P-MARCOS

P-MARCOS - P-MARCOS yönteminin Plithogenic uzantısı

Plithogenic üstünlük/sıralama - Plitojenik Küme (PltK: çelişki dereceleriyle nitelik değerleri)

Formül adımları

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

Contradiction adjustment; cost complement.

${\hat{p}}_{i j} = (T + c (1 - T), I (1 - c), F (1 - c)); cost: complement first$

LaTeX
\hat{p}_{ij}=(T+c(1-T),I(1-c),F(1-c));\;\text{cost: complement first}
Anti-Ideal AAI (min T, max I, max F) and Ideal AI (max T, min I, min F).

${A A I}_{j} = ({min}_{i} {\hat{T}}_{i j}, {max}_{i} {\hat{I}}_{i j}, {max}_{i} {\hat{F}}_{i j}); {A I}_{j} = ({max}_{i} {\hat{T}}_{i j}, {min}_{i} {\hat{I}}_{i j}, {min}_{i} {\hat{F}}_{i j})$

LaTeX
\mathrm{AAI}_j=(\min_i\hat{T}_{ij},\max_i\hat{I}_{ij},\max_i\hat{F}_{ij});\quad\mathrm{AI}_j=(\max_i\hat{T}_{ij},\min_i\hat{I}_{ij},\min_i\hat{F}_{ij})
Normalise using AI; PNWA aggregate per row.

${\hat{n}}_{i j} = ({\hat{T}}_{i j} / T_{A I, j}, {\hat{I}}_{i j} / I_{A I, j}, {\hat{F}}_{i j} / F_{A I, j}) clipped; {\tilde{S}}_{i} = ⨁_{j} (w_{j} \cdot {\hat{n}}_{i j}); S_{i} = s ({\tilde{S}}_{i})$

LaTeX
\hat{n}_{ij}=(\hat{T}_{ij}/T_{\mathrm{AI},j},\hat{I}_{ij}/I_{\mathrm{AI},j},\hat{F}_{ij}/F_{\mathrm{AI},j})\text{ clipped};\;\tilde{S}_i=\bigoplus_j(w_j\cdot\hat{n}_{ij});\;S_i=s(\tilde{S}_i)
Utility degrees K± relative to AI and AAI.

$K_{i}^{-} = S_{i} / S_{A A I}; K_{i}^{+} = S_{i} / S_{A I}$

LaTeX
K_i^-=S_i/S_{\mathrm{AAI}};\quad K_i^+=S_i/S_{\mathrm{AI}}
f(K_i) function value using individual utility functions.

$f (K_{i}^{+}) = K_{i}^{-} / (K_{i}^{-} + K_{i}^{+}); f (K_{i}^{-}) = K_{i}^{+} / (K_{i}^{-} + K_{i}^{+})$

LaTeX
f(K_i^+)=K_i^-/(K_i^-+K_i^+);\quad f(K_i^-)=K_i^+/(K_i^-+K_i^+)
Composite utility function f(K_i).

$f (K_{i}) = \frac{K_{i}^{+} + K_{i}^{-}}{1 + \frac{1 - f (K_{i}^{+})}{f (K_{i}^{+})} + \frac{1 - f (K_{i}^{-})}{f (K_{i}^{-})}}$

LaTeX
f(K_i)=\frac{K_i^++K_i^-}{1+\frac{1-f(K_i^+)}{f(K_i^+)}+\frac{1-f(K_i^-)}{f(K_i^-)}}
Rank descending by f(K_i).

$rank descending by f (K_{i})$

LaTeX
\text{rank descending by }f(K_i)

Yöntem ayrıntıları kaynak kütüphanedeki özgün (İngilizce) metindir.

Sezgi

Sonucu okuma: p-marcos extends P-MARCOS 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 MARCOS 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.