P-ARAS

P-ARAS - P-ARAS 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. Augment matrix with optimal row A0.

${\hat{p}}_{i j} = (T + c (1 - T), I (1 - c), F (1 - c)); {\hat{p}}_{0 j} = ({max}_{i} {\hat{T}}_{i j}, {min}_{i} {\hat{I}}_{i j}, {min}_{i} {\hat{F}}_{i j})$

LaTeX
\hat{p}_{ij}=(T+c(1-T),I(1-c),F(1-c));\;\hat{p}_{0j}=(\max_i\hat{T}_{ij},\min_i\hat{I}_{ij},\min_i\hat{F}_{ij})
Score shift [0,2]; column-sum normalisation.

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

LaTeX
s_{ij}=s(\hat{p}_{ij});\;\tilde{s}_{ij}=s_{ij}+1;\;\hat{s}_{ij}=\tilde{s}_{ij}/\sum_{i=0}^m\tilde{s}_{ij}
PNWA weighted PN + row aggregate score.

${\tilde{p}}_{i j} = (1 - (1 - {\hat{T}}_{i j})^{w_{j}}, {\hat{I}}_{i j}^{w_{j}}, {\hat{F}}_{i j}^{w_{j}}); {\tilde{S}}_{i} = ⨁_{j} {\tilde{p}}_{i j}; S_{i} = s ({\tilde{S}}_{i})$

LaTeX
\tilde{p}_{ij}=(1-(1-\hat{T}_{ij})^{w_j},\hat{I}_{ij}^{w_j},\hat{F}_{ij}^{w_j});\;\tilde{S}_i=\bigoplus_j\tilde{p}_{ij};\;S_i=s(\tilde{S}_i)
Degree of utility K_i relative to optimal A0.

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

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: p-aras extends P-ARAS 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 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 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.