ARTASI - Alternative Ranking Technique based on Adaptive Standardized Intervals

Overview

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.

Output

utility, higher is better

Data

Crisp, complete numeric matrix

Weights

Needs a weight source

Size

2+ alternatives, 3-12 criteria works best

Used for

Website performance, executive recruitment

How it works

1. 1

   Adaptive standardized intervals: 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).

   $$S_j^{\max }=\underset{i}{\max }{L}_{ij}+(\underset{i}{\max }{L}_{ij}{)}^{1/m};S_j^{\min }=\underset{i}{\min }{L}_{ij}-(\underset{i}{\min }{L}_{ij}{)}^{1/m}$$

   Kara et al. 2024, Eqs (17)-(18)

2. 2

   First-level standardization: linear rescaling of L_ij to interval [β^l, β^u] using adaptive bounds.

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

   Kara et al. 2024, Eq (19)

3. 3

   Second-level standardization with direction. C_ij = R_ij for benefit; C_ij = −R_ij + max R + min R for cost.

   $$C_{ij}=R_{ij}(J^{+});C_{ij}=-R_{ij}+\underset{i}{\max }{R}_{ij}+\underset{i}{\min }{R}_{ij}(J^{-})$$

   Kara et al. 2024, Eq (20)

4. 4

   Ideal utility P+_ij = (C_ij/max_i C_ij) · W_j · β^u.

   $$P_{ij}^{+}=(C_{ij}/\underset{i}{\max }{C}_{ij})\cdot W_j\cdot {\beta }^u$$

   Kara et al. 2024, Eq (21)

5. 5

   Anti-ideal utility P−_ij = (min_i C_ij/C_ij) · W_j · β^u.

   $$P_{ij}^{-}=(\underset{i}{\min }{C}_{ij}/C_{ij})\cdot W_j\cdot {\beta }^u$$

   Kara et al. 2024, Eq (22)

6. 6

   Aggregate utility N+ and N−.

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

   Kara et al. 2024, Eqs (24)-(25)

7. 7

   Final utility K_i = (N+ + N−) + (ψ f(N+)^τ + (1−ψ) f(N−)^τ)^(1/τ); f(N+) = N+/(N+ + N−).

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

   Kara et al. 2024, Eq (26)

Look elsewhere when

Assumptions to verify

• 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)

Edge cases and pitfalls

• Negative or zero column values: (·)^(1/m) is sign-sensitive - manifest's E-2 ensures non-negative range; for safety verifier uses signed power.

• ψ near 0 or 1 collapses K to only one of N+ or N−; choose carefully.

Works with

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