## 2 Preliminaries
To use the Choquet fuzzy approach, we must first establish the fuzzy measure values that define the strength of each classifier. We include three different types of interaction in this section: \(f\left\{A\ U\ B\right\}=f\{A\}+f\{B\}=\) sum of individual strength of \(A\) and \(B\) is equal to \(\{A\ U\ B\}\), \(f\left\{A\ U\ B\right\}\leq f\{A\}+f\{B\}\) and \(f\left\{A\ U\ B\right\}\geq f\{A\}+f\{B\}\); Where \(A\) and \(B\)  
Figure 1: GoogleNet architecture. are two subsets of classifiers and mutually exclusive. \(f(S)\) indicates the strength of a set of classifiers. After obtaining a complete set of fuzzy measure scores and relevant scores for each classifier, we can utilize the Choquet fuzzy method to compute the classifiers' aggregated global score. Let \(g\) ( ) generate the fuzzy measure score of a collection of classifiers \(D=(d_{1},d_{2},d_{3}.\ldots.,\ d_{n})\), and \(P=(p_{1},p_{2},p_{3}.\ldots.,\ p_{n})\) are the individual classifier performance scores in D. Assume \(L_{i}\) is a subset of D, such that \(L_{i}=(d_{1},d_{2},d_{3}.\ldots.,\ d_{n})\) of D, where i is in between 1 and n. This indicates that, if i = 1 then \(L_{1}=(d_{1})\), and if i = 3, then \(L_{3}=(d_{1},d_{2},d_{3})\). Wealsoassumethat \((\ p_{1}\geq p_{2}\geq p_{3}.\ldots.\ \geq p_{n})\), then the aggregated score may be computed using the Choquet fuzzy integral, as shown in Equation (3):  
\[Choquet_{g}(p_{1},p_{2},p_{3}.\ldots.,\ p_{n})=p_{n}^{*}g(L_{n})+(p_{n-1}-p_{n} )^{*}g(L_{n-1})+\ldots+(p_{1}-p_{2})^{*}g(L_{1}) \tag{3}\]  
We compute the value of \(\lambda\) for determination of the fuzzy membership values using Equation (4):  
\[1+\lambda=\prod\
olimits_{i=1}^{n}(g(\{d_{i}\})\lambda+1) \tag{4}\]  
By obtaining the roots of the characteristic equation, we can find the value of \(\lambda\). By repeating Equation (5), the fuzzy membership value of each classifier combination can be determined:  
\[g(\{d_{i},\ d_{o}\})=g(\{d_{l}\})+g(\{d_{o}\})+\lambda g(\{d_{l}\})g(\{d_{o}\}) \tag{5}\]  
where \(1\leq 1\), o \(\leq\) n.  
We have p classifiers that are used to categorize q classes when dealing with classifier combinations. Let \(x_{ij}\) denote the confidence score of the \(j\)th class of the \(i\)th classifier. Choquet integral is now utilized for each \(j\) to produce a fuzzy confidence score. In this scenario, \(g(\{b_{j}\})\) represents each classifier's fuzzy membership scores, which are empirically determined for \(j=1,\ 2,\ 3\ldots q\), \(b_{i}=x_{ij}\), where \(i=1,\ 2,\ 3\ldots p\). In this study, however, we set the fuzzy measure \(g(\{b_{i}\})=w_{i}/w_{1}+w_{2}+w_{3}\ldots+w_{p}\), where \(w_{i}\) indicates the validation accuracy of the \(i\)th classifier. Even after the values of fuzzy measures have been set, the Choquet fuzzy integral can modify the weightage of each classifier by considering the decision scores supplied by the rest of the classifiers. This makes the system dynamic, as opposed to other assembly techniques that employ the majority voting and sugeno integral system. We must first obtain fuzzy measure values for each classifier before we can use the Choquet fuzzy ensemble. The fuzzy measure values indicate the strength of each classifier and all possible classifiers. Algorithm 1 depicts the key phases of the proposed methodology. **Majority Voting:** MV is a basic but effective ensemble learning approach that has been effectively utilized in a variety of industries. The fundamental concept behind MV is to use the majority voting rule to aggregate the output results from many data sources [40]. The majority voting rule is divided into three types: (i) unanimous voting, in which all classifiers must agree on a prediction; (ii) simple majority voting, in which the prediction must be supported by at least one more than half of the classifiers; and (iii) plurality or majority voting, in which the highest number of votes is considered for the ensemble decision whether the sum of those exceeds 50%.