SMART Weighting - Direct importance rating normalisation (Edwards SMART weight step)

Overview

SMART-weight normalises DM-supplied importance ratings to sum-to-1 weights. Ratings can be on any positive scale (0-100, 1-9, etc.) - only ratios matter.

Output

Weight, higher is better

Data

Crisp, expert input required

Weights

Derived internally, no weight source needed

Size

2+ alternatives, 3-12 criteria works best

Used for

Expert-driven decision making, MAGDM

How it works

1. 1

   Normalise importance ratings r_j to criterion weights: w_j = r_j / Σ_k r_k.

   $$w_j=\frac{r_j}{{\sum }_{k=1}^n{r}_k},r_j>0$$

   Edwards & Barron 1994, p.308 (SMART weight step; pending PDF page verification)

Look elsewhere when

Assumptions to verify

• Domain experts available
• Experts can express consistent comparisons

Edge cases and pitfalls

• All equal ratings → equal weights (uniform). This is intentional - use SMART or ROC if ordinal rank information should produce non-uniform weights.

Works with

How to cite