FF-VIKOR

FF-VIKOR - FF-VIKOR yönteminin Fermatean uzantısı

Fermatean üstünlük/sıralama - Fermat Bulanık Küme (FBK: μ, ν; μ³+ν³ ≤ 1)

Formül adımları

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

FF matrix; cost complement.

$s (α) = μ^{3} - ν^{3}; π = (1 - μ^{3} - ν^{3})^{1 / 3}; cost complement: (ν, μ)$

LaTeX
s(\alpha)=\mu^3-\nu^3;\;\pi=(1-\mu^3-\nu^3)^{1/3};\;\text{cost complement: }(\nu,\mu)
Best and worst FF values per criterion.

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

LaTeX
f_j^*=(\max_i\mu_{ij},\min_i\nu_{ij});\quad f_j^-=(\min_i\mu_{ij},\max_i\nu_{ij})
Normalised FF gap ratio using Euclidean distance.

$d_{E} (α_{1}, α_{2}) = \sqrt{[(μ_{1}^{3} - μ_{2}^{3})^{2} + (ν_{1}^{3} - ν_{2}^{3})^{2} + (π_{1}^{3} - π_{2}^{3})^{2}] / 2}; d_{H} = [(| μ_{1}^{3} - μ_{2}^{3} | + | ν_{1}^{3} - ν_{2}^{3} | + | π_{1}^{3} - π_{2}^{3} |)] / 2; f_{i j} = d_{E} ({\tilde{a}}_{i j}, f_{j}^{*}) / d_{E} (f_{j}^{-}, f_{j}^{*})$

LaTeX
d_E(\alpha_1,\alpha_2)=\sqrt{[(\mu_1^3-\mu_2^3)^2+(\nu_1^3-\nu_2^3)^2+(\pi_1^3-\pi_2^3)^2]/2};\;d_H=[(|\mu_1^3-\mu_2^3|+|\nu_1^3-\nu_2^3|+|\pi_1^3-\pi_2^3|)]/2;\quad f_{ij}=d_E(\tilde{a}_{ij},f_j^*)/d_E(f_j^-,f_j^*)
S_i, R_i, Q_i; rank ascending.

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

LaTeX
S_i=\sum_j w_j f_{ij};\;R_i=\max_j w_j f_{ij};\;Q_i=v(S_i-S^*)/(S^--S^*)+(1-v)(R_i-R^*)/(R^--R^*),\;v=0.5;\;\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: ff-vikor extends FF-VIKOR to handle Fermatean uncertainty. All arithmetic operations (normalisation, weighting, distance computation) are performed using Fermatean Fuzzy Set (FFS: μ, ν; μ³+ν³ ≤ 1) algebra. The final scores are defuzzified via score function S = μ³ − ν³ before ranking.

Varsayımlar

Decision matrix entries are valid Fermatean 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 FFS: μ³+ν³ ≤ 1 (q=3 special case of q-ROF) koşulunu sağladığından emin olun.
Defuzzifikasyon yöntemi sıralamayı etkiler: score function S = μ³ − ν³ kanonik seçimdir.