## 6 Application of Methodology and Modeling to Museum Visitors  
To develop an AI model based on the multi-step process described for evaluating the emotional states of museum visitors, we created a structured algorithm that leverages machine learning and AI techniques for real-time analysis and response. Below, we present an AI model design with an associated flowchart for better understanding. **STEP Level 1: Stimulus-Response in the Museum Context**  
Figure 1: Emotion classes for emotivity. Figure 2: Emotion classes for affectivity (* means to distinguish the term when referring to a passionate person who has a comnotation of sensual/sexual passion for the things synonymous with love). In the context of a museum visit, an individual's state can be characterized as a four-dimensional tuple, S = (A, B, C, D), within the four-dimensional space, V. Our primary objective is to stimulate museum visitors with learning experiences (LEs) provided by the system, aiming to pre-quantify their emotional states. It is essential to note that this pre-quantification yields a trivalent output (\(-1\), \(0\), \(1\)), representing qualitative, rather than quantitative, emotional responses. For instance, consider a questionnaire consisting of twelve questions, three for each of the variable's A, B, C, and D. The outcome will be a score (\(-1\), \(0\), or \(1\)) for each emotion class:  
\[A=\frac{\sum  
**STEP LEVEL 4.1: EVALUATION OF EMOTIONS**  
In this phase, we introduce one or more parameters to derive a representative variable for the emotive state of the visitor. These parameters include the following quantities:  
1. Absolute current emotion \[\varepsilon(s)=\frac{\overset{\sim}{A}\overset{\sim}{B}\overset{\sim}{C}+\overset {\sim}{D}}{4}\leq 100\] (9)
2. Subjective emotion \[\xi(s)=\frac{\varepsilon(s)}{\varepsilon_{M}(s)}\times 100\] (10) where \(\varepsilon_{M}(s)\) is the maximum observed activity of the individual; if \(\varepsilon(s)>\varepsilon_{M}(s)\), then \[\frac{\varepsilon(s)}{\varepsilon_{M}(s)}=1\;e\;\varepsilon_{M}\;\text{becomes the new}\;\varepsilon(s).\] (11)  
Moreover, \(\overline{\varepsilon}(s)\) is the cumulative mean value of emotionality in different actions (different questionnaires given at different times); in other words, \(\overline{\varepsilon}(s)\) has the memory of the emotive state of the visitors. 3. Emotive distance of the visitor with respect to their mean value \[\zeta(s)=\varepsilon(s)-\overline{\varepsilon}(s)\] (12)
4. Emotive distance of the visitor with respect to the mean value of a group \[\rho(s)=\varepsilon(s)-\overline{\varepsilon}(s_{G})\] (13) where \(\text{s}_{G}\) is the relative state to a group. 5. Emotive derivative of a visitor with respect to their group \[\sigma(s)=\frac{\varepsilon(s)-\overline{\varepsilon}(s)}{\varepsilon(s)- \overline{\varepsilon}(s_{G})}\] (14)  
These parameters provide a comprehensive evaluation of the visitor's emotional and affective status within the museum context. **STEP LEVEL 4.2: Characterization OF EMOTIVITY IN THE MUSEUM**  
The status of a museum visitor can be characterized using the four parameters, A, B, C, and D. This approach is valid for both emotivity and affectivity states. As there are three possible values (\(-1\), \(0\), \(1\)) for each of the four parameters, there are a total of \(3^{4}=81\) possible combinations, describing the full range of emotional states when using emotive parameters. The same is true for the affections, meaning we have 81 possible combinations. When considering the total emotive and effective state, we have \(3^{8}\) different profiles of visitors, that is, 6561 different profiles of visitors. In summary, this methodology allows us to effectively assess and quantify the emotional and affective states of museum visitors, offering a valuable tool for enhancing the overall museum experience. Here, in the following, we set out the AI Implementation Strategy:  
* Neural Network: Use a Convolutional Neural Network (CNN) trained with supervised learning to predict real-time emotional states.