## 4 Research Methodology
### The Proposed Fuzzy KNN (TFKNN) Based on Uncertainty  
Based on the discovered research gap of the regular fuzzy KNN, Algorithm 1 demonstrates the steps of the standard fuzzy KNN classifier that has been proposed by [PERSON] et al. [49]. It is based on calculating the membership value using Equation (8) in line 10. It has complexity estimated as \(O(kn^{2}d)\), where \(k\) represents the number of available cluster(s), \(n\) represents the number of available instance(s), and \(d\) represents the dimensionality of the instance data. Their proposal has been widely used for classification based on measuring the distance of instance (x) between different available classes. The algorithm works to indicate the belief degree of classification in a simulation of the expert's experience and knowledge. The proposed fuzzy KNN works on handling the trade-off between classification accuracy and operational law for detecting diabetes. In [49], [PERSON] et al. have proposed a fuzzy KNN that differ from the regular classic fuzzy KNN in terms of the membership function. In which, they have used Equation (8) instead of Equation (7) as the membership function. This change in the membership function allows instance (x) to be assigned in each class based only on the distance from the class prototype. We use the uncertainty membership function, Equation (9), instead of Equation (8) to enhance the fuzzy KNN classification for the PIDD. If we deal with the belief degree (i.e., classification output) by probability theory, it will lead to wrong decisions. However, decision-making in the health system is critical, and the fuzzy set is not suitable for unsharp concepts. We need to enhance the uncertainty theory that is mainly characterized by the membership function and operation law. \[u_{i}(x)\ =\ \frac{\sum_{j=1}^{K}u_{ij}\Big{(}1/\left\|x-X_{j}\right\|^{2/(m-1 )}\Big{)}}{\sum_{j=1}^{K}\Big{(}1/\left\|x-X_{j}\right\|^{2/(m-1)}\Big{)}} \tag{7}\]  
Figure 5: The resulting confusion matrix represents the correlation of features based on PIDD. (**a**) Before processing. (**b**) After processing. \[u_{i}(x)\ =\ \frac{1/\left\|x-Z_{i}\right\|^{2/(m-1)}}{\sum_{j=1}^{c}\left(1/ \left\|x-Z_{i}\right\|^{2/(m-1)}\right)} \tag{8}\]  
\[u_{i}(x)\ =\ 0\leq\left(\sum_{j=1}^{m}w_{j}\ u_{ij}{}^{(x)}\right)\leq 1 \tag{9}\]  
Let us consider that Equations (7) and (8) are two available empirical membership functions by two domain experts. These empirical values can be applied using \(\max\ (0,Z)\)_where_\(Z=\frac{1}{1-e^{u_{A}(x)}}\) to make it easy for the model to generalize or adapt to a variety of possible ranges and to distinguish between the decisions. Hence, the membership value of instance (\(x\)) can be defined using Equation (10) as follows:  
\[\mu_{1}(x)\ =0\leq\ (\omega_{1}\mu_{A}(x)+\omega_{2}\mu_{B}(x))\ \leq 1 \tag{10}\]  
where (\(\omega_{1},\omega_{2}\)) are convex combination coefficients representing weights,  
\[\omega_{1}=\max\left(0,\frac{1}{1-e^{u_{A}(x)}}\right),\ \omega_{2}=\max \left(0,\frac{1}{1-e^{u_{B}(x)}}\right),\ \text{and}\ \omega_{1}+\omega_{2}=1\]  
where \(\mu_{A}(x)\) is a membership for \(x\) by Equation (7), and \(\mu_{B}(x)\) is a membership for \(x\) by Equation (8). In turn, \(\mu_{1}(x)\) is an uncertainty member function for instance (\(x\)). The proposed function has been widely accepted as effective for forecasting classification groups and applicable in a wide range of applications. The proposed membership function is used as a judgment or decision-aiding. Algorithm 2 has the same time complexity as Algorithm 1, determined by \(O(kn^{2}d)\). ```
Input:\(x\) instance Output:\(l\) class Label BEGIN
2 Input \(x\), vector to be classified. 3 Initialize \(i=1\). 4 DOUNTIL (distance from each prototype to \(x\) computed)
5 Compute distance from \(Z_{i}\) to \(x\). 6 Increment \(i\). 7 ENDDOUNTIL
8 Initialize \(i=1\).