P-COPRAS

P-COPRAS - P-COPRAS yönteminin Plithogenic uzantısı

Plithogenic üstünlük/sıralama - Plitojenik Küme (PltK: çelişki dereceleriyle nitelik değerleri)

Formül adımları

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

Contradiction adjustment; score shift to [0,2]; column-sum normalisation.

${\hat{p}}_{i j} = (T + c (1 - T), I (1 - c), F (1 - c)); s_{i j} = (1 + \hat{T} - 2 \hat{I} - \hat{F}) / 2; {\tilde{s}}_{i j} = s_{i j} + 1; {\hat{s}}_{i j} = {\tilde{s}}_{i j} / \sum_{i} {\tilde{s}}_{i j}; v_{i j} = w_{j} {\hat{s}}_{i j}$

LaTeX
\hat{p}_{ij}=(T+c(1-T),I(1-c),F(1-c));\;s_{ij}=(1+\hat{T}-2\hat{I}-\hat{F})/2;\;\tilde{s}_{ij}=s_{ij}+1;\;\hat{s}_{ij}=\tilde{s}_{ij}/\sum_i\tilde{s}_{ij};\;v_{ij}=w_j\hat{s}_{ij}
Benefit S⁺ and cost S⁻ sums.

$S_{i}^{+} = \sum_{j \in Ω_{b}} v_{i j}; S_{i}^{-} = \sum_{j \in Ω_{c}} v_{i j}$

LaTeX
S_i^+=\sum_{j\in\Omega_b}v_{ij};\quad S_i^-=\sum_{j\in\Omega_c}v_{ij}
Relative significance Q_i.

$Q_{i} = S_{i}^{+} + \frac{\sum_{k} S_{k}^{-}}{S_{i}^{-} \cdot \sum_{k} (1 / S_{k}^{-})}$

LaTeX
Q_i=S_i^++\frac{\sum_k S_k^-}{S_i^-\cdot\sum_k(1/S_k^-)}
Utility degree N_i; rank descending.

$N_{i} = Q_{i} / Q_{max} \times 100 %; rank descending$

LaTeX
N_i=Q_i/Q_{\max}\times 100\%;\quad\text{rank descending}
Final alternative ranking.

$Rank alternatives by descending Q_{i}$

LaTeX
\text{Rank alternatives by descending }Q_i

Yöntem ayrıntıları kaynak kütüphanedeki özgün (İngilizce) metindir.

Sezgi

Sonucu okuma: p-copras extends P-COPRAS to handle Plithogenic uncertainty. All arithmetic operations (normalisation, weighting, distance computation) are performed using Plithogenic Set (PltS: attribute values with contradiction degrees) algebra. The final scores are defuzzified via dominant value defuzzification; approach varies by appurtenance function before ranking.

Varsayımlar

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

Sık yapılan hatalar

Değer-uzayı ihlali: hesaplamadan önce tüm girişlerin Plithogenic: each attribute has a set of values V with appurtenance degrees and contradiction degrees c(v,D) koşulunu sağladığından emin olun.
Defuzzifikasyon yöntemi sıralamayı etkiler: dominant value defuzzification; approach varies by appurtenance function kanonik seçimdir.