Goal:
Criteria:
Alternatives:
General formula for weight calculation:
$$ w_i = \frac{\sqrt[n]{\prod_{j=1}^n a_{ij}}}{\sum_{k=1}^n \sqrt[n]{\prod_{j=1}^n a_{kj}}} $$Where:
$w_i$ is the weight of the $i$-th element
$n$ is the number of elements
$a_ij$ is the comparison value of the $i$-th element with respect to the $j$-th element
Formula for final score calculation:
$$ S_i = \sum_{j=1}^m w_j \cdot a_{ij} $$Where:
$S_i$ is the final score of the $i$-th alternative
$w_j$ is the weight of the $j$-th criterion
$a_ij$ is the score of the $i$-th alternative with respect to the $j$-th criterion
$m$ is the number of criteria
Formulas for consistency check:
$$ \begin{align} CI &= \frac{\lambda_{max} - n}{n - 1} \\ CR &= \frac{CI}{RI} \end{align} $$Where:
$CI$ is the Consistency Index
$CR$ is the Consistency Ratio
$\\lambda_max$ is the principal eigenvalue
$n$ is the number of criteria/alternatives
$RI$ is the Random Index (predefined for different matrix sizes)