IF-MARCOS

IF-MARCOS - MARCOS yönteminin Intuitionistic uzantısı

Intuitionistic üstünlük/sıralama - Sezgisel Bulanık Sayı (IFS: μ, ν; μ+ν ≤ 1)

Formül adımları

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

ranking_computation

$AAI = ({min}_{i} μ_{i j}, {max}_{i} ν_{i j}), AI = ({max}_{i} μ_{i j}, {min}_{i} ν_{i j})$

LaTeX
\text{AAI}=\bigl(\min_i\mu_{ij},\max_i\nu_{ij}\bigr),\quad\text{AI}=\bigl(\max_i\mu_{ij},\min_i\nu_{ij}\bigr)
normalisation

${\hat{s}}_{i j} = \frac{s ({\tilde{a}}_{i j})}{s ({AI}_{j})}, s (\tilde{a}) = μ - ν$

LaTeX
\hat{s}_{ij}=\frac{s(\tilde{a}_{ij})}{s(\text{AI}_j)},\quad s(\tilde{a})=\mu-\nu
aggregation

${\tilde{S}}_{i} = I F W A (w, \tilde{v}) = (1 - \prod_{j = 1}^{n} (1 - μ_{i j})^{w_{j}}, \prod_{j = 1}^{n} ν_{i j}^{w_{j}})$

LaTeX
\tilde{S}_i=\mathrm{IFWA}(w,\tilde{v})=\Bigl(1-\prod_{j=1}^n(1-\mu_{ij})^{w_j},\;\prod_{j=1}^n\nu_{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

$f (K_{i}) = \frac{K_{i}^{+} + K_{i}^{-}}{1 + \frac{1 - f (K_{i}^{+})}{f (K_{i}^{+})} + \frac{1 - f (K_{i}^{-})}{f (K_{i}^{-})}}, f (K_{i}^{\pm}) = \frac{K_{i}^{\pm}}{K_{i}^{+} + K_{i}^{-}}, rank descending$

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^-)}},\quad f(K_i^{\pm})=\frac{K_i^{\pm}}{K_i^++K_i^-},\quad\text{rank descending}

Yöntem ayrıntıları kaynak kütüphanedeki özgün (İngilizce) metindir.

Sezgi

Sonucu okuma: if-marcos extends MARCOS to handle Intuitionistic uncertainty. All arithmetic operations (normalisation, weighting, distance computation) are performed using Intuitionistic Fuzzy Number (IFN: μ, ν; μ+ν ≤ 1) algebra. The final scores are defuzzified via score function S = μ − ν before ranking.

Varsayımlar

Decision matrix entries are valid Intuitionistic Fuzzy 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 IFN: μ ∈ [0,1], ν ∈ [0,1], μ+ν ≤ 1; π = 1−μ−ν ≥ 0 koşulunu sağladığından emin olun.
Defuzzifikasyon yöntemi sıralamayı etkiler: score function S = μ − ν kanonik seçimdir.