**3. VASMA Weighting Methodology**

VASMA weighting (VAS Matrix for criteria weighting) is an easy to apply survey-based criteria weighting technique. It employs WASPAS-SVNS for the determination of the subjective weights and analyzes information entropy for the determination of the objective weights. VASMA weighting is constructed to decrease the uncertainties noticed in the survey-based criteria evaluation preserving the simplicity of the DR alike data collection. The overall VASMA weighting methodology is presented in Figure 2.

Answers provided by the respondents of the online survey are extracted from the survey database and saved in the data matrix *R* consisting of the values *rnl*:

$$R = \begin{bmatrix} r\_{11} & r\_{12} & \dots & r\_{1l} \\ r\_{21} & r\_{22} & \dots & r\_{2l} \\ \vdots & \vdots & \ddots & \vdots \\ r\_{n1} & r\_{n2} & \dots & r\_{nl} \end{bmatrix} \tag{1}$$

Here *l* = 1, 2, . . . *L* denote the number of the criteria and *n* = 1, 2, . . . *N* denote the number of the respondents.

moment [49].

*2.3. VAS Matrix for the Criteria Weighting* 

products of the functioning level and the relative weights.

the survey-based criteria weighting is performed.

**3. VASMA Weighting Methodology** 

elicited by DR are more reliable than those elicited by PA [44]. However, a little variation of the averaged weights is repeatedly identified as the downside of the straightforward DR technique [48].

VAS matrix can be used as the data collection tool in the survey-based decision. For instance, VAS scales are implemented in the SEIQoL methodology, which is widely used to nominate, weight, and rate different aspects of life quality [49]. SEIQoL with a direct weighting technique (SEIQoL-DW) is an interview-based tool that involves the interviewer to manage the evaluation process. The respondents are asked to nominate the five most important areas of their life (domains) in these semistructured interviews. For the evaluation of the importance of these domains, point allocation weighting is applied. Vertical VAS matrix with five adjacent VAS scales is used to assess the current functioning in the chosen domains. Finally, five separate indexes are calculated summing up the

Such a methodology is widely applied in various studies [50]. However, experiments with the SEIQoL-DW revealed that looking at the VAS matrix respondents comprehends the task as the assessment of the domain importance rather than the scoring of their functioning at the research

Burckhardt et al. [46] proposed to employ VAS scales and the direct weighting for both the scoring and the weighting of the chosen domains. He also excluded the interviewer from the experiment and used a self-explanatory paper questionnaire to collect the data. In total, 100 participants were involved in this research. Since the averaged values of the VAS based DR technique showed a tendency toward the low variability of the domain weights, the usefulness of the improved methodology was highly questioned. Nevertheless, it must be noted that neither the subjectivity of the respondents nor the psychometric features of the VAS scales were analyzed in the domain importance assessments. We strongly believe that these aspects should be cautiously analyzed when

VASMA weighting (VAS Matrix for criteria weighting) is an easy to apply survey-based criteria weighting technique. It employs WASPAS-SVNS for the determination of the subjective weights and analyzes information entropy for the determination of the objective weights. VASMA weighting is constructed to decrease the uncertainties noticed in the survey-based criteria evaluation preserving

**Figure 2. Figure 2.** VASMA weighting methodology. VASMA weighting methodology.

All the evaluations are automatically transformed from the VAS scales to the integer numbers. The linguistic value at the negative anchor ("Absolutely unimportant") is determined as 1, and the linguistic value at the positive anchor ("Extremely important") is determined as 100. Other values are calculated as the distance between these two values. If the respondent *n* did not move a marker from the default position and left it in the middle of the VAS scales, we assume that he did not express his opinion on the specific criterion *l*, therefore the *rnl* = 0. Finally, the simple data cleaning procedure must be done deleting the entries where the respondent *n* did not evaluate either of the criteria *l*.

Data saved in the matrix *R* is later exploited to construct two different matrixes *P* and *X*. Decision matrix *P* is used to calculate the entropy weights; the decision matrix *X* is constructed to calculate subjective weights via the WASPAS-SVNS approach. The matrixes *R* and *X* and their usage for the VASMA weighting will be explicitly described in the following subsections.
