## 4 Proposed Framework
### Adaptive Fuzzy Logic Deep-Learning Equalizer (AFL-DLE)
The excellent efficiency of the ReLU activating mechanism led to its selection. Equation (2)'s expression for the complexity ReLU activating factor, which assigns distinct ReLUs to neuron \(z\)'s real and imaginary parts, is what we utilize. \[\mathbb{C}ReLU(z)=ReLU(Re(z))+iReLU(im(z)) \tag{2}\]  
Figure 2: The architectural structure of the proposed AFL-DLE. In Equation (3), the mean square loss provides the complicated network's loss rate. \[E=\frac{1}{M}\sum_{m=1}^{M}e_{inner}\tilde{e_{inner}} \tag{3}\]  
The network values and biases are then adjusted using the suggested method. The sectioned equalization is prepared to normalize the input signs that still need to be seen after the training processes for \(Y_{\text{inner}}\) and \(Y_{\text{outer}}\) have been completed. Numerous traditional approaches fall short of expectations because they rely so much on precise statistical assumptions. Because of the inconsistencies and large deformations present in reality, it is not simple to derive an exact solution. Fortunately, these restrictions are not current with soft computing techniques since they are not dependent on a formal model, allowing for faster speed. In practice, these techniques are primarily used in several situations where the accuracy of statistical equations cannot be assured owing to massive inputs with high noise levels and continually shifting characteristics. Figure 2 depicts the adaptive fuzzy logic design. It has four levels: layers 1 and 2 make up the fuzzy rules' anterior portion and are made up of the inputs and fuzzification nodes, accordingly; layers 3 and 4 make up the fuzzy rules' subsequent portion and are made up of the fuzzy regulation and outcome nodes, accordingly. The variable matrix connects these layers. Any well-described nonlinear function may be consistently approximated by fuzzy logic over a limited set U to any level of precision. A participation mechanism named A that assigns each component of the discussion language \(X\) a participation score named A(l) in the range \([0,1]\) may be used to construct fuzzy series. As a result, the fuzzifier step entails translating a sharp input \(X\) into a fuzzy output A. The inferred mechanism is crucial for any fuzzy units because it combines the fuzzy values supplied by the fuzzification step with the information base IF-THEN rules to build a complete result fuzzy set. When paired with the fuzzified inputs, every rule in the information base is seen as having a fuzzy consequence, and Equation (4) defines the fuzzy set Bl as a result. \[\mu_{B}{}^{l}(\beta)=\sqcup_{a\in X}\Big{[}\mu A_{a}(\alpha)\cap R^{l}(\alpha, \beta)\Big{]} \tag{4}\]  
A phase of defuzzification is required before the sharp factor of the finalized result can be calculated. For fuzzy logic, various defuzzification strategies are available, such as the centroid and center-of-sums defuzzifiers. The result at the moment \(k\) may be represented as the following Equation (5) if a defuzzification technique that is routinely used, such as centroid, is utilized. \[\text{y}\hat{j}^{(k)}=\frac{\sum_{l=1}^{r}\theta_{l}\mu B^{l}(\beta)}{\sum_{l=1 }^{r}\mu B^{l}(\beta)} \tag{5}\]