PF-COCOSO

PF-CoCoSo - COCOSO yönteminin Pythagorean uzantısı

Pythagorean üstünlük/sıralama - Pisagoryan Bulanık Sayı (PFS: μ, ν; μ²+ν² ≤ 1)

Formül adımları

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

PF scores; shift; min-max.

$s_{i j} = μ_{i j}^{2} - ν_{i j}^{2}; {\tilde{s}}_{i j} = s_{i j} + 1; {\hat{s}}_{i j} = ({\tilde{s}}_{i j} - {\tilde{s}}_{j}^{min}) / ({\tilde{s}}_{j}^{max} - {\tilde{s}}_{j}^{min})$

LaTeX
s_{ij}=\mu_{ij}^2-\nu_{ij}^2;\;\tilde{s}_{ij}=s_{ij}+1;\;\hat{s}_{ij}=(\tilde{s}_{ij}-\tilde{s}_j^{\min})/(\tilde{s}_j^{\max}-\tilde{s}_j^{\min})
P_i and R_i.

$P_{i} = \sum_{j} w_{j} {\hat{s}}_{i j}; R_{i} = \sum_{j} {\hat{s}}_{i j}^{w_{j}}$

LaTeX
P_i=\sum_j w_j\hat{s}_{ij};\;R_i=\sum_j\hat{s}_{ij}^{w_j}
Three compromise scores.

$k_{i a} = (P_{i} + R_{i}) / \sum (P + R); k_{i b} = P_{i} / min P + R_{i} / min R; k_{i c} = (λ P_{i} + (1 - λ) R_{i}) / (λ max P + (1 - λ) max R), λ = 0.5$

LaTeX
k_{ia}=(P_i+R_i)/\sum(P+R);\;k_{ib}=P_i/\min P+R_i/\min R;\;k_{ic}=(\lambda P_i+(1-\lambda)R_i)/(\lambda\max P+(1-\lambda)\max R),\;\lambda=0.5
CoCoSo k_i.

$k_{i} = (k_{i a} k_{i b} k_{i c})^{1 / 3} + \frac{1}{3} (k_{i a} + k_{i b} + k_{i c})$

LaTeX
k_i=(k_{ia}k_{ib}k_{ic})^{1/3}+\tfrac{1}{3}(k_{ia}+k_{ib}+k_{ic})
Rank descending.

$rank descending by k_{i}$

LaTeX
\text{rank descending by }k_i
Final output.

$A_{σ (1)} ≻ \dots ≻ A_{σ (m)}$

LaTeX
A_{\sigma(1)}\succ\cdots\succ A_{\sigma(m)}

Yöntem ayrıntıları kaynak kütüphanedeki özgün (İngilizce) metindir.

Sezgi

Sonucu okuma: pf-cocoso extends COCOSO to handle Pythagorean uncertainty. All arithmetic operations (normalisation, weighting, distance computation) are performed using Pythagorean Fuzzy Number (PFN: μ, ν; μ²+ν² ≤ 1) algebra. The final scores are defuzzified via score function S = μ² − ν² before ranking.

Varsayımlar

Decision matrix entries are valid Pythagorean 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 COCOSO directly (avoid unnecessary uncertainty layer)
Aggregation operator (PFWA/PFOWA/etc.) not specified - output ambiguous

Sık yapılan hatalar

Değer-uzayı ihlali: hesaplamadan önce tüm girişlerin PFN: μ ∈ [0,1], ν ∈ [0,1], μ²+ν² ≤ 1 koşulunu sağladığından emin olun.
Defuzzifikasyon yöntemi sıralamayı etkiler: score function S = μ² − ν² kanonik seçimdir.