FF-CODAS

FF-CODAS - FF-CODAS 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.

Cost complement; scalar weighting.

$j \in Ω_{c} : {\hat{a}}_{i j} = (ν_{i j}, μ_{i j}); {\tilde{v}}_{i j} = w_{j} \cdot {\tilde{a}}_{i j} = ((1 - (1 - μ_{i j}^{3})^{w_{j}})^{1 / 3}, ν_{i j}^{w_{j}})$

LaTeX
j\in\Omega_c:\;\hat{a}_{ij}=(\nu_{ij},\mu_{ij});\;\tilde{v}_{ij}=w_j\cdot\tilde{a}_{ij}=\bigl((1-(1-\mu_{ij}^3)^{w_j})^{1/3},\;\nu_{ij}^{w_j}\bigr)
FF NIS.

$α_{j}^{-} = ({min}_{i} {\tilde{μ}}_{i j}^{v}, {max}_{i} {\tilde{ν}}_{i j}^{v})$

LaTeX
\alpha_j^-=(\min_i\tilde{\mu}_{ij}^v,\max_i\tilde{\nu}_{ij}^v)
Euclidean E_i and Hamming T_i separations.

$d_{E} (α_{1}, α_{2}) = \sqrt{[(μ_{1}^{3} - μ_{2}^{3})^{2} + (ν_{1}^{3} - ν_{2}^{3})^{2} + (π_{1}^{3} - π_{2}^{3})^{2}] / 2}; d_{H} = [(| μ_{1}^{3} - μ_{2}^{3} | + | ν_{1}^{3} - ν_{2}^{3} | + | π_{1}^{3} - π_{2}^{3} |)] / 2; E_{i} = \sqrt{\sum_{j} w_{j} [d_{E} ({\tilde{v}}_{i j}, α_{j}^{-})]^{2}}; T_{i} = \sum_{j} w_{j} d_{H} ({\tilde{v}}_{i j}, α_{j}^{-})$

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;\;E_i=\sqrt{\sum_j w_j[d_E(\tilde{v}_{ij},\alpha_j^-)]^2};\;T_i=\sum_j w_j d_H(\tilde{v}_{ij},\alpha_j^-)
Relative assessment matrix.

$h_{i k} = (E_{i} - E_{k}) + ψ (E_{i} - E_{k}) (T_{i} - T_{k}); ψ (x) = 1 if | x | \geq 0.02$

LaTeX
h_{ik}=(E_i-E_k)+\psi(E_i-E_k)(T_i-T_k);\;\psi(x)=1\;\text{if }|x|\geq 0.02
Appraisal score AS_i.

$A S_{i} = \sum_{k} h_{i k}$

LaTeX
AS_i=\sum_k h_{ik}
Rank descending by AS_i.

$rank descending$

LaTeX
\text{rank descending}

Yöntem ayrıntıları kaynak kütüphanedeki özgün (İngilizce) metindir.

Sezgi

Sonucu okuma: ff-codas extends FF-CODAS 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 CODAS 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.