ARTASI - Uyarlanabilir Standartlaştırılmış Aralıklara Dayalı Alternatif Sıralama Tekniği

Formül adımları

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

1. Adım 1 — Uyarlanabilir standartlaştırılmış aralıklar.

   $$S_j^{max}={max}_i{L}_{ij}+({max}_i{L}_{ij}{)}^{1/m};S_j^{min}={min}_i{L}_{ij}-({min}_i{L}_{ij}{)}^{1/m}$$
   LaTeX

   S_{j}^{\max} = \max_{i} L_{ij} + (\max_{i} L_{ij})^{1/m};\quad S_{j}^{\min} = \min_{i} L_{ij} - (\min_{i} L_{ij})^{1/m}

2. Adım 2 — Birinci-seviye standartlaştırma.

   $$R_{ij}={\displaystyle \frac{L_{ij}-S_j^{min}}{S_j^{max}-S_j^{min}}}({\beta }^u-{\beta }^l)+{\beta }^l$$
   LaTeX

   R_{ij} = \dfrac{L_{ij} - S_{j}^{\min}}{S_{j}^{\max} - S_{j}^{\min}}\,(\beta^{u}-\beta^{l}) + \beta^{l}

3. Adım 3 — İkinci-seviye standartlaştırma (yön).

   $$C_{ij}=R_{ij}(J^{+});C_{ij}=-R_{ij}+{max}_i{R}_{ij}+{min}_i{R}_{ij}(J^{-})$$
   LaTeX

   C_{ij} = R_{ij}\ (J^{+});\quad C_{ij} = -R_{ij} + \max_{i} R_{ij} + \min_{i} R_{ij}\ (J^{-})

4. Adım 4 — İdeal fayda P+.

   $$P_{ij}^{+}=(C_{ij}/{max}_i{C}_{ij})·W_j·{\beta }^u$$
   LaTeX

   P^{+}_{ij} = (C_{ij}/\max_{i} C_{ij}) \cdot W_{j} \cdot \beta^{u}

5. Adım 5 — Anti-ideal fayda P−.

   $$P_{ij}^{-}=({min}_i{C}_{ij}/C_{ij})·W_j·{\beta }^u$$
   LaTeX

   P^{-}_{ij} = (\min_{i} C_{ij}/C_{ij}) \cdot W_{j} \cdot \beta^{u}

6. Adım 6 — Birleşik fayda N+ ve N−.

   $$N_i^{+}=\sum _j{P}_{ij}^{+};N_i^{-}=\sum _j{P}_{ij}^{-}$$
   LaTeX

   N^{+}_{i} = \sum_{j} P^{+}_{ij};\quad N^{-}_{i} = \sum_{j} P^{-}_{ij}

7. Adım 7 — Son fayda K_i.

   $$K_i=(N_i^{+}+N_i^{-})+(\psi (f(N_i^{+}){)}^{\tau }+(1-\psi )(f(N_i^{-}){)}^{\tau }{)}^{1/\tau }$$
   LaTeX

   K_{i} = (N^{+}_{i} + N^{-}_{i}) + (\psi (f(N^{+}_{i}))^{\tau} + (1-\psi)(f(N^{-}_{i}))^{\tau})^{1/\tau}

Sezgi

Two-level standardization + ideal/anti-ideal utility (β-anchored). Output typically utility (higher value = preferred).

Sonucu okuma: K_i ∈ ℝ; higher K means better alternative. ARTASI uses two-level standardisation with adaptive bounds (S_max, S_min go slightly beyond the data via the (·)^(1/m) term) and combines ideal-direction utility (P+) with anti-ideal utility (P−). ψ controls the trade-off and τ controls the Minkowski-style aggregation strength.

Varsayımlar

• Criteria preferences are independent (no synergistic interactions)
• Compensation is acceptable: high score on one criterion can offset low on another
• Decision matrix is complete (no missing values)

Ne zaman kullanılmaz

• Criteria strongly correlated → consider DEMATEL/ANP for interdependence
• Non-compensatory preferences → consider outranking (ELECTRE/PROMETHEE)

Sınırlılıklar

• Assumes: Criteria preferences are independent (no synergistic interactions)
• Assumes: Compensation is acceptable: high score on one criterion can offset low on another
• Assumes: Decision matrix is complete (no missing values)

Sık yapılan hatalar

• Negatif değer durumu: işaretli üs.
• ψ uç değerlerde K'nın bir tarafı dominant olur.