P-TODIM

P-TODIM - P-TODIM 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.

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

LaTeX
\hat{p}_{ij}=(T+c(1-T),I(1-c),F(1-c));\;\text{cost complement first}
Relative criterion weights; reference criterion w_r = max w_j.

${\bar{w}}_{j r} = w_{j} / w_{r}, w_{r} = {max}_{j} w_{j}$

LaTeX
\bar{w}_{jr}=w_j/w_r,\;w_r=\max_j w_j
Dominance contribution: gain (√) and loss (−1/θ·√); Plithogenic distance.

$d_{j} (i, k) = d ({\hat{p}}_{i j}, {\hat{p}}_{k j}) = \sqrt{[({\hat{T}}_{i j} - {\hat{T}}_{k j})^{2} + ({\hat{I}}_{i j} - {\hat{I}}_{k j})^{2} + ({\hat{F}}_{i j} - {\hat{F}}_{k j})^{2}] / 3}; ϕ_{j} (A_{i}, A_{k}) = {\begin{matrix} + \sqrt{{\bar{w}}_{j r} d_{j} / \sum_{j} {\bar{w}}_{j r}} & s_{i j} > s_{k j} \\ 0 & s_{i j} = s_{k j} \\ - \frac{1}{θ} \sqrt{(\sum {\bar{w}}_{j r}) d_{j} / {\bar{w}}_{j r}} & s_{i j} < s_{k j} \end{matrix}$

LaTeX
d_j(i,k)=d(\hat{p}_{ij},\hat{p}_{kj})=\sqrt{[(\hat{T}_{ij}-\hat{T}_{kj})^2+(\hat{I}_{ij}-\hat{I}_{kj})^2+(\hat{F}_{ij}-\hat{F}_{kj})^2]/3};\;\phi_j(A_i,A_k)=\begin{cases}+\sqrt{\bar{w}_{jr}d_j/\sum_j\bar{w}_{jr}}&s_{ij}>s_{kj}\\0&s_{ij}=s_{kj}\\-\tfrac{1}{\theta}\sqrt{(\sum\bar{w}_{jr})d_j/\bar{w}_{jr}}&s_{ij}<s_{kj}\end{cases}
Overall dominance δ(A_i,A_k).

$δ (A_{i}, A_{k}) = \sum_{j} ϕ_{j} (A_{i}, A_{k})$

LaTeX
\delta(A_i,A_k)=\sum_j\phi_j(A_i,A_k)
Global normalised value ξ_i; rank descending.

$ξ_{i} = (\sum_{k} δ (A_{i}, A_{k}) - min) / (max - min); rank descending$

LaTeX
\xi_i=(\sum_k\delta(A_i,A_k)-\min)/(\max-\min);\quad\text{rank descending}

Yöntem ayrıntıları kaynak kütüphanedeki özgün (İngilizce) metindir.

Sezgi

Sonucu okuma: p-todim extends P-TODIM 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 TODIM 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.