## 4 The Model
### Modelling User-Exhibition Elements
#### 4.1.2 Implementing the Fuzzy Inference System  
Unlike other models that use different paradigms through heuristics, our proposed model adopts a fuzzy set theory to build knowledge provided by users. We present uncertainty of information in a better and more appropriate manner. We have represented, in accordance with environmental inputs, variables (Pre, Int, Ctl, Fbk, Cty, Pdt, Com and Ada) with their respective membership functions which define the output (interaction level). The result of this implementation is written by a fuzzy value and, in this case, is given a linguistic value. The update process is dynamic and is altered according to a user's performance during interaction. Membership functions were modelled by considering an initial user profile, ensuring a more accurate result for assessing the level of user interaction. Different activities were created with the intention to vary from low to high uncertainty to assess the level of interaction by each user. The implementation of a FIS for the purpose of effective utilization requires the use of programs that directly apply fuzzy logic functions. Some utility programs have specific modules to facilitate the accomplishment of this task, as is the case of the Fuzzy Logic Toolbox of MATLAB (MATLAB vR2017B. The MathWorks Inc., Natick, MA, USA, 2017) [26] that contains a library based on the C language, that contains a library based on the C language, providing the necessary tools to conduct effective fuzzification. JTZFIS (JT2 FIS v1.0. Universidad Autonoma del Estado de Baja California, Mexicali, BC, Mexico, 2016) [27], a tool-kit for interval Type-2 fuzzy inference system, can be used to build intelligent object-oriented applications and provide an effective fuzzification method and tools; this utility was used to implement the proposed FIS (see Figure 5). The model inputs are the variables that can be perceived by the exhibition; these are the performance data of the user interaction. As we consider the input variables (Pre, Int, Ctl, Fbk, City, Pdt, Com and Ada) and the output variable (interaction level) to the FIS, these are associated with a set of membership functions. The output function comprises six linguistic variables: (ELI, VLI, LI, MI, HI and EHI). Gaussian functions were used as this type of membership function has a soft non-abrupt decay. The FIS was implemented building inference rules covering all linguistic variables, composed by the operator associated with the minimum method. Aggregation rules are made by the maximum method. Table 1 depicts these base rules; thus, this is identified as the knowledge base representation. At this stage, to enable the FIS, the fuzzy toolboxes of MATLAB [26] and JT2 FIS [27] Tool-kits were used, simulating and entering the 500 users to be analysed; modifying user inputs generates a set of inputs with each one with set values, exemplifying the performance of the user's interaction. These values are subjected to the FIS that return an output variable (Interaction level). The proposed fuzzy model provides a universe of six levels of interaction. These levels were defined with different values for the parameters of membership levels. This makes it possible to develop a knowledge base that allows a set of applications of membership functions that vary according to interaction and user performance; this is because the membership functions are altered to represent states with different degrees of uncertainty. One example is to build an initial function that is more flexible and categorizes users within sets (ELI, VLI LI MI, HI and EHI). Figure 6 depicts the variations of uncertainty from the first to last level of our fuzzy universe. To verify the user's corresponding level of interaction, according to their inputs, we evaluate the defuzzification output of the resulting level.