P-PROMETHEE - P-PROMETHEE yönteminin Plithogenic uzantısı

Formül adımları

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

1. Contradiction adjustment; cost complement.

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

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

2. Signed Plithogenic differences.

   $$d_j(i,k)=\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}(s({\widehat{p}}_{ij})-s({\widehat{p}}_{kj}))·d({\widehat{p}}_{ij},{\widehat{p}}_{kj});d(p_1,p_2)=\sqrt{[(T_1-T_2{)}^2+(I_1-I_2{)}^2+(F_1-F_2{)}^2]/3}$$
   LaTeX

   d_j(i,k)=\mathrm{sign}(s(\hat{p}_{ij})-s(\hat{p}_{kj}))\cdot d(\hat{p}_{ij},\hat{p}_{kj});\;d(p_1,p_2)=\sqrt{[(T_1-T_2)^2+(I_1-I_2)^2+(F_1-F_2)^2]/3}

3. Type V linear preference function; aggregated preference index.

   $$P_j(i,k)=0(d_j\le 0);d_j/p_j(0<d_j\le p_j);1(d_j>p_j);\pi (A_i,A_k)=\sum _j{w}_j{P}_j(i,k)$$
   LaTeX

   P_j(i,k)=0\;(d_j\leq 0);\;d_j/p_j\;(0<d_j\leq p_j);\;1\;(d_j>p_j);\;\pi(A_i,A_k)=\sum_j w_j P_j(i,k)

4. Positive and negative outranking flows.

   $${\varphi }^{+}(A_i)=\frac{1}{m-1}\sum _{k\ne i}\pi (A_i,A_k);{\varphi }^{-}(A_i)=\frac{1}{m-1}\sum _{k\ne i}\pi (A_k,A_i)$$
   LaTeX

   \phi^+(A_i)=\tfrac{1}{m-1}\sum_{k\neq i}\pi(A_i,A_k);\;\phi^-(A_i)=\tfrac{1}{m-1}\sum_{k\neq i}\pi(A_k,A_i)

5. Net flow PROMETHEE II; rank descending.

   $$\varphi (A_i)={\varphi }^{+}(A_i)-{\varphi }^{-}(A_i);\text{rank descending (PROMETHEE II)}$$
   LaTeX

   \phi(A_i)=\phi^+(A_i)-\phi^-(A_i);\quad\text{rank descending (PROMETHEE II)}

Sezgi

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

Sonucu okuma: p-promethee extends P-PROMETHEE 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

• Thresholds (q, p, v) can be expressed in Plithogenic scale
• Veto + concordance semantics adapted to fuzzy arithmetic

Ne zaman kullanılmaz

• Small dataset (m<3) - outranking machinery underutilised

Sınırlılıklar

• Rank reversal known on alternative-set changes (ref: inherited from crisp base; cf. Belton-Gear 1983, Wang-Luo 2009)
• Assumes: Thresholds (q, p, v) can be expressed in Plithogenic scale
• Assumes: Veto + concordance semantics adapted to fuzzy arithmetic

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.