SPC (Symmetry Point of Criterion)

1. 1. Read the decision matrix DM = |x_ij|_{m x n} and check that it is finite and strictly positive.

   $$DM=|x_{ij}{|}_{m\times n}$$

2. 2. Compute the symmetry point of every criterion as the midpoint of its smallest and largest value.

   $$SP{C}_j=\frac{{\min }_i\{x_{ij}\}+{\max }_i\{x_{ij}\}}{2}$$

3. 3. Build the matrix of absolute distances between every value and the symmetry point of its criterion.

   $$D=\Vert d_{ij}{\Vert }_{m\times n},d_{ij}=|x_{ij}-SP{C}_j|$$

4. 4. Form the matrix of moduli of symmetry: the mean absolute distance of a criterion divided by each of its values.

   $$R=|r_{ij}{|}_{m\times n},r_{ij}=\frac{{\sum }_{i=1}^m{d}_{ij}/m}{x_{ij}}$$

5. 5. Average the moduli of symmetry column-wise to obtain the modulus of symmetry vector Q.

   $$Q=|q_j{|}_{1\times n},q_j=\frac{{\sum }_{i=1}^m{r}_{ij}}{m}$$

6. 6. Normalise the modulus of symmetry vector to the criterion weight simplex and order the criteria by weight.

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