P-MOORA - P-MOORA yönteminin Plithogenic uzantısı

Formül adımları

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

1. Contradiction adjustment; score extraction + shift; vector normalisation.

   $$s_{ij}=s({\widehat{p}}_{ij});{\tilde{s}}_{ij}=s_{ij}+1;{\overline{s}}_{ij}={\tilde{s}}_{ij}/\sqrt{{\sum }_i{\tilde{s}}_{ij}^2}$$
   LaTeX

   s_{ij}=s(\hat{p}_{ij});\;\tilde{s}_{ij}=s_{ij}+1;\;\bar{s}_{ij}=\tilde{s}_{ij}/\sqrt{\sum_i\tilde{s}_{ij}^2}

2. Ratio system score.

   $$y_i^{*}=\sum _{j\in {\Omega }_b}{w}_j{\overline{s}}_{ij}-\sum _{j\in {\Omega }_c}{w}_j{\overline{s}}_{ij};\text{rank descending}$$
   LaTeX

   y_i^*=\sum_{j\in\Omega_b}w_j\bar{s}_{ij}-\sum_{j\in\Omega_c}w_j\bar{s}_{ij};\quad\text{rank descending}

3. Reference point approach (optional).

   $$r_j^{*}={max}_i{\overline{s}}_{ij}(j\in {\Omega }_b);y_i^{**}={max}_j{w}_j|r_j^{*}-{\overline{s}}_{ij}|;\text{rank ascending}$$
   LaTeX

   r_j^*=\max_i\bar{s}_{ij}\;(j\in\Omega_b);\;y_i^{**}=\max_j w_j|r_j^*-\bar{s}_{ij}|;\;\text{rank ascending}

4. Final ranking from RS; RP for cross-check.

   $$\text{Final rank by }{y}_i^{*}\text{ (RS, descending)}$$
   LaTeX

   \text{Final rank by }y_i^*\text{ (RS, descending)}

Sezgi

Sonucu okuma: p-moora extends P-MOORA 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 MOORA 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.