PF-ARAS

PF-ARAS - ARAS 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.

Cost complement; optimal A0.

$j \in Ω_{c} : {\hat{α}}_{i j} = (ν_{i j}, μ_{i j}); {\hat{α}}_{0 j} = ({max}_{i} {\hat{μ}}_{i j}, {min}_{i} {\hat{ν}}_{i j})$

LaTeX
j\in\Omega_c:\;\hat{\alpha}_{ij}=(\nu_{ij},\mu_{ij});\;\hat{\alpha}_{0j}=(\max_i\hat{\mu}_{ij},\min_i\hat{\nu}_{ij})
Column-sum normalisation on scores.

$s_{i j} = s ({\hat{α}}_{i j}); {\tilde{s}}_{i j} = s_{i j} + 1; {\hat{s}}_{i j} = {\tilde{s}}_{i j} / \sum_{i = 0}^{m} {\tilde{s}}_{i j}$

LaTeX
s_{ij}=s(\hat{\alpha}_{ij});\;\tilde{s}_{ij}=s_{ij}+1;\;\hat{s}_{ij}=\tilde{s}_{ij}/\sum_{i=0}^m\tilde{s}_{ij}
PFWA aggregate score.

${\tilde{S}}_{i} = {P F W A}_{w} ({\hat{α}}_{i 1}^{n}, \dots, {\hat{α}}_{i n}^{n}); S_{i} = s ({\tilde{S}}_{i})$

LaTeX
\tilde{S}_i=\mathrm{PFWA}_w(\hat{\alpha}_{i1}^n,\ldots,\hat{\alpha}_{in}^n);\;S_i=s(\tilde{S}_i)
Degree of utility K_i.

$K_{i} = S_{i} / S_{0}$

LaTeX
K_i=S_i/S_0
Rank descending by K_i.

$rank descending by K_{i}$

LaTeX
\text{rank descending by }K_i

Yöntem ayrıntıları kaynak kütüphanedeki özgün (İngilizce) metindir.

Sezgi

Sonucu okuma: pf-aras extends ARAS 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 ARAS 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.