RAM - Root Assessment Method

Overview

r_i > 1 always (since base ≥ 2, exponent > 0). Higher r_i = better. RAM naturally penalises cost criteria through the exponent denominator.

Data

Crisp

Weights

Needs a weight source

How it works

1. 1

   Sum normalization (direction-unaware: r_ij = x_ij / Σ_k x_kj). All columns treated uniformly; benefit/cost distinction applied in F3 by separating columns.

   $$r_{ij}=\frac{x_{ij}}{{\sum }_k{x}_{kj}}$$

   Sotoudeh-Anvari 2023 §2

2. 2

   Weighted normalized matrix y_ij = w_j · r_ij.

   $$y_{ij}=w_j\cdot r_{ij}$$

   Sotoudeh-Anvari 2023 §2

3. 3

   Separate benefit and cost sums: S+_i = sum of wnmatrix columns for benefit criteria; S-_i = sum of cost criteria columns.

   $$S_i^{+}=\sum _{j\in J^{+}}{y}_{ij};S_i^{-}=\sum _{j\in J^{-}}{y}_{ij}$$

   Sotoudeh-Anvari 2023 §2

4. 4

   RAM score r_i = (2 + S+_i)^(1/(2 + S-_i)). Rank descending (higher = better). Note: high S-_i (cost) decreases the exponent's denominator → lowers r_i; high S+_i (benefit) increases base → raises r_i.

   $$r_i=(2+S_i^{+}{)}^{\frac{1}{2+S_i^{-}}},\text{rank descending}$$

   Sotoudeh-Anvari 2023 §2 Eq.(main)

Edge cases and pitfalls

• Sum normalization is direction-unaware: for cost criteria, high original value → high normalized value → high S- → lower r_i (correct penalisation). Do NOT pre-invert cost columns.

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