P-CODAS

P-CODAS - P-CODAS 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.

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

LaTeX
\hat{p}_{ij}=(T+c(1-T),I(1-c),F(1-c))
PNWA weighting and Plithogenic NIS.

${\tilde{v}}_{i j} = (1 - (1 - {\hat{T}}_{i j})^{w_{j}}, {\hat{I}}_{i j}^{w_{j}}, {\hat{F}}_{i j}^{w_{j}}); p_{j}^{-} = ({min}_{i} {\tilde{T}}_{i j}, {max}_{i} {\tilde{I}}_{i j}, {max}_{i} {\tilde{F}}_{i j})$

LaTeX
\tilde{v}_{ij}=(1-(1-\hat{T}_{ij})^{w_j},\hat{I}_{ij}^{w_j},\hat{F}_{ij}^{w_j});\quad p_j^-=(\min_i\tilde{T}_{ij},\max_i\tilde{I}_{ij},\max_i\tilde{F}_{ij})
Euclidean E_i and Taxicab T_i separations.

$d_{E} (p_{1}, p_{2}) = \sqrt{[(T_{1} - T_{2})^{2} + (I_{1} - I_{2})^{2} + (F_{1} - F_{2})^{2}] / 3}; d_{H} = [(| T_{1} - T_{2} | + | I_{1} - I_{2} | + | F_{1} - F_{2} |)] / 3; E_{i} = \sqrt{\sum_{j} w_{j} [d_{E} ({\tilde{v}}_{i j}, p_{j}^{-})]^{2}}; T_{i} = \sum_{j} w_{j} d_{H} ({\tilde{v}}_{i j}, p_{j}^{-})$

LaTeX
d_E(p_1,p_2)=\sqrt{[(T_1-T_2)^2+(I_1-I_2)^2+(F_1-F_2)^2]/3};\;d_H=[(|T_1-T_2|+|I_1-I_2|+|F_1-F_2|)]/3;\;E_i=\sqrt{\sum_j w_j[d_E(\tilde{v}_{ij},p_j^-)]^2};\;T_i=\sum_j w_j d_H(\tilde{v}_{ij},p_j^-)
Relative assessment matrix h_ik; threshold τ=0.02.

$h_{i k} = (E_{i} - E_{k}) + ψ (E_{i} - E_{k}) (T_{i} - T_{k}); ψ (x) = 1 if | x | \geq 0.02 else 0$

LaTeX
h_{ik}=(E_i-E_k)+\psi(E_i-E_k)(T_i-T_k);\;\psi(x)=1\;\text{if }|x|\geq 0.02\text{ else }0
Appraisal score.

$A S_{i} = \sum_{k = 1}^{m} h_{i k}$

LaTeX
AS_i=\sum_{k=1}^m h_{ik}
Rank descending by AS_i.

$rank descending by A S_{i}$

LaTeX
\text{rank descending by }AS_i

Yöntem ayrıntıları kaynak kütüphanedeki özgün (İngilizce) metindir.

Sezgi

Sonucu okuma: p-codas extends P-CODAS 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 CODAS 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.