P-MAUT - P-MAUT 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. Marginal utility function.

   $$u_{ij}=(s_{ij}-s_j^{min})/(s_j^{max}-s_j^{min})(j\in {\Omega }_b);u_{ij}=(s_j^{max}-s_{ij})/(s_j^{max}-s_j^{min})(j\in {\Omega }_c)$$
   LaTeX

   u_{ij}=(s_{ij}-s_j^{\min})/(s_j^{\max}-s_j^{\min})\;(j\in\Omega_b);\;u_{ij}=(s_j^{\max}-s_{ij})/(s_j^{\max}-s_j^{\min})\;(j\in\Omega_c)

3. Global additive utility.

   $$U_i=\sum _j{w}_j{u}_{ij}$$
   LaTeX

   U_i=\sum_j w_j u_{ij}

4. Rank descending by U_i.

   $$\text{rank descending by }{U}_i$$
   LaTeX

   \text{rank descending by }U_i

Sezgi

Sonucu okuma: p-maut extends P-MAUT 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 MAUT 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.