SWARA - Step-Wise Weight Assessment Ratio Analysis

Overview

SWARA requires the DM to first rank criteria from most to least important, then specify how much more important each criterion is relative to the next one (s_j ≥ 0). s_j = 0 means criterion j and j+1 are equally important; s_j = 0.5 means j is 50% more important. Only n−1 judgements are needed.

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

Hierarchical weighting, expert-driven

How it works

1. 1

   Rank criteria by importance C_(1) ≻ C_(2) ≻ … ≻ C_(n).

   $$C_{(1)}⪰C_{(2)}⪰\cdots ⪰C_{(n)}$$

   Kersuliene 2010, p.246 Sec.3

2. 2

   Comparative importance s_j of each criterion vs the previous one (s_1 = 0).

   $$s_j=\text{relative importance of }{C}_{(j)}\text{ vs }{C}_{(j-1)},s_1=0$$

   Kersuliene 2010, p.247 Eq.(1)

3. 3

   Coefficient k_j = s_j + 1; recalculated weight q_j = q_{j-1}/k_j (q_1 = 1).

   $$k_j=s_j+1,q_j=\frac{q_{j-1}}{k_j},q_1=1$$

   Kersuliene 2010, p.247 Eqs.(2)-(3)

4. 4

   Final weights w_j = q_j / Σ q_k.

   $$w_j=\frac{q_j}{{\sum }_{k=1}^n{q}_k}$$

   Kersuliene 2010, p.247 Eq.(4)

Fits when / Look elsewhere when

Assumptions to verify

• Domain experts available
• Experts can express consistent comparisons

Edge cases and pitfalls

• s_1 ≠ 0: the most important criterion must have s_1 = 0.

Works with

How to cite