## 5 Supervised Classification of Clients
### Customized Naive Associative Classifier (CNAC)
\begin{array}{ll}1&\quad if\ [x_{i}=?\lor y_{i}=?]\lor x_{i}=y_{i}\\ 0.3&\quad if\ x_{i},\ y_{i}\in\{dislikes,\ indirect\}\\ 0.3&\quad if\ x_{i},\ y_{i}\in\{dislikes,\ indirect\}\\ 0.3&\quad if\ x_{i},\ y_{i}\in\{dislikes,\ likes\}\\ \end{array} \right. \tag{28}\]  
\[s_{13}(x,\ y,\ A_{i})=\left\{\begin{array}{ll}1&\quad if\ [x_{i}=?\lor y_{i}=? ]\lor x_{i}=y_{i}\\ 0.3&\quad if\ x_{i},\ y_{i}\in\{A,B\}\\ 0.  
slower than NAC. This is due to, in our opinion, the change in the similarity operator, due to MIDSO is faster than the proposed AMIDSO. The computational complexity of NAC and CNAC algorithms includes its storage complexity and its training and classification complexity. The storing computational complexity of NAC is bounded by \(O(n*m)+O(3m)\) where \(n\) is the number of instances and \(m\) is the number of features, due to NAC stores the training set as well as the minimum, maximum and standard deviation values of each feature. For CNAC, the storage complexity is bounded by \(O(n*m)\) because it only stores the training set. Regarding storage, CNAC is less complex, although by little. The training complexity of the NAC is given by the computation of the standard deviations of features bounded by \(O(n*m)\) and the use of Differential Evolution (DE) to obtain feature weights. Using DE has a complexity bounded by \(O(it*np*f_{NAC})\), where \(it\) is the number of evaluations, \(np\) is the population number and \(S_{NAC}\) is the complexity of computing the fitness function (classifier performance of NAC over a portion of the testing set). Thus, the training complexity of NAC is bounded by \(O(n*m)+O(it*np*f_{NAC})\). The training complexity of CNAC is also given by the use of Differential Evolution to obtain feature weights. That is, it is bounded by \(O(it*np*f_{CNAC})\), where \(f_{CNAC}\) is the complexity of computing the fitness function (classifier performance of CNAC over a portion of the testing set). Regarding training complexity, there are two differences between NAC and CNAC: (a) the computing of standard deviations in NAC and (b) the similarity function used in the classifier, which affects the value of the fitness function. For the case of study, having a small number of instances, we can disregard the difference (a), and due to we are using the same values of \(it\) and \(np\), we consider the difference of NAC and CNAC with respect to execution time is given by the use of a different similarity function. The classification complexity of NAC is given by the similarity comparison of the unclassified instance with respect to the instances in the training set. The similarity computation complexity using the AMIDSO operator is given by \(O(m*1)=O(m)\) due to it only compares the feature values in a predefined way. Thus, the classification complexity of the NAC is bounded by \(O(n*m)\). The classification complexity of CNAC is also given by the similarity comparison of the unclassified instance with respect to the instances in the training set. This complexity is given by \(O(n*s)\) where \(s\) is the complexity of computing the similarity between instances. The complexity of AMIDSO operator is bounded by \(O(c*m)\), where c is the complexity of computing the feature similarity criterion. Thus, the total classification complexity of CNAC is bounded by \(O(n*m*c)\). According to classification, CNAC is more complex than NAC, due to the use of a customized similarity, which adds complexity to the classifier. Nevertheless, expending only ten seconds once to train the model is good enough for using it in a real environment, inside the electronic Customer Relationship Management system implemented in the hotel. Apart from the quantitative comparison, a qualitative comparison between our proposed CNAC and the other compared supervised classifiers is provided in Table 5. Due to all compared classifiers deal with mixed and incomplete data, and have some kind of transparency in their decisions, we include other aspects in the qualitative comparison.