## 4 The Model
### Modelling User-Exhibition Elements
#### 4.1.1 Representing Interaction Levels Using a Fuzzy Inference System
In our propositions, we represent the level of interaction that is assumed, where the user has a specified evaluated level. Within this context, we consider it relevant to integrate fuzzy logic modelling to formalise levels of representation. In this case, the level of interaction is not a result of interaction or non-interaction type; instead, it is a result of all elements that complement the interaction (user profile, preferences, actions, behaviour, performance etc.). The fuzzy logic maintains its knowledge base using rules, making the implementation process more appropriate for exhibition reasoning in order to measure the level of user interaction. This proposed format makes the rules easier to maintain and easier to update the knowledge base. In this sense, this research analyses the data obtained directly from the user, in the context of interaction between user and exhibition using fuzzy logic to infer relevant information on the level of user interaction in relation to activities conducted. This information is obtained through fuzzy inputs that are used as inputs to the FIS; these inputs are: Presence (Pre), Interactivity (Int), Control (Ctl), Feedback (Fbk), Creativity (Cty), Productivity (Pdt), Communication (Com) and Adaptation (Ada). Each input value was collected using a scale from 0 (minimal value) to 1 (maximum value) derived from the user interaction behaviour. By performing ethnographic research, in a non-invasive way, we get the values based on human expert evaluations with inherent uncertainty. This research is developed in such a way that the model can be applied to different environment scenarios. The integration of the proposed scale and the FIS helps measure the level of interactions performed by users during user-exhibition interaction. To recognise the level of interaction, the variables are defined as resources generated by the user performance, considering data analysis simulations and real-time monitoring. The obtained variables are evaluated to identify its level of interaction, analysing the proposed scale through applying the FIS. We analysed information available about the exhibition, including its features, media communication, content, etc. and studied the performance data of users, considering their individual actions. The changes that occurred are of great importance to the interaction as they are used to feedback information to the model. The user has a set level of interactions during a given period. This measurement can handle uncertainty determined by a set of membership functions. The states caused by the user are the states that can be induced. We define plans, with each being specified by different membership functions, by linguistic variables that receive the level of user interaction in the process of interaction. Through these, the model can determine the most appropriate content, service or information to be shown to the user. The measurement of the level of interaction is composed of the input variables that are defined. Each variable has different membership values in the actions of users. When each user interaction begins, it results in different membership values being created that can vary the result of the actions. The interaction may have different levels (ELI, VLI, LI, MI, HI and EHI) to make a decision in order to provide services or information that are really needed by the user. The values of these levels can be interpreted in the calculations when monitoring and analysing the interaction between the user and exhibition; this is also used to determine subsequent interaction.