P-MULTIMOORA

P-MULTIMOORA - MULTIMOORA 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; scores; vector normalisation.

$s_{i j} = s ({\hat{p}}_{i j}); {\tilde{s}}_{i j} = s_{i j} + 1; {\bar{s}}_{i j} = {\tilde{s}}_{i j} / \sqrt{\sum_{i} {\tilde{s}}_{i j}^{2}}$

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}
Sub-method 1: Ratio System score.

$y_{i}^{R S} = \sum_{j} w_{j} {\bar{s}}_{i j}; rank descending$

LaTeX
y_i^{\mathrm{RS}}=\sum_j w_j\bar{s}_{ij};\quad\text{rank descending}
Sub-method 2: Reference Point score.

$r_{j}^{*} = {max}_{i} {\bar{s}}_{i j}; y_{i}^{R P} = {max}_{j} w_{j} | r_{j}^{*} - {\bar{s}}_{i j} |; rank ascending$

LaTeX
r_j^*=\max_i\bar{s}_{ij};\;y_i^{\mathrm{RP}}=\max_j w_j|r_j^*-\bar{s}_{ij}|;\;\text{rank ascending}
Sub-method 3: Full Multiplicative Form via PNWG.

${\tilde{U}}_{i} = ⨂_{j} {\hat{p}}_{i j}^{w_{j}} = (\prod_{j} {\hat{T}}_{i j}^{w_{j}}, 1 - \prod_{j} (1 - {\hat{I}}_{i j})^{w_{j}}, 1 - \prod_{j} (1 - {\hat{F}}_{i j})^{w_{j}}); y_{i}^{F M F} = s ({\tilde{U}}_{i}); rank descending$

LaTeX
\tilde{U}_i=\bigotimes_j\hat{p}_{ij}^{w_j}=(\prod_j\hat{T}_{ij}^{w_j},\;1-\prod_j(1-\hat{I}_{ij})^{w_j},\;1-\prod_j(1-\hat{F}_{ij})^{w_j});\;y_i^{\mathrm{FMF}}=s(\tilde{U}_i);\;\text{rank descending}
Theory of Dominance: final rank from pairwise dominance across RS/RP/FMF.

$A_{i} ≻ A_{k} ⟺ ranks better in \geq 2 of {R S, R P, F M F}$

LaTeX
A_i\succ A_k\iff\text{ranks better in }\geq 2\text{ of }\{RS,RP,FMF\}

Yöntem ayrıntıları kaynak kütüphanedeki özgün (İngilizce) metindir.

Sezgi

Sonucu okuma: p-multimoora extends P-MULTIMOORA 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 MULTIMOORA 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.