# A New Approach for Deepfake Detection with the Choquet Fuzzy Integral
## 3 Proposed Method  
In our proposed method, we utilize different deepfake detection algorithms to process a video input, resulting in numerical outputs ranging from 0 to 1. These numerical values are then employed in the Choquet fuzzy integral algorithm. The Choquet fuzzy integral combines the outputs of the three algorithms, taking into account both the results and their assigned importance levels. If the output value from the Choquet fuzzy integral is below 0.50, the video is classified as fake; if it is above 0.50, it is considered real. Our goal in using the proposed method is to enhance deepfake detection by combining the outputs of three algorithms using the Choquet fuzzy integral. The steps of our proposed method are illustrated in Figure 3.  
Unlike the traditional fuzzy Choquet integral, we determined the fuzzy measures (\(g\)) with the help of genetic algorithms. This allows combinatorial fuzzy measures (\(g_{1,2}\), \(g_{1,3}\) etc.) to be calculated independently from the \(\lambda\) value calculated in the classical Choquet fuzzy integral method. In fuzzy measure notation, \(g_{1,2}=g\{x_{1},x_{2}\}\) and \(x\) corresponds to the DDAs in our study. Since \(g\{\varnothing\}=0\) and \(g\{x_{1},x_{2},x_{3}\}=1\) in fuzzy measure values, these are not included in the calculation. The constraint used to calculate fuzzy measure values with genetic algorithms is given in Equation (1). The super-additive interaction type was selected because having more than one model produce the same result will increase the confidence value for the result [15].  
\[g\{x_{i},x_{j}\}>g\{x_{i}\}+g\{x_{j}\},\ \ \ \ \ for\ all\ i,j\ where\ i\
eq j \tag{1}\]  
Figure 3: General diagram of the proposed method.  
The parameters pop_size = 16, max_iter = 50, and early_stopping = 10, which gave the best results through trial and error, were used to run the genetic algorithms. The crossover probability was set to 0.7 and the mutation probability was set to 0.3. Crossover and mutation operations were carried out as given in Equation (2) and Equation (3) respectively, where \(\{C_{1},C_{2},C_{3}\ldots,C_{n}\}\) is the population, and \(r\) refers to the randomly generated number. The correct classification rate was determined as the fitness function. Calculation of fuzzy measures with genetic algorithms is given in Figure 4.  
\[\begin{array}{l}h_{1}=0.5\ (C_{1}+C_{2})\\ h_{2}=1.5C_{1}-0.5C_{2}\end{array} \tag{2}\]  
\[C_{m}=h_{i}\pm r/4 \tag{3}\]  
Due to the fact that detection performance depends on extracted faces and models, we employed 3 different deepfake detection algorithms (DDAs), as summarized in Figure 5. We chose these algorithms because it has been observed that, while the Xception model gives better results in detection of real videos, the EfficientNet model gives better results in the detection of fake videos [14]. The main purpose of the study is demonstrating the usability of the Choquet fuzzy integral to increase the overall success. Therefore, we employed different face-extraction algorithms to obtain the output variety. For all models, a batch size of 64 is chosen, and default parameter values are used.  
Figure 4: Calculating fuzzy measures (\(g\) values) by genetic algorithm.