# Multicriteria Decision Making in Tourism Industry Based on Visualization of Aggregation Operators
## 5 Case Study  
The tourist industry often deals with the task of choosing a hotel stay based on multiple criteria. The decision maker in this case may be a tourist, a travel agency manager providing tours, or both. The decision maker's preferences can be clarified and formalized with the implementation of the 3D balance model. Let us review an example of aggregation-operator synthesis reflecting tourist preferences for hotel choice. During the first stage of this synthesis, it is necessary to choose hotel attributes that take part in this assessment. Research [32] represents the main 20 hotel attributes that provide this choice. Among these attributes we can define the most important ones: sleep quality, location, room quality, service, price, cleanliness [33]. These attributes were derived by means of studying text reviews by travelers from tripadviser.com which is one of the world's most popular web sites for travelers. On the one hand, the Choquet integral was implemented for modeling user preferences for hotel choices [15]. Keeping in mind that an average person can only keep track of seven objects in the operative memory simultaneously [34], we will limit this illustrative example of the 3D balance model to six criteria and will take the hotel attributes as described in [15,33]. We have chosen three generalized quantitative attributes: \(y_{1}\)--comfort, \(y_{2}\)--service, \(y_{3}\)--price. As well as that, we have chosen the following binary attributes, the values of which will be 0 for no and 1 for yes: \(z_{1}\)--attribute of presence or absence of services in the hotel provided with the use of intellectual technologies; \(z_{2}\)--attribute of safety hazard presence in the hotel; \(z_{3}\)--attribute of an event at the hotel that the tourist would like to visit if safety is ensured. The chosen attributes themselves can be presented as aggregation results of more detailed attributes. For example, attribute \(y_{1}\) (comfort) can be presented as a result of aggregating such attributes as room quality, sleep quality, location, air conditioning, safe deposit box and so on. Thus a decision-making model can be built for the decision maker as a hierarchy of aggregation operators using several instances of the balance model, each of which serves the purpose of corresponding to aggregation-operator synthesis. This entire hierarchy of 3D balance models can be reflected in the same virtual reality. Our illustrational case corresponds with the top level of such a hierarchy. In accordance with the above described procedure, the normalization of the chosen hotel attributes was realized. At Step 1 of the procedure, the values \(\min(y_{1})=\min(y_{2})=\min(y_{3})=0\); \(\max(y_{1})=\max(y_{2})=\max(y_{3})=100\) were obtained. The result of the step is explained by the fact that the first two top level attributes have fuzzy character and therefore can be estimated in percent values, and the price (third attribute) can be estimated in universal units. Though it should be noted that lower hierarchy aggregation levels can include other scales for such parameters, such as the distance to the beach or the average waiting time at the bar. At Step 2, the dependencies are built for those criteria where the growth of corresponding attributes leads to increases in aggregation results. These attributes are \(y_{1}\) and \(y_{2}\) because, according to the decision maker's reasoning, the higher the comfort and service quality, the higher the hotel assessment result should be. The mentioned dependencies are as follows:  
\[g[1]=\frac{y_{1}}{100} \tag{7}\]  
\[g[2]=\frac{y_{2}}{100} \tag{8}\]  
According to the decision maker, the higher the price per night, the lower the final hotel assessment shall be. Considering this, Step 3 of the normalization procedure constructs the equation:  
\[g[3]=1-\frac{y_{1}}{100} \tag{9}\]  
Steps 4 and 5 of the normalization procedure build dependencies for binary attributes \(z_{1}\) and \(z_{2}\). The decision maker's vision of this is the following.