P-EDAS - P-EDAS yönteminin Plithogenic uzantısı

Formül adımları

Analiz motorunun yöntem bildirimindeki (manifest F.steps) adımlar; raporlardaki formüllerle aynı kaynaktır.

1. PN matrix; cost complement; contradiction adjustment; score.

   $${\widehat{p}}_{ij}=(T+c(1-T),I(1-c),F(1-c));s_{ij}=(1+{\widehat{T}}_{ij}-2{\widehat{I}}_{ij}-{\widehat{F}}_{ij})/2$$
   LaTeX

   \hat{p}_{ij}=(T+c(1-T),I(1-c),F(1-c));\quad s_{ij}=(1+\hat{T}_{ij}-2\hat{I}_{ij}-\hat{F}_{ij})/2

2. Average score per criterion.

   $${\overline{s}}_j=\frac{1}{m}\sum _i{s}_{ij}$$
   LaTeX

   \bar{s}_j=\tfrac{1}{m}\sum_i s_{ij}

3. PDA and NDA from average (benefit/cost reversed for cost).

   $${\mathrm{P}\mathrm{D}\mathrm{A}}_{ij}=max(0,s_{ij}-{\overline{s}}_j)/|{\overline{s}}_j|(j\in {\Omega }_b);{\mathrm{N}\mathrm{D}\mathrm{A}}_{ij}=max(0,{\overline{s}}_j-s_{ij})/|{\overline{s}}_j|$$
   LaTeX

   \mathrm{PDA}_{ij}=\max(0,s_{ij}-\bar{s}_j)/|\bar{s}_j|\;(j\in\Omega_b);\quad\mathrm{NDA}_{ij}=\max(0,\bar{s}_j-s_{ij})/|\bar{s}_j|

4. Weighted sums SP_i and SN_i.

   $$S{P}_i=\sum _j{w}_j{\mathrm{P}\mathrm{D}\mathrm{A}}_{ij};S{N}_i=\sum _j{w}_j{\mathrm{N}\mathrm{D}\mathrm{A}}_{ij}$$
   LaTeX

   SP_i=\sum_j w_j\mathrm{PDA}_{ij};\quad SN_i=\sum_j w_j\mathrm{NDA}_{ij}

5. Normalise SP and SN.

   $$NS{P}_i=S{P}_i/{max}_{k}S{P}_k;NS{N}_i=1-S{N}_i/{max}_{k}S{N}_k$$
   LaTeX

   NSP_i=SP_i/\max_k SP_k;\quad NSN_i=1-SN_i/\max_k SN_k

6. Appraisal score; rank descending.

   $$A{S}_i=(NS{P}_i+NS{N}_i)/2;\text{rank descending}$$
   LaTeX

   AS_i=(NSP_i+NSN_i)/2;\quad\text{rank descending}

Sezgi

Sonucu okuma: p-edas extends P-EDAS 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 EDAS 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.