k)} while Q (A^{(k)}) - Q (A^{(1)}) < D Q$

LaTeX
Q_i=v\frac{S_i-S^*}{S^--S^*}+(1-v)\frac{R_i-R^*}{R^--R^*},\quad v=0.5,\quad\text{rank ascending};\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

Yöntem ayrıntıları kaynak kütüphanedeki özgün (İngilizce) metindir.

Sezgi

Sonucu okuma: if-vikor extends VIKOR to handle Intuitionistic uncertainty. All arithmetic operations (normalisation, weighting, distance computation) are performed using Intuitionistic Fuzzy Number (IFN: μ, ν; μ+ν ≤ 1) algebra. The final scores are defuzzified via score function S = μ − ν before ranking.

Varsayımlar

Decision matrix entries are valid Intuitionistic Fuzzy 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

Sık yapılan hatalar

Değer-uzayı ihlali: hesaplamadan önce tüm girişlerin IFN: μ ∈ [0,1], ν ∈ [0,1], μ+ν ≤ 1; π = 1−μ−ν ≥ 0 koşulunu sağladığından emin olun.
Defuzzifikasyon yöntemi sıralamayı etkiler: score function S = μ − ν kanonik seçimdir.