P-TOPSIS

P-TOPSIS - P-TOPSIS 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.

PN matrix; cost complement (F,I,T); contradiction adjustment.

$cost: p^{c} = (F, I, T); {\hat{p}}_{i j} = (T_{i j} + c_{i j} (1 - T_{i j}), I_{i j} (1 - c_{i j}), F_{i j} (1 - c_{i j}))$

LaTeX
\text{cost: }p^c=(F,I,T);\quad\hat{p}_{ij}=\bigl(T_{ij}+c_{ij}(1-T_{ij}),\;I_{ij}(1-c_{ij}),\;F_{ij}(1-c_{ij})\bigr)
Scalar weight multiplication (PNWA component).

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

LaTeX
\tilde{p}_{ij}=\bigl(1-(1-\hat{T}_{ij})^{w_j},\;\hat{I}_{ij}^{w_j},\;\hat{F}_{ij}^{w_j}\bigr)
Plithogenic PIS and NIS (component-wise extrema of weighted PNs).

${P I S}_{j} = ({max}_{i} {\tilde{T}}_{i j}, {min}_{i} {\tilde{I}}_{i j}, {min}_{i} {\tilde{F}}_{i j}); {N I S}_{j} = ({min}_{i} {\tilde{T}}_{i j}, {max}_{i} {\tilde{I}}_{i j}, {max}_{i} {\tilde{F}}_{i j})$

LaTeX
\mathrm{PIS}_j=(\max_i\tilde{T}_{ij},\min_i\tilde{I}_{ij},\min_i\tilde{F}_{ij});\quad\mathrm{NIS}_j=(\min_i\tilde{T}_{ij},\max_i\tilde{I}_{ij},\max_i\tilde{F}_{ij})
Weighted Euclidean separations from PIS and NIS.

$d_{i}^{\pm} = \sqrt{\sum_{j = 1}^{n} w_{j} \cdot \frac{({\tilde{T}}_{i j} - T_{j}^{\pm})^{2} + ({\tilde{I}}_{i j} - I_{j}^{\pm})^{2} + ({\tilde{F}}_{i j} - F_{j}^{\pm})^{2}}{3}}$

LaTeX
d_i^\pm=\sqrt{\sum_{j=1}^n w_j\cdot\tfrac{(\tilde{T}_{ij}-T_j^\pm)^2+(\tilde{I}_{ij}-I_j^\pm)^2+(\tilde{F}_{ij}-F_j^\pm)^2}{3}}
Closeness coefficient CC_i; rank descending.

$C C_{i} = d_{i}^{-} / (d_{i}^{+} + d_{i}^{-}); rank descending$

LaTeX
CC_i=d_i^-/(d_i^++d_i^-);\quad\text{rank descending}

Yöntem ayrıntıları kaynak kütüphanedeki özgün (İngilizce) metindir.

Sezgi

Sonucu okuma: p-topsis extends P-TOPSIS 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 TOPSIS 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.