IV-MARCOS

IV-MARCOS - MARCOS yönteminin Aralık Değerli Sezgisel Bulanık uzantısı

Aralık Değerli Sezgisel Bulanık üstünlük/sıralama - IVIFS (Atanassov 1989)

Formül adımları

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

ranking_computation

${AAI}_{j} = ([{min}_{i} μ_{i j}^{L}, {min}_{i} μ_{i j}^{U}], [{max}_{i} ν_{i j}^{L}, {max}_{i} ν_{i j}^{U}]), {AI}_{j} = ([{max}_{i} μ_{i j}^{L}, {max}_{i} μ_{i j}^{U}], [{min}_{i} ν_{i j}^{L}, {min}_{i} ν_{i j}^{U}])$

LaTeX
\text{AAI}_j=\bigl([\min_i\mu^L_{ij},\min_i\mu^U_{ij}],[\max_i\nu^L_{ij},\max_i\nu^U_{ij}]\bigr),\quad\text{AI}_j=\bigl([\max_i\mu^L_{ij},\max_i\mu^U_{ij}],[\min_i\nu^L_{ij},\min_i\nu^U_{ij}]\bigr)
normalisation

${\hat{s}}_{i j} = \frac{s ({\tilde{a}}_{i j})}{s ({AI}_{j})}, s (α) = \frac{μ^{L} + μ^{U} - ν^{L} - ν^{U}}{2}$

LaTeX
\hat{s}_{ij}=\frac{s(\tilde{a}_{ij})}{s(\text{AI}_j)},\quad s(\alpha)=\frac{\mu^L+\mu^U-\nu^L-\nu^U}{2}
aggregation

${\tilde{S}}_{i} = I I F W A (w, {\hat{a}}_{i}) = ([1 - \prod_{j} (1 - μ_{i j}^{L})^{w_{j}}, 1 - \prod_{j} (1 - μ_{i j}^{U})^{w_{j}}], [\prod_{j} ν_{i j}^{L}^{w_{j}}, \prod_{j} ν_{i j}^{U}^{w_{j}}])$

LaTeX
\tilde{S}_i=\mathrm{IIFWA}(w,\hat{a}_i)=\Bigl([1-\textstyle\prod_j(1-\mu^L_{ij})^{w_j},\;1-\textstyle\prod_j(1-\mu^U_{ij})^{w_j}],\;[\textstyle\prod_j\nu^L_{ij}{}^{w_j},\textstyle\prod_j\nu^U_{ij}{}^{w_j}]\Bigr)
ranking_computation

$K_{i}^{+} = \frac{s ({\tilde{S}}_{i})}{s ({\tilde{S}}_{A I})}, K_{i}^{-} = \frac{s ({\tilde{S}}_{i})}{s ({\tilde{S}}_{A A I})}$

LaTeX
K_i^+=\frac{s(\tilde{S}_i)}{s(\tilde{S}_{\mathrm{AI}})},\quad K_i^-=\frac{s(\tilde{S}_i)}{s(\tilde{S}_{\mathrm{AAI}})}
ranking_computation

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

LaTeX
f(K_i^+)=\frac{K_i^-}{K_i^++K_i^-},\quad f(K_i^-)=\frac{K_i^+}{K_i^++K_i^-}
ranking_computation

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

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^-)}}
ranking_computation

$rank (A_{i}) = {argsort}_{↓} (f (K_{1}), \dots, f (K_{m}))$

LaTeX
\text{rank}(A_i)=\operatorname{argsort}_\downarrow(f(K_1),\ldots,f(K_m))

Yöntem ayrıntıları kaynak kütüphanedeki özgün (İngilizce) metindir.

Sezgi

Sonucu okuma: iv-marcos extends MARCOS to handle Interval uncertainty. All arithmetic operations (normalisation, weighting, distance computation) are performed using Interval Number (IN: [a, b]) algebra. The final scores are defuzzified via midpoint (a+b)/2 before ranking.

Varsayımlar

Decision matrix entries are valid Interval 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 IN: a ≤ b koşulunu sağladığından emin olun.
Defuzzifikasyon yöntemi sıralamayı etkiler: midpoint (a+b)/2 kanonik seçimdir.