## 4 The Model
### Modelling User-Exhibition Elements
#### 4.1.1 Representing Interaction Levels Using a Fuzzy Inference System  
The Interaction Levels Scale, proposed by [PERSON] and [PERSON] [8], has been used as a basis for our proposal of Interaction Levels Scale, but it is still unknown how we represent this interaction level using a FIS? First, we defined our own interaction levels scale. The scale was defined against six levels: (1) Extremely Low Interaction (ELI), (2) Very Low Interaction (VLI), (3) Low Interaction (LI), (4) Medium Interaction (MI), (5) High Interaction (HI) and (6) Extremely High Interaction (EHI). Against the scale, we defined the key features of each level and assigned a linguistic value with the finality to represent these in a FIS as output variables. The following is a summary of the proposed scale. **Level 0. ** The user is present in the exhibition module area and is shown a welcome message and related content. The user does not answer, only presence is confirmed. No interaction exists, only the action of being present. **Key Features**. Interactivity Null. No significant movements, only presence. **Linguistic Value**. Extremely Low Interaction (ELI). **Level 1. ** The user hears or sees the content, but no meaningful action is perceived. The exhibition module only provides general content (welcome message or content and basic exhibition information). The user receives information, but does not control the interaction. **Key Features**. Very Low Interactivity. Few movements. **Linguistic Value**. Very Low Interaction (VLI). **Level 2. ** The user has mental reasoning of the content provided by the exhibition, while the exhibition can analyse interactions, raise questions, encourage feedback and summarise fundamental ideas or relevant passages. Approaches arise from responses to user questions. **Key Features**. Low Interactivity. Few movements, comment stimulation, mental analysis. **Linguistic Value**. Low Interaction (LI). **Level 3. ** The User reasons with the content offered by the exhibition, while the exhibition indicates pauses in which the user develops different types of activities, including oral queries, complementing support material etc., allowing them to control the sequence of the activity, its flow and its continuity. **Key Features**. Medium Interactivity. Pauses indicated, oral activities, queries. **Linguistic Value**. Medium Interaction (MI). **Level 4. ** At this level, there is greater control between user-exhibition. The user can alter the message they receive by means of feedback i.e., they can select the desired information to receive. The user has the option to decide how, when and what part of the activity they want to develop. **Key Features**. High Interactivity. Control, feedback, desired data selection. **Linguistic Value**. High Interaction (HI). Figure 5: The agent system of the interactive museum exhibition module. Level 5 The user has the ability to feedback, control, create, communicate, adapt and produce the information provided by the exhibition. This level represents all the qualities of interactivity. During parts of the interaction, \"talk\" can occur between the user and exhibition (a \"talk\" using different means of interaction). **Key Features**. Extremely High Interactivity. Control, feedback, creativity, adaptation, productivity and desired data selection. **Linguistic Value**. Extremely High Interaction (EHI). The proposed scale was used as a reference to create the suitable model to measure the level of interaction. The ability to measure levels of interaction is essential to provide services or information that the user really needs; this is developed only by understanding the user. Nevertheless, how can we measure and represent this level of interaction using a FIS? It is desirable to have propositions of the reached level of interaction by the user for specific interactive activities. Computational solutions involved in the development of real-time interaction can be implemented to help in this process.