## 3 Proposed Model
### Fuzzy Inference System  
Fuzzy logic helps to identify the crucial genes among the available chromosomes. Hence, to determine the useful gene in the offspring population, fuzzy logic is incorporated in this block. A trapezoidal member function (MF) maps every element in the input space into a membership value called membership degree. Thus, it is expressed as a collection of four points (\(a,b,c,d\)) given in the below equation:  
\[\mu(y)=\left\{ \begin{array}{l}0,y\leq a,d\leq y\\ \frac{y-a}{b-a},a\leq y\leq b\\ 1,b\leq y\leq c\\ \frac{d-y}{d-c},c\leq y\leq d\end{array} \right\} \tag{1}\]  
In Equation (1), the Y coordinates of four edges of the underlying MF are (\(a<b<c<d\)). FIS contains the if-then rules to encode conditional propositions. The different fuzzy rules developed in our system are as follows:  
If smart_bin_distance_sensor < 0.2 THEN;  
Bin is empty;  
Else if smart_bin_distance_sensor > 0.2 AND smart_bin_distance_sensor < 0.6 THEN;  
Bin is partial_full;  
Else;  
Bin is Full. A Mamdani FIS is implemented in our proposed system. In this model, the consequences of the rules are represented using fuzzy sets. The mechanism is described below:  
1. Real inputs: The numerical data are observed as GA characteristics. The inputs are non-fuzzy values. 2. Fuzzify inputs: All fuzzy statements are resolved to a membership degree in the range of 0 to 1. 3. Fuzzy rules: The if-then rule statements are utilized as given below:
4. \(R_{i}\): If (in\({}_{1}\) is \(A_{11}\)) and \(\ldots\) (in\({}_{m}\) is \(A_{mi}\))then (out\({}_{1}\) is \(B_{1i}\)) and \(\ldots\) and (out\({}_{n}\) is \(B_{ni}\)). 5. Fuzzy operator applied to multi antecedents: If the antecedent has multiple fragments, antecedent is resolved to a single value between 0 and 1 is performed by fuzzy logic. 6. Applying implication technique: The degree of support is used for the entire rule to determine the output fuzzy set shape. The entire fuzzy set is assigned to the output. 7. Aggregation: The fuzzy set \(\mathrm{B_{r}}\) for every rule is aggregated as a single output fuzzy set \(\mathrm{B_{0}}\). 8. Defuzzification: The defuzzification input is a fuzzy set\(\mathrm{\mu}\) which is the aggregate output fuzzy set, and the output is a single value \(\mathrm{y^{*}}\). The centroid method is utilized for defuzzification. A defuzzification process given in Equation (2) is used to extract the output as follows:  
\[y^{*}=defuzz(B_{0})=\frac{\int_{y}y_{n}.\sum_{r=1}^{n}\mu B_{r}(y)dy}{\int_{y} \sum_{r=1}^{n}\mu B_{r}(y)dy} \tag{2}\]  
Defuzzified rate is the directly acceptable value of GA parameters, for example:  
Output#1 is tournament selection power;  
Output#2 is bit-mutation probability;y\({}_{1}\)* = 2 represents selection of binary tournament;  
y\({}_{2}\)* = 0.03 characterizes 3% mutation probability. A test function is deployed with the integration of cosine modulation to result in local minima. The function is highly continuous and multimodal. Achieving a global minimum standardization to a zero value of the objective function facilitates minimization. The function is given below:  
\[f_{1}\left(\overset{\rightarrow}{x}\right)=A.n+\sum_{i=1}^{n}\left(x_{i}^{2} -A.\cos(2\pi.x_{i})\right), \begin{array}{c}\overset{\rightarrow}{x}\in[-5.1 2,\ 5.12];\min f_{1}(\overset{\rightarrow}{x})=\\ 0,\ n\ldots\ dimensionality,\ A=10\end{array}  \tag{3}\]  
After defuzzification, the coefficient of the below equation is used to determine the final solid waste segregation represented in Equation (3). \[Totalwaste=\sum_{i=1}^{m}a_{i}x_{i}+\sum_{j=1}^{n}b_{iy}y_{ij} \tag{4}\]  
where \(a_{i}\) represents the population of a specific area, \(i\); \(x_{i}\) is the daily waste production value per person in the area \(i\); and \(b_{ij}\) is the total area of activity \(j\) in the area \(i\)_as_ determined by the defuzzification process. In addition, \(m\) specifies the distinct regions, and \(n\) represents the activities in every region.