Fuzzy Neighbor Research Articles

General Quasi Overlap Functions and Fuzzy Neighborhood Systems-Based Fuzzy Rough Sets With Their Applications

General Quasi Overlap Functions and Fuzzy Neighborhood Systems-Based Fuzzy Rough Sets With Their Applications

Adaptive fuzzy neighborhood decision tree

Decision tree algorithms have gained widespread acceptance in machine learning, with the central challenge lying in devising an optimal splitting strategy for node sample subspaces. In the context of continuous data, conventional approaches typically involve fuzzifying data or adopting a dichotomous scheme akin to the CART tree. Nevertheless, fuzzifying continuous features often entails information loss, whereas the dichotomous approach can generate an excessive number of classification rules, potentially leading to overfitting. To address these limitations, this study introduces an adaptive growth decision tree framework, termed the fuzzy neighborhood decision tree (FNDT). Initially, we establish a fuzzy neighborhood decision model by leveraging the concept of fuzzy inclusion degree. Furthermore, we delve into the topological structure of misclassified samples under the proposed decision model, providing a theoretical foundation for the construction of FNDT. Subsequently, we utilize conditional information entropy to sift through original features, prioritizing those that offer the maximum information gain for decision tree nodes. By leveraging the conditional decision partitions derived from the fuzzy neighborhood decision model, we achieve an adaptive splitting method for optimal features, culminating in an adaptive growth decision tree algorithm that relies solely on the inherent structure of real-valued data. Experimental evaluations reveal that, compared with advanced decision tree algorithms, FNDT exhibits a simple tree structure, stronger generalization capabilities, and superior performance in classifying continuous data.

Granular Ball Fuzzy Neighborhood Rough Sets-Based Feature Selection via Multiobjective Mayfly Optimization

Granular Ball Fuzzy Neighborhood Rough Sets-Based Feature Selection via Multiobjective Mayfly Optimization

Properties of Cubic Fuzzy Competition Graphs with Applications

This study extends the concept of competition graphs to cubic fuzzy competition graphs by introducing additional variations including cubic fuzzy out-neighbourhoods, cubic fuzzy in-neighbourhoods, open neighbourhood cubic fuzzy graphs, closed neighbourhood cubic fuzzy graphs, cubic fuzzy (k) neighbourhood graphs and cubic fuzzy [k]-neighbourhood graphs. These variations provide further insights into the relationships and competition within the graph structure, each with its own defined characteristics and examples. These cubic fuzzy CMGs are further classified as cubic fuzzy k-competition graphs that show competition in the k th order between components, p -competition cubic fuzzy graphs that concentrate on competition in terms of membership degrees, and m -step cubic fuzzy competition graphs that analyze competition in terms of steps. Further, some related results about independent strong vertices and edges have been obtained for these cubic fuzzy competition graph classes. Finally, the proposed concept of cubic fuzzy competition graphs is supported by a numerical example. This example showcases how the framework of cubic fuzzy competition graphs can be practically applied to the predator-prey model to illustrate the representation and analysis of ambiguous information within the graph structures.

Noise-resistant fuzzy multineighbourhood rough set-based feature selection with label enhancement and its application for multilabel classification

Noise pollution in process of feature selection greatly reduces the classification efficacy of multilabel data, and the estimation of label descriptions is insufficient because of the lack of label enhancement for label distribution learning. To overcome the limitations, this work presents a noise-resistant fuzzy multineighbourhood rough set-based feature selection methodology with label enhancement and its application for multilabel classification. First, under the fuzzy T-equivalence relation, to construct new adaptive fuzzy neighbourhood class, the multineighbourhood radius set on feature space is integrated with fuzzy neighbourhood radius via sample interval on label space; then, the adaptive fuzzy multineighbourhood granules are obtained. Second, by integrating the parameterized fuzzy decision of labels and adaptive fuzzy multineighbourhood granules, noise-resistant lower and upper approximations via fuzzy multineighbourhood are constructed. A noise-resistant multilabel fuzzy multineighbourhood rough set model and its noise-resistant approximate accuracy can be proposed. Third, the description degree of label is computed to design label proportion after label enhancement. Certain fuzzy multineighbourhood entropy measures are developed to obtain label enhancement-based mutual information. When the algebraic and information perspectives are fused, label enhancement-based mutual information with fuzzy multineighbourhood via approximate accuracy is presented to evaluate the final association relationship between the features and label sets. Finally, a multilabel feature selection strategy via label enhancement will be constructed to obtain the best feature subset. The experimental results applied to 14 multilabel datasets indicate that this algorithm is significant.

Enhancing wind power generation prediction using relevance assessment-based transfer learning

Accurate wind power generation forecasting can help build a reliable grid; however, the limited dataset makes accurate forecasting results a challenging work. This study introduces a relevant assessment-based transfer learning architecture to solve this problem. Linear fuzzy neighborhood mutual information is adopted to assess the relevance of the source domain selection. A convolutional structure with long-term memory architecture is designed as the deep learning model. The pre-trained model is transferred to the other wind turbines by calculating the linear fuzzy neighborhood mutual information. The proposed model avoids the lack of a dataset from analogous turbines. The simulation results indicate the proposed model surpasses the popular models in forecasting accuracy and exhibits superior time efficiency compared to popular deep-learning approaches.

Density peaks clustering based on Gaussian fuzzy neighborhood with noise parameter

Density peak clustering (DPC) is an effective clustering method known for its robustness, non-iterative nature, and hybrid approach. However, it is not without limitations: (a) the determination of the cutoff distance (dc) relies on human experience, which can significantly impact the clustering outcome; (b) DPC does not take into account the local structure of the data when computing local densities; (c) it employs a crisp kernel for density computation; (d) the performance of DPC is affected by chain reactions; and (e) DPC often struggles to handle noisy data. In order to address these limitations, this paper proposes a novel approach called DPC based on Gaussian fuzzy neighborhood with noise parameter (DPC-GFNN). The proposed method leverages a Gaussian fuzzy kernel to enhance the separation between clusters and mitigates the influence of outliers through an adjustable noise parameter (λ). DPC-GFNN utilizes a k-nearest neighbor graph based on density to label highly dense regions. This technique effectively avoids chain reactions by assigning accurate labels to points in border areas, enabling proper clustering of data with diverse shapes and densities. To evaluate the effectiveness of DPC-GFNN, a series of experiments are conducted on both real-world and synthetic datasets. The experimental results demonstrate that DPC-GFNN exhibits superior robustness and clustering accuracy compared to other modified variants of DPC including DPC based on k-nearest neighbors (DPC-KNN), improved DPC (IDPC), DPC based on density backbone and fuzzy neighborhood (DPC-DBFN), and DPC based on fuzzy weighted k-nearest neighbors (FKNN).

Joint Projected Fuzzy Neighborhood Preserving C-means Clustering with Local Adaptive Learning

Graph-based dimensionality reduction approaches are extensively applied for preserving the intrinsic structures of high-dimensional data. To capture discriminative information from data clusters that lack a clear manifold structure, previous studies have combined clustering algorithms with local manifold structure preservation. These methods assume that two neighbor data points share the same cluster label. However, the assumption may not hold for Fuzzy C-Means which may assign two nearby data points to different clusters depending on the distance between data points and cluster centroids. This inconsistency degrades the performance in clustering and dimensionality reduction. To tackle this issue, we propose a novel approach for dimensionality reduction, termed joint Projected Fuzzy Neighborhood Preserving C-means Clustering with Local Adaptive Learning (PFNPCM). PFNPCM learns cluster centroids, sparse membership grades, embedded subspaces, and structured graphs simultaneously and extracts both global and local structures of data. Through clustering data that preserves the local neighborhood structure in a low-dimensional space instead of the original one, PFNPCM can effectively capture both global and local information from the inherent manifold structure and cluster structure. The employment of ℓ2,1-norm as the distance metric in the clustering and the preservation of neighborhood structure further ensure the robustness of clustering results against noise or outliers. To achieve the consistency of the captured global and local discriminative information, PFNPCM adopts a novel fuzzy local similarity measure based on the manifold structure, and the manifold assumption thus holds when partitioning unlabeled samples into subgroups. Massive experiments on diverse well-known datasets demonstrate that PFNPCM is superior to some state-of-the-art methods.

Fuzzy Neighborhood-Based Manifold Learning and Feature Weight Matrix for Multilabel Feature Selection

In recent years, it has been difficult to determine neighborhood radii with almost all feature selection methodologies, and the existing multilabel feature selection approaches neglect these correlations among labels, which results in poor classification efficiency. To address these flaws, a fuzzy neighborhood-based manifold learning model and a feature weight matrix are developed to study multilabel feature selection in this article. First, the difference coefficient of the given samples and the new classification margin of each sample are defined to construct an adaptive fuzzy neighborhood radius. While considering the influences of features and labels on the similarity relationships of samples, a novel fuzzy neighborhood similarity relationship is developed by combining it with the label similarity approach that uses the Jaccard similarity coefficient. Second, the least-squares regression model is introduced to design a loss function for learning the mapping relationship between the feature and label spaces. To constrain the objective function, a regularization term based on the fuzzy neighborhood similarity relationship matrix is developed to establish a manifold learning model. To reduce the complexity of the loss function and to reduce the induced structural risk, the final objective function is constructed by incorporating two graph Laplacian matrices. Third, positive and negative confidence values are presented to incorporate the frequency parameter and to form the dependencies between labels into a new label correlation matrix. A new feature weight matrix integrated with the dependencies between labels is defined to learn the correlations between features and labels. Finally, an embedded feature selection method with an objective function is designed, where the objective function is optimized by the gradient descent scheme. Experiments conducted on 12 multilabel datasets reveal that the proposed approach yields better classification results than do other algorithms.

Multi-label feature selection using self-information in divergence-based fuzzy neighborhood rough sets

Multi-label feature selection corresponds to pattern recognition and knowledge mining, and its application has been expanded to different scenarios. As an excellent processing platform for uncertain and ambiguous information, divergence-based fuzzy rough sets (Div-FRSs) have been proposed and applied to feature selection. However, there are three critical problems to be solved when applying Div-FRSs to multi-label learning. The first is how to effectively dispose the noise produced by features in multi-label data. The second is how to synthetically consider the relevance among all labels. The last is how to thoroughly mine the uncertainty brought by upper approximations neglected in Div-FRSs existing researches. To address these issues, this study presents a new divergence-based fuzzy neighborhood rough set model (Div-FNRSs) for multi-label learning using self-information. First, the divergence-based fuzzy neighborhood relation and class are gradually raised to manage the noise in multi-label data, and fuzzy decision is introduced to dispose all labels as a whole. Combining them together, a new model Div-FNRSs is constructed. Then, divergence-based fuzzy neighborhood self-information containing upper approximations and lower approximations is designed to depict distinguishing ability of features through three-level uncertainty measure establishment and granulation property exploration. Furthermore, feature significance for choosing the optimal features is given and it motivates a heuristic feature-selection algorithm DivFNSI-FS. Finally, data experiments are completed to validate DivFNSI-FS effectiveness with six state-of-the-art multi-label feature selection approaches on fourteen multi-label datasets. A conclusion can be drawn that DivFNSI-FS outperforms existing algorithms to obtain better performance on eight commonly-used evaluation indexes.

Consistency approximation: Incremental feature selection based on fuzzy rough set theory

Fuzzy Rough Set Theory (FRST)-based feature selection has been widely used as a preprocessing step to handle dynamic and large datasets. However, large-scale or high-dimensional datasets remain intractable for FRST-based feature selection approaches due to high space complexity and unsatisfactory classification performance. To overcome these challenges, we propose a Consistency Approximation (CA)-based framework for incremental feature selection. By exploring CA, we introduce a novel significance measure and a tri-accelerator. The CA-based significance measure provides a mechanism for each sample in the universe to keep members with different class labels within its fuzzy neighbourhood as far as possible, while keeping members with the same label as close as possible. Furthermore, our tri-accelerator reduces the search space and decreases the computational space with a theoretical lower bound. The experimental results demonstrate the superiority of our proposed algorithm compared to state-of-the-art methods on efficiency and classification accuracy, especially for large-scale and high-dimensional datasets.

Multigranulation variable-scale fuzzy neighborhood measures and corresponding Choquet-like integrals for feature selection

Choquet-like integrals, a nonlinear fuzzy aggregation function, are diffusely applied in several real problems. However, the corresponding fuzzy measures in them are provided by human intervention and not by data-driven methods. As an effective knowledge representation tool, rough set models in different approximation spaces are established for data processing. Particularly, the multigranulation fuzzy β-covering approximation space has been concerned with only a single scale β∈(0,1]. However, different granulation structures should have different scales. Therefore, establishing a multigranulation approximation space with a variable scale by inducing fuzzy measures through data-driven methods and using corresponding Choquet-like integrals in practical problems is a significant challenge. To address this challenge, the notion of multigranulation variable-scale fuzzy Θ-covering group approximation space is presented here, as well as multigranulation variable-scale fuzzy neighborhood measures in it. Furthermore, Choquet-like integrals with the presented measures are constructed to solve the issue of feature selection (i.e., attribute reduction) under the new approximation spaces. Firstly, the concept of multigranulation variable-scale fuzzy Θ-covering group approximation space is presented, where different fuzzy β-coverings have different scales β∈Θ. Moreover, multigranulation variable-scale fuzzy neighborhood measures in it, as fuzzy measures, are presented. Subsequently, Choquet-like integrals with multigranulation variable-scale fuzzy neighborhood measures are constructed. A novel attribute reduction method under Choquet-like integrals with multigranulation variable-scale fuzzy neighborhood measures is proposed for any decision information table. Finally, the presented method is selected for solving problems of classification and diagnosis of rolling bearing faults. Several public data sets are used to demonstrate the effectiveness and feasibility of the presented methods mentioned above.

M-step inverse fuzzy mixed competition graphs

The notion of competition graphs has a wide range of applications and has been utilized in designing various ecological problems and real-world competitions. Here, the idea of m-step inverse fuzzy mixed competition graphs has been introduced and some of its basic properties have been discussed. Also, some ideas associated with the concept of m-step inverse fuzzy mixed competition graphs, such as m-step inverse fuzzy neighborhood graph, inverse fuzzy mixed economic competition graph, and m-step inverse fuzzy mixed economic competition graph have been defined. Our motive was to focus on the real-life problems that can be properly addressed with graphs involving directed and undirected edges. In this case, the concept of an m-step fuzzy competition graph is not appropriate for solving these problems. However, the idea of m-step inverse fuzzy mixed competition graphs is more relevant to address them. An application of m-step inverse fuzzy mixed competition graphs has been identified as a suitable solution to a real-life problem.

Uncertainty measures and feature selection based on composite entropy for generalized multigranulation fuzzy neighborhood rough set

With the continuous advancement of information technology, the information and data covered by various information systems become increasingly complex and diverse, it is essential to perform knowledge mining from multiple perspectives to extract valuable insights. Fuzzy neighborhood multigranulation rough set, as an excellent feature selection model, is capable of handling heterogeneous datasets more effectively, significantly improving learning efficiency. In this study, we investigate a feature selection method based on a generalized multigranulation fuzzy rough set (GMFNRS) in fuzzy decision systems. First, the concepts of fuzzy neighborhood rough sets and generalized multigranulation rough sets are introduced. Subsequently, the GMFNRS model is established to enable data mining and rule extraction from various perspectives. Secondly, from an informational perspective, the study investigates uncertainty measurement methods through fuzzy neighborhood joint entropy. Furthermore, a novel fuzzy neighborhood generalized composite entropy is proposed by integrating the GMFNRS model with uncertainty measures. Finally, a forward greedy feature selection algorithm is considered to extract essential information from complex datasets. Experimental results on 15 public datasets demonstrate that the proposed model effectively selects important features in fuzzy systems and exhibits excellent classification performance.

Online group streaming feature selection based on fuzzy neighborhood granular ball rough sets

Online group streaming feature selection holds significant research value in large-scale streaming data processing scenarios, and the related work based on rough set theory has attracted academic interest. Nevertheless, most relevant algorithms come with parameters, and performing a grid search for the optimal parameters reduces the efficiency. Moreover, the existing online group streaming feature selection frameworks cannot effectively fit the situation in practice. Focusing on these issues, this paper investigates an online group streaming feature selection method based on fuzzy neighborhood granular ball rough sets. First, Canopy clustering is introduced to granular ball computing, and the adaptive neighborhood of samples is generated based on the granular ball distribution. Second, we construct a fuzzy neighborhood granular ball rough set (FNGBRS) model and propose the integrated dependence degree to achieve maximal dependency and minimum classification error. Then, the purity of granular balls is considered as the weight of features, and some uncertainty measures based on FNGBRS are presented. Finally, we define a random factor to control the size of streaming groups and design an online group streaming feature selection algorithm. Comparative experimental results on sixteen public datasets demonstrate that the proposed algorithm exhibits superior and stable classification performance, coupled with increased efficiency from its parameter-free design.

DFNO: Detecting Fuzzy Neighborhood Outliers

DFNO: Detecting Fuzzy Neighborhood Outliers

Forecasting cryptocurrencies volatility using statistical and machine learning methods: A comparative study

Forecasting cryptocurrency volatility can help investors make better-informed investment decisions in order to minimize risks and maximize potential profits. Accurate forecasting of cryptocurrency price fluctuations is crucial for effective portfolio management and contributes to the stability of the financial system by identifying potential threats and developing risk management strategies. The objective of this paper is to provide a comprehensive study of statistical and machine learning methods for predicting daily and weekly volatility of the following four cryptocurrencies: Bitcoin, Ethereum, Litecoin, and Monero. Several models and forecasting methods are compared in terms of their forecasting accuracy, i.e., HAR (heterogeneous autoregressive), ARFIMA (autoregressive fractionally integrated moving average), GARCH (generalized autoregressive conditional heteroscedasticity), LASSO (least absolute shrinkage and selection operator), RR (ridge regression), SVR (support vector regression), MLP (multilayer perceptron), FNM (fuzzy neighbourhood model), RF (random forest), and LSTM (long short-term memory). The realized variance calculated from intraday returns is used as the input variable for the models. In order to assess the predictive power of the models considered, the model confidence set (MCS) procedure is applied. Our experimental results demonstrate that there is no single best method for forecasting volatility of each cryptocurrency, and different models may perform better depending on the specific cryptocurrency, choice of the error metric and forecast horizon. For daily forecasts, the method that is always found in a set of best models is linear SVR, while for weekly forecasts, there are two such methods, namely FNM and RR. Furthermore, we show that simple linear models such as HAR and ridge regression, perform not worse than more complex models like LSTM and RF. The research provides a useful reference point for the development of more sophisticated models.

Working Memory Classification Enhancement of EEG Activity in Dementia: A Comparative Study

The purpose of the current investigation is to distinguish between working memory ( ) in five patients with vascular dementia ( ), fifteen post-stroke patients with mild cognitive impairment ( ), and fifteen healthy control individuals ( ) based on background electroencephalography (EEG) activity. The elimination of EEG artifacts using wavelet (WT) pre-processing denoising is demonstrated in this study. In the current study, spectral entropy ( ), permutation entropy ( ), and approximation entropy ( ) were all explored. To improve the classification using the k-nearest neighbors ( NN) classifier scheme, a comparative study of using fuzzy neighbourhood preserving analysis with -decomposition ( ) as a dimensionality reduction technique and the improved binary gravitation search ( ) optimization algorithm as a channel selection method has been conducted. The NN classification accuracy was increased from 86.67% to 88.09% and 90.52% using the dimensionality reduction technique and the channel selection algorithm, respectively. According to the findings, reliably enhances discrimination of , , and participants. Therefore, WT, entropy features, IBGSA and NN classifiers provide a valid dementia index for looking at EEG background activity in patients with and .

Fuzzy neighborhood Choquet integrals with overlap functions and their applications in attribute reduction

In fuzzy rough sets, fuzzy neighborhood operators and fuzzy rough approximate operators are mainly used by traditional methods to deal with the problem of attribute reduction (i.e., feature selection). However, they are parametric linear, while the corresponding weights are additive measures. For complex data, parametric linear operators and additive measures do not reflect correlations among data (or attributes). Therefore, it is important to develop non-additive measures and nonlinear operators for attribute reduction, which can effectively find those attributes that are not needed to reach a decision from the viewpoint of correlations. Along these lines, in this work, OI-fuzzy β-neighborhood measures (i.e., non-additive measures) and generalized Choquet integrals (i.e., nonlinear integrals) are presented by using overlap functions to deal with the problem of attribute reduction under the fuzzy β-covering approximation space. First, four pairs of OI-fuzzy β-neighborhood operators are constructed based on the implementation of overlap functions and their residual implications in a fuzzy β-covering approximation space. Furthermore, four pairs of OI-fuzzy β-neighborhood measures, as non-additive measures, are introduced to instead of rough approximate operators in data mining. Then, a novel method with respect to OI-fuzzy β-neighborhood measures is presented to deal with the attribute reduction in a fuzzy β-covering information decision table. Third, four pairs of generalized Choquet integrals based on the employment of OI-fuzzy β-neighborhood measures are constructed. On top of that, another method with respect to these generalized Choquet integrals is proposed to deal with the attribute reduction in a fuzzy β-covering information decision table. Finally, the presented methods are used to deal with the problem of classification. Several public data sets are applied to illustrate the feasibility and effectiveness of the above-mentioned proposed methods.

Adaptive intuitionistic fuzzy neighborhood classifier

Adaptive intuitionistic fuzzy neighborhood classifier