Table 5 Illustration of OWA calculation for four criteria values, for the linguistic quantifier 2
From: A multi-criteria spatial deprivation index to support health inequality analyses
j | Criterion values | Criterion weights w j | Ordered criterion values z ij | Ordered criterion weights u ij | \( {\left({\displaystyle \sum_{\boldsymbol{k}=1}^{\boldsymbol{j}}}{\boldsymbol{u}}_{\boldsymbol{k}}\right)}^{\propto } \) | v j | v j * z ij |
|---|---|---|---|---|---|---|---|
1 | 0,20 | 0,30 | 0,80 | 0,35 | (0,35)2 = 0,1225 | (0,1225 - 0) = 0,1225 | 0,098 |
2 | 0,80 | 0,35 | 0,50 | 0,10 | (0,45)2 = 0,2025 | (0,2025 -0,1225) = 0,08 | 0,04 |
3 | 0,50 | 0,10 | 0,30 | 0,25 | (0,70)2 = 0,49 | (0,49-0,2025) = 0,2875 | 0,08625 |
4 | 0,30 | 0,25 | 0,20 | 0,30 | (1)2 = 1 | (1–0,49) = 0,51 | 0,102 |
∑ | 1 | 1 | 1 | OWA i =0,33 |