3.2.1. Construction of the Decision Matrix

Decision matrix *X*, where *xij* is the number of *mth* variable and *l* is the number of the criteria (*i* = 1, 2, . . . *m*; *j* = 1, 2, . . . *l*) has to be constructed prior to the other steps of the WASPAS-SVNS approach:

$$X = \begin{bmatrix} \mathbf{x}\_{11} & \mathbf{x}\_{12} & \dots & \mathbf{x}\_{1l} \\ \mathbf{x}\_{21} & \mathbf{x}\_{22} & \dots & \mathbf{x}\_{2l} \\ \vdots & \vdots & \ddots & \vdots \\ \mathbf{x}\_{m1} & \mathbf{x}\_{m2} & \dots & \mathbf{x}\_{ml} \end{bmatrix} \tag{7}$$

Six variables *m* are determined to assess each of the preferences *l*. Five variables analyze the nominal aspects of the collected data, and the sixth of them examines the ordinal information extracted from the matrix *R*.

**Nominal variables**. Nominal variable for the criterion *l* is expressed as the frequency of the values *rnl* belonging to the predefined interval [a,b]. *Dnl* is a binary indicator that gives a value of 1 if *rnl*[*a*, *b*]. Otherwise, *Dnl* = 0. Nominal variables V1–V5 for each of the criterions *l* are determined as the matrix *X* elements *xml* via the Equation (8).

$$\chi\_{nl} = \frac{\sum\_{n=1}^{N} D\_{nl}}{N\_l}, \text{ for each } \mathbf{m} = 1, \, 2, \dots, 5; \tag{8}$$

here *N* is the total number of the respondents participated in the survey, *N<sup>l</sup>* is the amount of the non-zero assessments *rnl* for the criterion *l*.

Ranges [a,b] for the nominal variables V1–V5 were determined based on the medical research where VAS scales are widely used in pain studies. The physical manifestation of the pain is measured as the linear distance in the VAS scales of 100 mm length. It was revealed that VAS ratings of 0–4 mm might be considered as no pain; 5–44 mm—mild pain; 45–74 mm—moderate pain; 75–100 mm—severe pain, and 100 mm means the worst imaginable pain [57]. Similar intervals were determined as the five importance groups of the VAS scales (Table 1).

**Table 1.** Variables and their weights determined for the WASPAS-SVNS criteria weighting.


**Ordinal variable.** VAS matrix provides a possibility to rank the several latent criteria visually. Scientific research proved that respondents actively use this feature and increase the precision of their answers. For instance, if the pointer of the VAS scales presenting the criterion *l* is moved to the right side more comparing with the others (Figure 1), it can be understood as criterion *l* is the most important for the respondent *n*. This concept can be used to determine the new variable called Overanking level (OVL). The OVL level for the criterion *l* is calculated individually for all the respondents *n* by the following algorithm:

$$\text{Let } OVI\_{nl} = 0; \text{ } j = 1 \text{ and } \mathbb{C}\_{nl} = r\_{nl}. \tag{9}$$

$$\text{While } j \le l:$$

$$\text{if } \left( \mathbb{C}\_{nl} > r\_{\text{nj}} \right) \text{ and } \left( r\_{\text{nj}} \neq 0 \right) \text{, } \text{OVL}\_{\text{nl}} = \text{OVL}\_{\text{nl}} + 1 \text{,} \tag{10}$$

$$j = j + 1.\tag{11}$$
