# Multicriteria Decision Making in Tourism Industry Based on Visualization of Aggregation Operators
## 5 Case Study
Attribute \(z_{1}\) reflects the propensity of the decision maker to use \"smart\" technologies. Initially the decision maker considered attribute \(z_{1}\), dealing with client interaction at the hotel using \"smart\" technologies to be binary, but clarified that they later started to envision this attribute as quantitative with a scale from 0% (total lack of communication with smart systems, only with human personnel) to 100% (interaction only with smart systems and no humans). Depending on the decision maker's opinion, this criterion can affect the aggregation result differently in terms of general hotel assessment. In particular, the use of \"smart\" technologies can facilitate lowering or total removal of tourist discrimination by race, sex, sexual orientation, social status [35]. In our case, the decision maker would like to minimize communication with human personnel, so for criterion \(g[4]\), we can write:  
\[g[4]=\frac{z_{1}}{100} \tag{10}\]  
Attribute \(z_{2}\) reflects the acceptability of personal safety risks in the hotel (0--no risks, 1--risks present). As these risks are unacceptable for the decision maker, so we can write for criterion \(g[5]\):  
\[g[5]=1-z_{2} \tag{11}\]  
At the same time, the zero value of criterion \(g[5]\) corresponds with zeroing out the aggregation result (\"veto\" effect). Attribute \(z_{3}\) reflects the decision maker's motivation to visit an event held at the hotel under safety conditions (1--yes, 0--no):  
\[g[6]=z_{3} \tag{12}\]  
Here, the value of 1 for criterion \(g[6]\) leads to the corresponding aggregation result equaling 1 (\"favor\" effect). In this case, normalization leads to a list of aggregation criteria that are calculated from the hotel attribute values according to Equations (7)-(12). During the second synthesis stage, the aggregation operator for criteria \(g[1],\dots,g[6]\) is built using the aggregation-operator synthesis procedure from the previous section. At Step 1 of the procedure, the quantitative criteria \(g[1],g[2],g[3]\) are assigned with all equal weights in the 3D balance model at 0.5 distance from the support line (green cylinders in Figure 5, on the left). Auxiliary weights that serve the purpose of showing mutual dependencies of criteria for aggregation results are absent at this step. The binary criteria are assigned with gray-colored weights at the support line that are equal in mass to the green weights (Figure 5, on the right). We need it for visual separation between the quantitative criteria and the binary criteria. At Step 2 of the procedure, we examine the binary criteria that make decisions in the {0, 1} segment. As the decision maker considers criterion \(g[4]\) to be quantitative, this criterion shall be reviewed at Steps 2-7 of the procedure and the corresponding \(g[4]\) weight shall be marked green as a quantitative criterion (Figure 6). It was already mentioned above that for the decision maker, any safety risks are unacceptable, and the corresponding \(g[5]\) criterion should possess a \"veto\" effect and \"overweigh\", in the case of a zero value, all other influences on the plane. This is why the weight corresponding with criterion \(g[5]\)is additionally provided with an auxiliary heavy enough weight \(l[5]\) (gray parallelepiped on line \(l[5]\) in Figure 6) allowing the result to be zeroed out in the case of \(g[5]\) equaling zero: \(l[5]=\left\{ \begin{array}{ll}0,\;if\;g[5]=1\\ -1,\;if\;g[5]=0\end{array} ,\omega_{5}=2\right.\). The weight value \(\psi_{5}\) is assumed to be equal to zero as the influence of criterion \(g[5]\) on the plane tilt is only driven by weight \(l[5]\). Criterion \(g[6]\) of an intentional visit to an event at the hotel has a \"favor\" effect and \"overweighs\" all other influences on the plane in the case of a positive 1 value.