P-GRA

P-GRA - P-GRA 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; cost complement.

${\hat{p}}_{i j} = (T + c (1 - T), I (1 - c), F (1 - c)); cost: pre-apply complement$

LaTeX
\hat{p}_{ij}=(T+c(1-T),I(1-c),F(1-c));\quad\text{cost: pre-apply complement}
Plithogenic ideal reference sequence.

$p_{j}^{0} = ({max}_{i} {\hat{T}}_{i j}, {min}_{i} {\hat{I}}_{i j}, {min}_{i} {\hat{F}}_{i j})$

LaTeX
p_j^0=(\max_i\hat{T}_{ij},\min_i\hat{I}_{ij},\min_i\hat{F}_{ij})
Distances to reference; global extremes.

$Δ_{i j} = d ({\hat{p}}_{i j}, p_{j}^{0}) = \sqrt{[({\hat{T}}_{i j} - T_{j}^{0})^{2} + ({\hat{I}}_{i j} - I_{j}^{0})^{2} + ({\hat{F}}_{i j} - F_{j}^{0})^{2}] / 3}; Δ_{min} = min min Δ_{i j}; Δ_{max} = max max Δ_{i j}$

LaTeX
\Delta_{ij}=d(\hat{p}_{ij},p_j^0)=\sqrt{[(\hat{T}_{ij}-T_j^0)^2+(\hat{I}_{ij}-I_j^0)^2+(\hat{F}_{ij}-F_j^0)^2]/3};\quad\Delta_{\min}=\min\min\Delta_{ij};\;\Delta_{\max}=\max\max\Delta_{ij}
Grey Relational Coefficient ρ=0.5.

$ξ_{i j} = (Δ_{min} + ρ Δ_{max}) / (Δ_{i j} + ρ Δ_{max}), ρ = 0.5$

LaTeX
\xi_{ij}=(\Delta_{\min}+\rho\Delta_{\max})/(\Delta_{ij}+\rho\Delta_{\max}),\;\rho=0.5
Grey Relational Grade; rank descending.

$Γ_{i} = \sum_{j} w_{j} ξ_{i j}; rank descending$

LaTeX
\Gamma_i=\sum_j w_j\xi_{ij};\quad\text{rank descending}

Yöntem ayrıntıları kaynak kütüphanedeki özgün (İngilizce) metindir.

Sezgi

Sonucu okuma: p-gra extends P-GRA 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 GRA 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.