PL-MULTIMOORA - MULTIMOORA yönteminin Probabilistic Linguistic uzantısı

Formül adımları

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

1. Adım 1 — PLEF ile PLTS karar matrisini normalleştir.

   $$\mathrm{P}\mathrm{L}\mathrm{E}\mathrm{F}(L(p))=\frac{{\sum }_{k}r(L^{(k)})·p^{(k)}}{{\sum }_k{p}^{(k)}};{\overline{x}}_{ij}=\frac{x_{ij}}{\sqrt{{\sum }_i[\mathrm{P}\mathrm{L}\mathrm{E}\mathrm{F}(x_{ij}){]}^2}}$$
   LaTeX

   \mathrm{PLEF}(L(p)) = \frac{\sum_{k} r(L^{(k)}) \cdot p^{(k)}}{\sum_{k} p^{(k)}};\quad \bar{x}_{ij} = \frac{x_{ij}}{\sqrt{\sum_{i} [\mathrm{PLEF}(x_{ij})]^2}}

2. Adım 2 — Oran Sistemi (RS): ağırlıklı PLEF farkı y_i; azalan sıralama.

   $$y_i=\sum _{j\in J^{+}}{w}_j·\mathrm{P}\mathrm{L}\mathrm{E}\mathrm{F}({\overline{x}}_{ij})-\sum _{j\in J^{-}}{w}_j·\mathrm{P}\mathrm{L}\mathrm{E}\mathrm{F}({\overline{x}}_{ij})$$
   LaTeX

   y_i = \sum_{j \in J^+} w_j \cdot \mathrm{PLEF}(\bar{x}_{ij}) - \sum_{j \in J^-} w_j \cdot \mathrm{PLEF}(\bar{x}_{ij})

3. Adım 3 — Referans Nokta (RP): r_j referans noktası, z_i = max_j d(x_ij,r_j); artan sıralama.

   $$r_j=\{\begin{array}{cc}{max}_i\mathrm{P}\mathrm{L}\mathrm{E}\mathrm{F}({\overline{x}}_{ij})\hfill & j\in J^{+}\hfill \\ {min}_i\mathrm{P}\mathrm{L}\mathrm{E}\mathrm{F}({\overline{x}}_{ij})\hfill & j\in J^{-}\hfill \end{array};z_i={max}_{j}d({\overline{x}}_{ij},r_j)$$
   LaTeX

   r_j = \begin{cases} \max_i \mathrm{PLEF}(\bar{x}_{ij}) & j \in J^+ \\ \min_i \mathrm{PLEF}(\bar{x}_{ij}) & j \in J^- \end{cases};\quad z_i = \max_j\, d(\bar{x}_{ij}, r_j)

4. Adım 4 — Tam Çarpımsal Form (FMF): u_i faydalı/faydasız PLEF çarpımları oranı; azalan sıralama.

   $$u_i=\frac{{\prod }_{j\in J^{+}}\mathrm{P}\mathrm{L}\mathrm{E}\mathrm{F}({\overline{x}}_{ij})}{{\prod }_{j\in J^{-}}\mathrm{P}\mathrm{L}\mathrm{E}\mathrm{F}({\overline{x}}_{ij})}$$
   LaTeX

   u_i = \frac{\prod_{j \in J^+} \mathrm{PLEF}(\bar{x}_{ij})}{\prod_{j \in J^-} \mathrm{PLEF}(\bar{x}_{ij})}

5. Adım 5 — Geliştirilmiş Borda Kuralı: B_i = Σ (m − sıra); azalan B_i nihai sıralama.

   $$B_i=\sum _{\text{sub}\in \{\text{RS},\text{RP},\text{FMF}\}}(m-{\text{rank}}_{\text{sub}}(i));\text{final rank}={\text{argsort}}_{\text{desc}}(B_i)$$
   LaTeX

   B_i = \sum_{\text{sub} \in \{\text{RS},\text{RP},\text{FMF}\}} (m - \text{rank}_{\text{sub}}(i));\quad \text{final rank} = \text{argsort}_{\text{desc}}(B_i)

Sezgi

Sonucu okuma: PL-MULTIMOORA extends MULTIMOORA to PLTS context. It runs three sub-approaches (Ratio System, Reference Point, Full Multiplicative Form) all operating on PLEF-normalised PLTS values. The improved Borda rule aggregates the three sub-rankings into a final consensus ranking.

Varsayımlar

• All PLTS entries satisfy Σ p_k ≤ 1
• FMF requires all PLEF(x̄_ij) > 0 - zero PLEF violates multiplicative form
• Linguistic term set S is the same across all experts/criteria

Ne zaman kullanılmaz

• Classical data sufficient - use base MULTIMOORA directly
• Single sub-approach preferred (use PL-TOPSIS or PL-VIKOR instead)

Sık yapılan hatalar

• FMF, tüm girişlerde PLEF(x̄_ij) > 0 gerektirir; sıfır PLEF değerleri bölme hatası verir.