P-VIKOR

P-VIKOR - P-VIKOR 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.

PN matrix; cost complement; contradiction adjustment.

${\hat{p}}_{i j} = (T_{i j} + c_{i j} (1 - T_{i j}), I_{i j} (1 - c_{i j}), F_{i j} (1 - c_{i j})); s (p) = (1 + T - 2 I - F) / 2$

LaTeX
\hat{p}_{ij}=(T_{ij}+c_{ij}(1-T_{ij}),\;I_{ij}(1-c_{ij}),\;F_{ij}(1-c_{ij}));\quad s(p)=(1+T-2I-F)/2
Best and worst PNs per criterion.

$f_{j}^{*} = ({max}_{i} {\hat{T}}_{i j}, {min}_{i} {\hat{I}}_{i j}, {min}_{i} {\hat{F}}_{i j}); f_{j}^{-} = ({min}_{i} {\hat{T}}_{i j}, {max}_{i} {\hat{I}}_{i j}, {max}_{i} {\hat{F}}_{i j})$

LaTeX
f_j^*=(\max_i\hat{T}_{ij},\min_i\hat{I}_{ij},\min_i\hat{F}_{ij});\quad f_j^-=(\min_i\hat{T}_{ij},\max_i\hat{I}_{ij},\max_i\hat{F}_{ij})
Normalised Plithogenic distance gap.

$d (p_{1}, p_{2}) = \sqrt{[(T_{1} - T_{2})^{2} + (I_{1} - I_{2})^{2} + (F_{1} - F_{2})^{2}] / 3}; f_{i j} = d ({\hat{p}}_{i j}, f_{j}^{*}) / d (f_{j}^{-}, f_{j}^{*})$

LaTeX
d(p_1,p_2)=\sqrt{[(T_1-T_2)^2+(I_1-I_2)^2+(F_1-F_2)^2]/3};\quad f_{ij}=d(\hat{p}_{ij},f_j^*)/d(f_j^-,f_j^*)
S_i, R_i, Q_i; rank ascending by Q; check C1+C2.

$S_{i} = \sum_{j} w_{j} f_{i j}; R_{i} = {max}_{j} w_{j} f_{i j}; Q_{i} = v (S_{i} - S^{*}) / (S^{-} - S^{*}) + (1 - v) (R_{i} - R^{*}) / (R^{-} - R^{*}), v = 0.5; 𝒞 = {A^{(1)}} if C1 and C2; {A^{(1)}, A^{(2)}} if only C2 fails; otherwise include ordered A^{(k)} while Q (A^{(k)}) - Q (A^{(1)}) < D Q$

LaTeX
S_i=\sum_j w_j f_{ij};\;R_i=\max_j w_j f_{ij};\;Q_i=v(S_i-S^*)/(S^--S^*)+(1-v)(R_i-R^*)/(R^--R^*),\;v=0.5;\quad \mathcal{C}=\{A^{(1)}\}\text{ if C1 and C2; }\{A^{(1)},A^{(2)}\}\text{ if only C2 fails; otherwise include ordered }A^{(k)}\text{ while }Q(A^{(k)})-Q(A^{(1)})<DQ

Yöntem ayrıntıları kaynak kütüphanedeki özgün (İngilizce) metindir.

Sezgi

Sonucu okuma: p-vikor extends P-VIKOR 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 VIKOR 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.