P-AROMAN - P-AROMAN yönteminin Plithogenic uzantısı

Formül adımları

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

1. Contradiction adjustment; score extraction.

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

   s_{ij}=s(\hat{p}_{ij})=(1+\hat{T}-2\hat{I}-\hat{F})/2

2. Step-1 linear + Step-2 vector normalisation; combined value.

   $$r_{ij}=s_{ij}/s_j^{max}(j\in {\Omega }_b);z_{ij}=r_{ij}/\sqrt{{\sum }_i{r}_{ij}^2};t_{ij}=(r_{ij}+z_{ij})/2$$
   LaTeX

   r_{ij}=s_{ij}/s_j^{\max}\;(j\in\Omega_b);\;z_{ij}=r_{ij}/\sqrt{\sum_i r_{ij}^2};\;t_{ij}=(r_{ij}+z_{ij})/2

3. AROMAN score.

   $$AROMA{N}_i=\sum _j{w}_j{t}_{ij}$$
   LaTeX

   AROMAN_i=\sum_j w_j t_{ij}

4. Rank descending by AROMAN_i.

   $$\text{rank descending}$$
   LaTeX

   \text{rank descending}

5. Final ranking output.

   $$A_{\sigma (1)}\succ A_{\sigma (2)}\succ \cdots \succ A_{\sigma (m)}$$
   LaTeX

   A_{\sigma(1)}\succ A_{\sigma(2)}\succ\cdots\succ A_{\sigma(m)}

Sezgi

Plithogenic outranking/ranking - Plithogenic Set (PltS: attribute values with contradiction degrees). Output typically utility (higher value = preferred).

Sonucu okuma: p-aroman extends P-AROMAN 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 AROMAN directly (avoid unnecessary uncertainty layer)
• Aggregation operator (PFWA/PFOWA/etc.) not specified - output ambiguous

Sınırlılıklar

• Assumes: Decision matrix entries are valid Plithogenic numbers/tuples
• Assumes: Underlying crisp method's compensation assumption holds in uncertain space
• Assumes: All decision-maker(s) and experts use the same linguistic/uncertainty scale

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.