WASPAS - Weighted Aggregated Sum Product Assessment

Overview

Q_i ∈ [0,1] when all raw values are positive and normalised to [0,1]. λ=0.5 (default) gives equal weight to the additive (SAW) and multiplicative (WPM) components. λ=1 reduces WASPAS to SAW; λ=0 reduces it to WPM. The seminal paper shows that λ=0.5 maximises accuracy compared to using either component alone.

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

Alternative selection, Supplier evaluation

How it works

1. 1

   Linear normalisation (max for benefit, min/x for cost).

   $${\bar{x}}_{ij}=\{\begin{array}{ll}{x}_{ij}/{\max }_i{x}_{ij}& j\in J^{+}\\ {\min }_i{x}_{ij}/x_{ij}& j\in J^{-}\end{array}$$

   Zavadskas 2012, p.4 Eq.(1)

2. 2

   Weighted Sum Model component Q^{(1)}_i.

   $$Q_i^{(1)}=\sum _{j=1}^n{w}_j{\bar{x}}_{ij}$$

   Zavadskas 2012, p.4 Eq.(2)

3. 3

   Weighted Product Model component Q^{(2)}_i.

   $$Q_i^{(2)}=\prod _{j=1}^n({\bar{x}}_{ij}{)}^{w_j}$$

   Zavadskas 2012, p.4 Eq.(3)

4. 4

   Joint WASPAS aggregation with λ∈[0,1] and descending ranking.

   $$Q_i=\lambda Q_i^{(1)}+(1-\lambda )Q_i^{(2)}$$

   Zavadskas 2012, p.4 Eq.(4)

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

• Ignoring λ sensitivity: ranking can change as λ varies from 0 to 1 - always run sensitivity analysis on λ.

• Zero or negative criterion values: WPM component (F3) is undefined - enforce E-2.

Works with

How to cite