PF-MOORA

PF-MOORA - MOORA 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; vector normalisation.

$s_{i j} = μ_{i j}^{2} - ν_{i j}^{2}; {\tilde{s}}_{i j} = s_{i j} + 1; {\bar{s}}_{i j} = {\tilde{s}}_{i j} / \sqrt{\sum_{i} {\tilde{s}}_{i j}^{2}}$

LaTeX
s_{ij}=\mu_{ij}^2-\nu_{ij}^2;\;\tilde{s}_{ij}=s_{ij}+1;\;\bar{s}_{ij}=\tilde{s}_{ij}/\sqrt{\sum_i\tilde{s}_{ij}^2}
Ratio system.

$y_{i}^{*} = \sum_{j \in Ω_{b}} w_{j} {\bar{s}}_{i j} - \sum_{j \in Ω_{c}} w_{j} {\bar{s}}_{i j}; rank descending$

LaTeX
y_i^*=\sum_{j\in\Omega_b}w_j\bar{s}_{ij}-\sum_{j\in\Omega_c}w_j\bar{s}_{ij};\quad\text{rank descending}
Reference point (optional).

$r_{j}^{*} = {max}_{i} {\bar{s}}_{i j} (j \in Ω_{b}); y_{i}^{* *} = {max}_{j} w_{j} | r_{j}^{*} - {\bar{s}}_{i j} |; rank ascending$

LaTeX
r_j^*=\max_i\bar{s}_{ij}\;(j\in\Omega_b);\;y_i^{**}=\max_j w_j|r_j^*-\bar{s}_{ij}|;\;\text{rank ascending}
Final ranking from RS.

$rank by y_{i}^{*} (descending)$

LaTeX
\text{rank by }y_i^*\text{ (descending)}
Final ranking 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-moora extends MOORA 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 MOORA 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.