3.1.1. Construction of the Decision Matrix

Data from the data matrix *R* should be transformed into the decision matrix *P*, where *pkl* is the proportion of response *k* for the criteria *l*:

$$P = \begin{bmatrix} p\_{11} & \cdots & p\_{1l} \\ \vdots & \ddots & \vdots \\ p\_{k1} & \cdots & p\_{kl} \end{bmatrix} \tag{2}$$

For each of the possible responses *k*, *pkl* is calculated by Equation (3):

$$p\_{kl} = \frac{\sum\_{i=1}^{N} D\_{kli}}{N}, \text{for each } k = 1, \ 2, \dots \ 100. \tag{3}$$

Here *N* is the number of the non-zero assessments for the criterion *l*. *Dkl* is a binary indicator that gives a value of 1 if the respondent *n* gave the response *k* for the criteria *l*, otherwise *Dkl* = 0. Consistent with most statistical principles, the proportions of the responses should follow three rules: <sup>0</sup> <sup>≤</sup> *<sup>p</sup>kl* <sup>≤</sup> 1 and <sup>P</sup>*<sup>K</sup> k*=1 *pkl* = 1 and *pkllog*2(*pkl*) = 0 *when pkl* = 0.
