The Fuzzy K-Nearest Neighbour (FKNN) method is a classification approach that integrates fuzzy theories with the K-Nearest Neighbour classifier. The algorithm computes the degree of membership for a given dataset within each class and then chooses the class with the highest degree of membership as the assigned classification outcome. This algorithm has several applications in regression problems. When the mathematical model of the data is not known, this method can be used to estimate and approximate the value of the response variable. This paper introduces a method, which incorporates a parameter distance measure to empower decision makers to make precise selections across several levels. Furthermore, we provide an analysis of the algorithm's strengths and shortcomings, as well as a comprehensive explanation of the distinctions between the closest neighbour approach in tasks of classification and regression. Finally, to further elucidate the principles, we present a range of examples that demonstrate the application of closest neighbour algorithms in the classification and regression of fuzzy numbers.

In this paper, we introduce an approximation for the $k$-nearest neighbor graph ($k$-NNG) on a point set $P$ in $\mathbb{R}^d$. For any given $\varepsilon>0$, we construct a graph, that we call the \emph{approximate $k$-NNG}, where the edge with the $i$th smallest length incident to a point $p$ in this graph is within a factor of $(1+\varepsilon)$ of the length of the edge with the $i$th smallest length incident to $p$ in the $k$-NNG. For a set $P$ of $n$ moving points in $\mathbb{R}^d$, where the trajectory of each point $p\in P$ is given by $d$ polynomial functions of constant bounded degree, where each function gives one of the $d$ coordinates of $p$, we compute the number of combinatorial changes to the approximate $k$-NNG, and provide a kinetic data structure (KDS) for maintenance of the edges of the approximate $k$-NNG over time. Our KDS processes $O(kn^2\log^{d+1} n)$ events, each in time $O(\log^{d+1}n)$.

Guanidine hydrochloride has been widely used in the initial recovery steps of active protein from the inclusion bodies in aqueous two-phase system (ATPS). Knowledge of the guanidine hydrochloride effect on the liquid-liquid equilibrium (LLE) phase diagram behavior is still inadequate and no comprehensive theory exists for the prediction of the experimental trends. Therefore, the effect of the guanidine hydrochloride on the phase behavior of PEG4000+potassium phosphate+ water system at different guanidine hydrochloride concentrations and pH was investigated in this study. To fill the theoretical gaps, the typical support vector machines were applied was applied to the k-nearest neighbor method in order to develop a regression model to predict the LLE equilibrium of guanidine hydrochloride in the above mentioned system. Its advantage is its simplicity and good performance, with the disadvantage of an increase in the execution time. The results of our method are quite promising; they were clearly better than those obtained by well-established methods such as Support Vector Machines, k-Nearest Neighbor and Random Forest. It is shown that the obtained results are more adequate than those provided by other common machine learning algorithms.

As networking and communication technology become more widespread, the quantity and impact of system attackers have been increased rapidly. The methodology of intrusion detection (IDS) is generally classified into two broad categories according to the detection approaches: misuse detection and anomaly detection. In misuse detection approach, abnormal system behavior is defined at first, and then any other behavior is defined as normal behavior. The main goal of the anomaly detection approach is to construct a model representing normal activities. Then, any deviation from this model can be considered as an anomaly, and recognized to be an attack. Recently much more attention is paid to the application of lattice theory in different fields. In this work we propose a lattice based nearest neighbor classifier capable of distinguishing between bad connections, called attacks, and good normal connections. A new nonlinear valuation function is introduced to tune the performance of the proposed model. The performance of the algorithm was evaluated by using KDD Cup 99 Data Set, the benchmark dataset used by Intrusion detection Systems researchers. Simulation results confirm the effectiveness of the proposed method.

Load forecasting is a key component of electric utility operations and planning. Because of today's highly developed electricity markets and rapidly growing power systems, load forecasting is becoming an essential part of power system operation scheduling. This paper proposes a new short-term load forecasting model based on the large margin nearest neighbor (LMNN) classification algorithm to improve prediction accuracy. The accuracy of many classification methods, such as k-nearest neighbor (k-NN), is significantly influenced by the technique used to calculate sample distances. The Mahalanobis distance is one of the most widely used methods for calculating distance. Numerous techniques have been used to enhance k-NN performance in recent years, including LMNN. Our proposed approach aims to solve the local optimum problem of LMNN, compute data similarities, and optimize the cost function that establishes the distances between instances. Before using gradient descent to determine the ideal parameter values for the cost function, we employ a genetic algorithm to shrink the size of the solution space. Additionally, our method's forecasting errors are contrasted with those of the BPNN and ARMA models. The comparative findings show how well the recommended forecasting model performs in short-term load forecasting.

Introduction: Diabetes or diabetes mellitus is a metabolic disorder in body when the body does not produce insulin, and produced insulin cannot function normally. The presence of various signs and symptoms of this disease makes it difficult for doctors to diagnose. Data mining allows analysis of patients’ clinical data for medical decision making. The aim of this study was to provide a model for increasing the accuracy of diabetes prediction. Method: In this study, the medical records of 1151 patients with diabetes were studied, with 19 features. Patients’ information were collected from the UCI standard database. Each patient has been followed for at least one year. Genetic Algorithm (GA) and the nearest neighbor algorithm were used to provide diabetes prediction model. Results: It was revealed that the prediction accuracy of the proposed model equals 0. 76. Also, for the methods of Naï ve Bayes, Multi-layer perceptron (MLP) neural network, and support vector machine (SVM), the prediction accuracy was 0. 62, 0. 65, and 0. 75, respectively. Conclusion: In predicting diabetes, the proposed model has the lowest error rate and the highest accuracy compared to the other models. Naï ve Bayes method has the highest error rate and the lowest accuracy.