IF-MULTIMOORA - MULTIMOORA yönteminin Intuitionistic uzantısı

Formül adımları

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

1. ranking_computation

   $$s_{ij}={\mu }_{ij}-{\nu }_{ij},{\widehat{s}}_{ij}=\frac{s_{ij}+1}{\sqrt{{\sum }_i(s_{ij}+1{)}^2}},v_{ij}=w_j{\widehat{s}}_{ij}$$
   LaTeX

   s_{ij}=\mu_{ij}-\nu_{ij},\quad\hat{s}_{ij}=\frac{s_{ij}+1}{\sqrt{\sum_i(s_{ij}+1)^2}},\quad v_{ij}=w_j\hat{s}_{ij}

2. ranking_computation

   $$R{S}_i=\sum _{j\in {\Omega }^{+}}{v}_{ij}-\sum _{j\in {\Omega }^{-}}{v}_{ij}$$
   LaTeX

   RS_i=\sum_{j\in\Omega^+}v_{ij}-\sum_{j\in\Omega^-}v_{ij}

3. ranking_computation

   $$r_j^{*}={max}_i{v}_{ij}(\text{benefit}),R{P}_i={max}_j|r_j^{*}-v_{ij}|$$
   LaTeX

   r_j^*=\max_i v_{ij}\;(\text{benefit}),\quad RP_i=\max_j\bigl|r_j^*-v_{ij}\bigr|

4. ranking_computation

   $${\tilde{U}}_i=\mathrm{I}\mathrm{F}\mathrm{W}\mathrm{G}(w^{+},{\tilde{v}}_{i,{\Omega }^{+}})\oslash \mathrm{I}\mathrm{F}\mathrm{W}\mathrm{G}(w^{-},{\tilde{v}}_{i,{\Omega }^{-}}),\mathrm{I}\mathrm{F}\mathrm{W}\mathrm{G}=(\prod {\mu }^w,1-\prod (1-\nu {)}^w)$$
   LaTeX

   \tilde{U}_i=\mathrm{IFWG}(w^+,\tilde{v}_{i,\Omega^+})\oslash\mathrm{IFWG}(w^-,\tilde{v}_{i,\Omega^-}),\quad\mathrm{IFWG}=\Bigl(\prod\mu^w,\,1-\prod(1-\nu)^w\Bigr)

5. ranking_computation

   $$\text{Rank}(A_i)\leftarrow \text{dominance count from RS, RP, FMF sub-rankings}$$
   LaTeX

   \text{Rank}(A_i)\leftarrow\text{dominance count from RS, RP, FMF sub-rankings}

Sezgi

Sonucu okuma: if-multimoora extends MULTIMOORA 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 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 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.