# Multicriteria Decision Making in Tourism Industry Based on Visualization of Aggregation Operators
## 5 Case Study
This leads to providing the corresponding criterion \(g[6]\) with a heavy auxiliary weight \(l[6]\) (gray parallelepiped on line \(l[6]\) in Figure 7) that forces a full 1 aggregation result in the case  
Figure 5: Initial view of the 3D balance model for criteria \(g[1],g[2],g[3]\). Figure 6: The 3D balance model after consideration of criteria \(g[4],g[5],g[6]\). \(g[6]\) equals 1: \(l[6]=\left\{ \begin{matrix}0,\;if\;g[6]=0\\ 1,\;if\;g[6]=1^{\prime}\end{matrix} ,\omega_{6}=2\right.\). The weight value \(\psi_{6}\) is assumed to be equal to zero because the influence of criterion \(g[6]\) on the plane tilt angle is conditioned only by weight \(l[6]\). We need such a difference in colors and shapes of weights corresponding to separate different types of criteria for the convenience of their visual perception by an expert. At Step 3 of the procedure, the decision maker thinks in the following way. At the previous step, all criteria combinations were derived with \(g[5]=0\) or \(g[6]=1\), for which the aggregation result is preset without considering all other criteria values. So, the values of other criteria are worthy of reviewing only if \(g[5]=1\) and \(g[6]=0\). The available criteria realizations mean criteria values for those hotels that can be judged by the decision maker. This, for example, shows that the decision maker personally stayed at those hotels and personally gave marks for these criteria in hotel surveys. The available realizations in our case are provided in Table 1.  
Hotel \(a\) has average comfort and service levels in comparison with other hotels, satisfies the decision maker in terms of pricing a little more than average; the \"smart\" technologies criterion is a little higher than average and satisfies the decision maker. Hotel \(b\) satisfies the decision maker most of all in terms of pricing compared to all known hotels but has relatively low comfort and service levels. Hotel \(c\) provides a relatively high level of comfort and services and uses \"smart\" technologies but satisfies the decision maker only by 0.1 in terms of pricing. The decision maker is hesitant to give each of the hotels a mark as the desired aggregation result and can only formulate personal preferences by a weak order for the set of available realizations. This weak order is as follows:  
\[a\succ_{A}b\succ_{A}c \tag{13}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Hotel**} & \multirow{2}{*}{**Comfort**} & \multirow{2}{*}{**Service**} & \multirow{2}{*}{**Price**} & \multicolumn{2}{c}{**“Smart”**} & \multirow{2}{*}{**Safety**} & \multirow{2}{*}{**Event**} \\  & & & & & & **Technologies** & \\ \hline  & \(g[1]\) & \(g[2]\) & \(g[3]\) & \(g[4]\) & \(g[5]\) & \(g[6]\) \\ \hline \(a\) & 0.6 & 0.8 & 0.8 & 0.6 & 1 & 0 \\ \hline \(b\) & 0.3 & 0.4 & 1.0 & 0.5 & 1 & 0 \\ \hline \(c\) & 0.8 & 0.9 & 0.1 & 0.7 & 1 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Available criteria realizations. Figure 7: The 3D balance model after fuzzy measure identification. At Step 4 of the procedure, the issue of the relative importance of the criteria is considered for the quantitative criteria \(g[1],\dots,\ g[4]\). The decision maker acknowledges that the most unimportant criterion is the use of \"smart\" technologies \(g[4]\). Among the remaining criteria, it is difficult for the decision maker to establish an importance range. The corresponding partial weak order over the set \(J\) of criteria indices can be viewed as:  
\[4\prec_{J}3;\ 4\prec_{J}1\ ;\ 4\prec_{J}2 \tag{14}\]  
At Step 5 of the procedure, the interactions between the criteria are considered. Here, the decision maker analyzes the quantitative criteria for their dependencies. And the decision maker thinks the following way at this step. In order to raise the general assessment of the hotel, it is sufficient to have either a high comfort level or a high service level. This is why the comfort criterion \(g[1]\) and service criterion \(g[2]\) have the effect of interchangeability and interact negatively.