Normalization technique

Condition of use

Formula

Linear sum-based

Cost criteria

$n_{ij}=\frac{1/r_{ij}}{{\displaystyle {\sum }_{i=1}^{m}1/r_{ij}}}$

Benefit criteria

$n_{ij}=\frac{r_{ij}}{{\displaystyle {\sum }_{i=1}^m{r}_{ij}}}$

Linear Max

Cost criteria

$n_{ij}=1-\frac{r_{ij}}{r_{\max }}$

Benefit criteria

$n_{ij}=\frac{r_{ij}}{r_{\max }}$

Linear Max-Min

Cost criteria

$n_{ij}=\frac{r_{\max }-r_{ij}}{r_{\max }-r_{\min }}$

Benefit criteria

$n_{ij}=\frac{r_{ij}-r_{\min }}{r_{\max }-r_{\min }}$