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Clustering is a crucial technique used to identify the structure of data sets. It involves the task of splitting groups into different clusters based on suitable similarity measures. Fuzzy C-Means is a clustering technique that extends the fuzzy set theory. It is a widely used method among existing fuzzy clustering algorithms due to its easy implementation and straightforward approach. However, it still has some drawbacks, such as high sensitivity to outliers or noisy data, as well as to initialization conditions. Therefore, this paper proposes a modification to the Fuzzy C-Means algorithm using Fuzzy Chebyshev. The preprocessing of raw datasets includes the use of MinMax Scaler. Additionally, dimensional reduction techniques are applied to effectively address issues related to high-dimensional data. To determine the optimal number of clusters in the data set, the Elbow method is implemented. The final clustering is achieved by employing Fuzzy Chebyshev to replace the distance measurement component in the Fuzzy C-Means algorithm. A comparison between the proposed method and previous methods is performed. The effectiveness of the proposed method is illustrated through a numerical example involving genomic data of prostate cancer. Comparable results are presented to validate the feasibility of the proposed method. The results demonstrate that the proposed method aligns with those obtained from previous methods. [ABSTRACT FROM AUTHOR]

Missing data imputation is a critical task in the data pre-processing stage to ensure the quality, stability, and reliability of machine learning models. If missing values are imputed incorrectly, it can result in erroneous predictions and inconsistent model performance. Traditional imputation methods often struggle with complex data patterns having non-linearity and uncertainties. By integrating soft clustering principles, the proposed work provides a flexible framework for imputing missing data by taking into account the underlying inherent data pattern. To address the missing data challenges, this paper presents a novel imputation technique called Radial Basis Kernel Intuitionistic Fuzzy Ⅽ-Means Imputation (KIFCMI), which builds upon the standard Intuitionistic Fuzzy Ⅽ-Means (IFCM) technique. KIFCMI explores the application of centroid-based imputation using IFCM by incorporating the RBF kernel-induced metric in the data space as a replacement for the original Euclidean norm metric. By employing a kernel function, KIFCMI enables the clustering of data that lacks linear separability within the original space, enabling the formation of homogeneous clusters in a space of higher dimensionality. The effectiveness of the proposed imputation technique is validated on ten diverse real-world datasets obtained from the Public Library UCI with 10% and 20% missing data. The comparative analyses of the proposed technique KIFCMI, is carried out with three conventional techniques, namely fuzzy c-means imputation (FCMI), kernelized fuzzy c-means imputation (KFCMI), and intuitionistic fuzzy c-means imputation (IFCMI). The experimental results using two performance measures, namely RMSE and MAE, showcase the robustness and versatility of the proposed technique across other imputation outcomes. This research paper contributes to the evolving landscape of missing data imputation, offering insights into the practical applications of fuzzy clustering techniques. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel approach for the early detection of skin disorders, aiming to improve the prediction accuracy and precision. Our motivation lies in addressing the challenges posed by the uncertainty in skin lesion features. To achieve this, we employ fuzzy-based segmentation techniques to enhance the quality of skin disorder image processing. Additionally, we explore the integration of intensity data to further refine the segmented images. Our methodology consists of three main steps: segmentation, feature extraction, and classification. We begin by inputting the image into the segmentation phase, followed by the application of a fuzzy c-means clustering process to improve the segmentation output. From the resulting segmented image, we extract features using local binary pattern and local Gabor XOR pattern techniques. These features are then subjected to classification, employing a hybrid classifier that combines Convolutional Neural Networks (CNN) and Long Short-Term Memory (LSTM) networks. The use of this hybrid classifier is particularly significant, as it leverages the strengths of both CNN and LSTM to enhance the predictive power of our model. Through rigorous experimentation, we have achieved promising results. Our proposed method exhibits an impressive accuracy of 94.6% and precision of 95.5% in comparison to the Conventional FCM Model, which only achieves an accuracy of 87% and precision of 82.5%. [ABSTRACT FROM AUTHOR]

This paper proposes a hierarchical support vector machine based classifier for autocoding. The purpose of this method is to improve classification accuracy utilizing numerical features obtained from probability scores by support vector machine (SVM). The proposed method captures the tendency to be incorrectly predicated for each label from the probability scores obtained from SVM. Using the captured information, we train new support vector machines for each targeted label considering the feature of the targeted label to improve the classification accuracy. The numerical examples with governmental survey data show a better performance of the proposed method. [ABSTRACT FROM AUTHOR]

Magnetic Resonance Fingerprinting (MRF) is a new quantitative technique of Magnetic Resonance Imaging (MRI). Conventionally, MRF requires sequential correlation of the acquired MRF signals with all the signals of (a large sized) MRF dictionary. This is a computationally intensive matching process and is a major challenge in MRF image reconstruction. This paper introduces the use of clustering techniques (to reduce the effective size of MRF dictionary) by splitting MRF dictionary into multiple small sized MRF dictionary components called MRF signal groups. The proposed method has been further optimized for parallel processing to reduce the computation time of MRF pattern matching. A multi-core GPU based parallel framework has been developed that enables the MRF algorithm to process multiple MRF signals simultaneously. Experiments have been performed on human head and phantom datasets. The results show that the proposed method accelerates the conventional MRF (MATLAB based) reconstruction time up to 25× with single-core CPU implementation, 300× with multi- core CPU implementation and 1035× with the proposed multi-core GPU based framework by keeping the SNR of the resulting images in a clinically acceptable range. Furthermore, experimental results show that the memory requirements of MRF dictionary get significantly reduced (due to efficient memory utilization) in the proposed method. • MRF is a new quantitative technique of acquiring and processing MRI data. • Major limitations of the MRF in its clinical utilization include long reconstruction time and significant memory requirement. • A new technique utilizing parallel architecture to reduce computation time as well as effective memory utilization of MRF. • Proposed method introduces clustering techniques to reduce the effective memory requirements of MRF dictionary. • Reduction in the memory requirements reduces the computation complexity, hence reduce the computation time of MRF. [ABSTRACT FROM AUTHOR]

The generalized multiplicative fuzzy C-means (GMFCM) clustering is a novel and potentially competitive fuzzy clustering method. However, the convergence speed of this method is relatively slow. Therefore, a fast generalized multiplicative fuzzy C-means clustering algorithm is proposed in this paper. First, an affinity filtering method based on triangular inequalities is utilized to identify a complete set of non-affinity cluster centers for each sample with low computational complexity. Then, a new multiplicative membership scaling scheme is proposed to modify the multiplicative fuzzy membership between each sample and its non-affinity cluster centers to a non-zero minimum, while increasing the multiplicative fuzzy membership between each sample and its affinity cluster centers. Finally, a new fast algorithm combining these two techniques is proposed to accelerate the convergence process of GMFCM. Extensive experiments on numerical data and images confirm that the proposed algorithm is faster and significantly reduces the number of GMFCM iterations. Specifically, the algorithm reduces the number of iterations by more than 60% compared with the original GMFCM algorithm. At the same time, the running time of the algorithmic process is also greatly reduced. [Display omitted] • An affinity filtering method for searching non-affinity cluster centers of samples is developed. • A scaling scheme for modifying multiplicative fuzzy membership is originally proposed. • A fast algorithm of multiplicative fuzzy partition clustering is designed in this paper. • Experimental results indicate that the proposed algorithm has higher running efficiency. [ABSTRACT FROM AUTHOR]

White button mushrooms (Agaricus bisporus) are soft-cellular and susceptible to color changes accounting significant postharvest losses due to brown spots on their cap surface. In this study, a portable hyperspectral imaging camera in the visible-near infrared wavelength range (400–1000 nm) was explored to determine browning effects in time series on white button mushrooms stored at 4 °C while relative humidity kept constant at 60 % and 80 % relative humidity (RH), respectively. This study proposed the combination of unsupervised training algorithms using principal component analysis (PCA) combined with fuzzy C-means clustering (FCM) for mushroom image segmentation and calibration data selection for further supervised training approaches. Thus, the supervised classification models of k-nearest neighbor (k-NN) and partial least square-discriminant analysis (PLS-DA) were developed for the determination of browning patterns on mushrooms and achieved the correct classification rate (CCR) values of 97.6 %-99.8 % and 94.7 %-97.7 %, respectively. Overall, this time-series study during storage demonstrated the potential of a portable hyperspectral imaging camera combined with machine learning models for post-harvest mushroom quality control purposes. • A time-series study was conducted for post-harvest mushroom quality control. • The portable HSI camera shows application potential to detect mushroom browning. • Fuzzy C-means with PCA boosted the reliability and accuracy of ML calibration. • Developed models achieved >94.7 % CCR in mushroom browning detection pixel wisely. [ABSTRACT FROM AUTHOR]

This study offers a novel country-level longitudinal investigation of conditions, including, income, urbanity, education, R&D, and entrepreneurial activity, driving international trade, for imports and exports. The configurational (clustering) approach places emphasis on country and year groupings, offering 'targeted' understanding on country level variations of international trade in cultural goods. The study explores context sensitive conditions affecting international trade in cultural goods, including environment for entrepreneurship, and entrepreneurial processes. Emphasis is given to configurational considerations of clusters of country-year observations based on conditions. Inferences inferred will be country groups-based perspectives. Using UIS and GEM datasets, fuzzy c-means clustering is employed for economic development-related conditions measuring, income, urbanity, education, R&D, and entrepreneurial activity, to establish clusters of country-year observations, based on differences in the condition values describing them. These clusters are defined to give qualitative understanding of their individuality. Validation of clusters is undertaken with consideration of differences on levels of international trade of cultural goods, in terms of forms of imports and exports. To complement the validation, cluster profiling is undertaken, with consideration of population age and poverty levels. The study contributes increased understanding concerning drivers (conditions) of trade in cultural goods, and impact of entrepreneurship in both imports and exports. • The study offers a novel country level analysis of international trade in cultural goods. • Contributes to discussion on trade drivers in cultural goods and impact of entrepreneurship in both imports and exports. • A country-level analysis of namely: income, urbanity, education, research and development, and entrepreneurial activity. • Uses longitudinal data and a fuzzy c-means clustering approach. • Employed a configurational approach focuses on country and year groupings, providing nuanced understanding. [ABSTRACT FROM AUTHOR]

For a wind farm, the collection system can directly influence the investment cost, the connected number of wind turbines, and the operation reliability. In general, it is difficult to generate a high-quality design solution for the collection system when considering various constraints (e.g., bypassing the obstacle zone), especially for a large-scale wind farm with numerous wind turbines. To address this complex and challenging issue, a region-partitioned obstacle avoidance strategy for large-scale offshore wind farm collection systems (OWFCS) considering buffer zones is innovatively presented. Firstly, the optimization model for OWFCS is formulated to minimize both cable investment and construction costs. A buffer zone with several buffer points is originally constructed, upon which the obstacle zone can be bypassed via connecting with buffer points instead of the inner points of the obstacle zone. Subsequently, a radial fuzzy C-means (RFCM) based region-partitioned clustering strategy for OWFCS is developed to narrow the solution space, thus reducing the complexity and difficulty of optimization. Furthermore, an automated submarine cable selection method named obstacle spanning tree (OST) is presented and integrated into a firefly algorithm (FA) to seek the optimal collector system topology. Finally, the case studies validate that the proposed method is effective in optimizing OWFCS topology with both single and multiple obstacle zones. Compared with other approaches, the proposed method demonstrated advantages in terms of stability and cost optimization effectiveness for OWFCS with obstacle zones after 10 independent runs. • Buffer zone is proposed for topology design of a large-scale offshore wind farm. • A novel region-partitioned obstacle avoidance strategy is designed. • The submarine cable type can be determined by the obstacle-spanning-tree method. • Both of single and multiple obstacle zones can be handled by the proposed method. • The proposed method is superior on the stability and cost optimization. [ABSTRACT FROM AUTHOR]

In this paper we study the fuzzy clustering problem with capacity constraints. Despite of the fact that the fuzzy clustering approach is widely encountered in the literature, the inclusion of capacity constraints is recent and has several practical applications. We propose a general formulation of the clustering problem, where each point has an associated weight and the sum of the weights of the points that compose each group is established a priori. We discuss existence of solutions of the involved problems, providing a mathematical foundation for the established formulas. Besides, we propose a practical algorithm for solving this problem and present its convergence analysis. This algorithm follows an alternate minimization scheme, wherein a given iteration addresses the problem first in terms of the probabilities of each point x j belonging to each cluster i , denoted as u i j , finding subsequently the position of the centroids, c i , i = 1 , ... , g , j = 1 , ... , n. This procedure is K-means-like, with the distinction that, as a point does not exclusively belong to a group, the computation of u i j requires optimization techniques. In our case, this involves solving a linear system derived from the Karush–Kuhn–Tucker (KKT) conditions. With the aim of validating our algorithm, we present numerical tests with synthetic and real-world data to demonstrate its performance for the given problems. Since the proposal successfully solved these numerical tests within a reasonable computational time, it can be considered a valuable resource for addressing real-world applications. [ABSTRACT FROM AUTHOR]

The Fuzzy C-means clustering (FCM) algorithm has gained prominence as a widely utilized technique for data partitioning and image segmentation in various applications. Nevertheless, it exhibits certain limitations in its current form, primarily in its inability to effectively incorporate spatial information from images and its diminished robustness and accuracy when confronted with noisy image data. This paper proposes an adaptive sparse regularization FCM algorithm for noisy image segmentation based on complementary spatial information. Firstly, a novel local spatial operation based on the non-averaging idea and a novel non-local spatial operation based on wavelet transform are proposed. Combining these two kinds of spatial information, we construct the FCM objective function incorporating the complementary spatial information. Secondly, the absolute pixel difference between the original image and the local and non-local information is computed, using the absolute difference and its inverse to achieve adaptation computation of critical parameters. Finally, the sparse regularization term is introduced into the objective function of FCM, which reduces the number of iterations of the algorithm. In addition, we also designed a three-step iterative algorithm to solve the sparse regularization-based FCM model, which consists of a Lagrange multiplier method, a hard threshold operator, and a normalization operator, respectively. Numerous experiments on synthetic images and authentic images on the BSDS500 dataset show that the proposed algorithm is superior to state-of-the-art algorithms. Furthermore, extensive experiments on different types of authentic images on different databases show that the proposed algorithm has good generalization performance and may be applied in most image segmentation situations. [ABSTRACT FROM AUTHOR]

The increasing demand for Indonesian female caregivers to Taiwan, raises issues related to caregiver burden. In this study, a segmentation analysis of 299 questionnaire data that consisted of Zarit Burden Interview (ZBI) instrument and four dimensions: personal strain, role strain, dependency, and guilt (PRDG) was conducted to find selection pattern strategies of prospective caregivers based on their characteristics. The results of confirmatory factor analysis (CFA) indicated the need to add "social life" as a new dimension (S+PRDG) representing the caregivers' social problems, while the results of multiple regression analysis indicated three most influential characteristics of a caregiver: number of children, education level, and work location. The segmentation analysis was carried out using Fuzzy C-Means on the modified PRDG model which is (S+PRDG) and resulted two best segments that have a fuzzy silhouette index value of 0.61. From the analysis of these two segments, the resilient caregivers were those in the second segment with the characteristics such as having children, having level of education up to junior high school, and working in the capital city of Taiwan. [ABSTRACT FROM AUTHOR]

After facing the COVID-19 pandemic, national and local governments in Indonesia realized a gap in the distribution of health care and human health practitioners. This research proposes two unsupervised learning methods, K-Means and Fuzzy C-Means (FCM), for clustering a list of hospital data in Jakarta, Indonesia, which contains information about the number of its human health resources. The datasets used in this study were obtained from the website the Ministry of the Health Republic of Indonesia provided through the content scraping method. The result shows that implementing K-Means and FCM clustering results in the same number of clusters. Nevertheless, both results have different areas and proportions that can be observed by three distance metrics, such as Hamming, Euclidean, and Manhattan distance. By using the clustering result using the K-Means algorithm, the hospital list was separated into three clusters with a proportion of 84.82%, 14.66%, and 0.52% for clusters 0, 1, and 2, respectively. Meanwhile, using the FCM algorithm, the hospital list was separated into three clusters with a proportion of 17.80%, 73.82%, and 8.38% for clusters 0, 1, and 2, respectively. To the best of our knowledge, this is the first discussion of clustering healthcare facilities in Indonesia, especially hospitals, based on their health professionals. [ABSTRACT FROM AUTHOR]

Gliomas are the brain tumors in glial cells, which are categorized into four numerical grades, I-II-III-IV, to quantize the aggressiveness and severity of the tumors; while divided into two major groups, high-grade (HG) and low-grade (LG), in general. Among many differences between these groups, one of the most distinct and characteristic features could be seen in the shape of the tumor boundaries by magnetic resonance imaging (MRI). Due to aggressive nature of the HG tumors in proliferation phase, the boundaries of HG tumors become more shape-wise complex compared to the LG tumors, which could be differentiated by analyzing the fractal complexity of the cell membranes. However, the complexity cannot be either manually calculated or estimated by eye inspection without a reference point with one single image or sometimes even with an image set. Therefore, we present an automated glioma grading framework to provide an insight on the grades with a novel contouring and fractal dimension analysis system. The primary component of the proposed system is an automated Nakagami imaging module with a specialized fuzzy c-means algorithm to contour the boundaries of the whole tumors. The contoured images, afterwards, are analyzed by the Minkowski–Bouligand and Hausdorff methods for two panning options to generate the fractal dimensions and to estimate the fractal complexities for classifying the gliomas The results are greatly encouraging that the overall classification accuracy is computed as 88.31 % using the basic support vector machines (SVM) classifier; while as 91.96 % with the arbitrary thresholding appended. The outcomes of this paper with implementable mathematical infrastructure would be very useful and beneficial as an expert system in intelligent and automatic glioma grading, for researchers and medical experts. • We proposed a novel automated glioma-grading framework. • 2D FLAIR MRI images consisting of HG and LG gliomas are analyzed. • Raw images are highlighted by Nakagami module and contoured by fuzzy 2-means. • Fractal dimensions of the contoured images are analyzed by two methods. • Overall accuracy is computed as ACC=91.96 % with a SVM classifier. [ABSTRACT FROM AUTHOR]

Medical image segmentation is crucial for understanding anatomical or pathological changes, playing a key role in computer-aided diagnosis and advancing intelligent healthcare. Currently, important issues in medical image segmentation need to be addressed, particularly the problem of segmenting blurry edge regions and the generalizability of segmentation models. Therefore, this study focuses on different medical image segmentation tasks and the issue of blurriness. By addressing these tasks, the study significantly improves diagnostic efficiency and accuracy, contributing to the overall enhancement of healthcare outcomes. To optimize segmentation performance and leverage feature information, we propose a Neighborhood Fuzzy c-Means Multiscale Pyramid Hybrid Attention Unet (NFMPAtt-Unet) model. NFMPAtt-Unet comprises three core components: the Multiscale Dynamic Weight Feature Pyramid module (MDWFP), the Hybrid Weighted Attention mechanism (HWA), and the Neighborhood Rough Set-based Fuzzy c-Means Feature Extraction module (NFCMFE). The MDWFP dynamically adjusts weights across multiple scales, improving feature information capture. The HWA enhances the network's ability to capture and utilize crucial features, while the NFCMFE, grounded in neighborhood rough set concepts, aids in fuzzy C-means feature extraction, addressing complex structures and uncertainties in medical images, thereby enhancing adaptability. Experimental results demonstrate that NFMPAtt-Unet outperforms state-of-the-art models, highlighting its efficacy in medical image segmentation. [ABSTRACT FROM AUTHOR]

A novel procedure to perform fuzzy clustering of multivariate time series generated from different dependence models is proposed. Different amounts of dissimilarity between the generating models or changes on the dynamic behaviours over time are some arguments justifying a fuzzy approach, where each series is associated to all the clusters with specific membership levels. Our procedure considers quantile-based cross-spectral features and consists of three stages: (i) each element is characterized by a vector of proper estimates of the quantile cross-spectral densities, (ii) principal component analysis is carried out to capture the main differences reducing the effects of the noise, and (iii) the squared Euclidean distance between the first retained principal components is used to perform clustering through the standard fuzzy C -means and fuzzy C -medoids algorithms. The performance of the proposed approach is evaluated in a broad simulation study where several types of generating processes are considered, including linear, nonlinear and dynamic conditional correlation models. Assessment is done in two different ways: by directly measuring the quality of the resulting fuzzy partition and by taking into account the ability of the technique to determine the overlapping nature of series located equidistant from well-defined clusters. The procedure is compared with the few alternatives suggested in the literature, substantially outperforming all of them whatever the underlying process and the evaluation scheme. Two specific applications involving air quality and financial databases illustrate the usefulness of our approach. • A novel approach to perform fuzzy clustering of multivariate time series. • Detecting general types of dependence in multivariate processes. • Effective and efficient clustering in time series datasets. • Combining the quantile-based metric and the fuzzy logic. • Meaningful clustering of the companies in the S&P 500 index. [ABSTRACT FROM AUTHOR]

Recently, the polynomial-based radial basis function neural networks (P-RBFNNs) have been successfully applied to regression tasks. However, the redundant and non-linear partitioned data easily interfere with accurate partitioning of clusters completed in P-RBFNNs, affecting the regression performance of this existing model. Because the squared error is used as the cost function of the learning method, P-RBFNNs are sensitive to noise interference. In order to cope with these problems, this study introduces a double iterative learning-based polynomial based-RBFNNs (DP-RBFNNs) modeling that focuses on the formation of architectures to improve the accuracy of regression performance as well as enhance the robustness through double iterative learning as follows: a) support vector-based Gaussian kernel fuzzy c-means (SV-GKFCM) as a kind of the support vector-based kernel fuzzy clustering are designed to determine connections (weights) between the input and hidden layers of the proposed model. SV-GKFCM helps effectively reduce the number of redundant data to re-modify the partitioning of clusters in the DP-RBFNNs. In addition, the cluster centers can be accurately updated from the non-linear partitioned data with the aid of Gaussian kernel distance in SV-GKFCM; b) least absolute shrinkage deviations (LASD) as a robust estimation are designed to update connection weights between the hidden and output layers. The SAE (sum of absolute error) function in the LASD method is used as a cost function to reduce the noise interference in the procedure of weight estimation as well as enhance the robustness of the DP-RBFNNs. The superiority of the proposed model is demonstrated through the experimental results. [ABSTRACT FROM AUTHOR]

As an important technology in artificial intelligence, Granular Computing has emerged as a new multi-disciplinary paradigm and received much attention in recent years. Information granules forming an abstract and efficient characterization of large volumes of numeric data have been considered as the fundamental constructs of Granular Computing. By generating centroids (prototypes) and partition matrix, fuzzy clustering is a commonly encountered way of information granulation. As a reverse process of granulation, degranulation involves data reconstruction completed on a basis of the granular representatives (decoding information granules into numeric data). Previous studies have shown that there is a relationship between the reconstruction error and the performance of the granulation process. Typically, the lower the degranulation error is, the better performance of granulation process becomes. However, the existing methods of degranulation usually cannot restore the original numeric data, which is one of the important reasons behind the occurrence of the reconstruction error. To enhance the quality of reconstruction (degranulation), in this study, we develop an augmented scheme through modifying the partition matrix. By proposing the augmented scheme, we elaborate on a novel collection of granulation-degranulation mechanisms. In the constructed approach, the prototypes can be expressed as the product of the dataset matrix and the partition matrix. Then, in the degranulation process, the reconstructed numeric data can be decomposed into the product of the partition matrix and the matrix of prototypes. By modifying the partition matrix, the new partition matrix is constructed through a series of matrix operations. We offer a thorough analysis of the developed scheme. The experimental results are in agreement with the underlying conceptual framework. The results obtained on both synthetic and publicly available datasets are reported to show the enhancement of the data reconstruction performance thanks to the proposed method. It is pointed out that by using the proposed approach in some cases the reconstruction errors can be reduced close to zero by using the proposed approach. [ABSTRACT FROM AUTHOR]

World is facing stress due to unpredicted pandemic of novel COVID-19. Daily growing magnitude of confirmed cases of COVID-19 put the whole world humanity at high risk and it has made a pressure on health professionals to get rid of it as soon as possible. So, it becomes necessary to predict the number of upcoming cases in future for the preparation of future plan-of-action and medical set-ups. The present manuscript proposed a hybrid fuzzy time series model for the prediction of upcoming COVID-19 infected cases and deaths in India by using modified fuzzy C-means clustering technique. Proposed model has two phases. In phase-I, modified fuzzy C-means clustering technique is used to form basic intervals with the help of clusters centroid while in phase-II, these intervals are upgraded to form sub-intervals. The proposed model is tested against available COVID-19 data for the measurement of its performance based on mean square error, root mean square error and average forecasting error rate. The novelty of the proposed model lies in the prediction of COVID-19 infected cases and deaths for next coming 31 days. Beside of this, estimation for the approximate number of isolation beds and ICU required has been carried out. The projection of the present model is to provide a base for the decision makers for making protection plan during COVID-19 pandemic. • A hybrid fuzzy time series based model is proposed. • FCM clustering is modified by using an exponential function to tolerate noisy data. • Present model is able to predict approximate COVID-19 infected cases and deaths. • The model presents prediction of COVID-19 infected cases and deaths for next 31 days. [ABSTRACT FROM AUTHOR]

In recent years, classical fuzzy clustering-based neural networks (FCNNs) have been successfully applied to regression tasks. The determination of the parameters such as cluster centers of the existing hard c-means (HCM) or fuzzy c-means (FCM), leads to the performance deterioration of the model because of the sensitivity of HCM or FCM to noise and outliers. Moreover, there are also several factors for over-fitting and degradation of the robustness of the ensuing model. To solve such problems, two improved clustering techniques and L 2 norm-regularization are considered in the proposed robust fuzzy clustering-based neural networks (RFCNNs) modeling. SVs-based hard c-means (SVs-based HCM) and SVs-based fuzzy c-means (SVs-based FCM) designed with support vectors (SVs) can reduce the interference of uncorrelated data, including noise and outliers, thereby enhancing the main data characteristics effectively, as well as leading to the construction on the improved network model. L 2 norm-regularization can be used to alleviate the degradation of robustness caused by overfitting. In terms of improving the performance of the model through SVs-based HCM or SVs-based FCM, as well as robustness completed through L 2 norm-regularization, the superiority of RFCNNs was verified by experimenting with synthetic data and publicly available data from machine learning datasets. [ABSTRACT FROM AUTHOR]

One of the most critical factors in SDN networks is the controller placement. The controller's location determines the network delay. Reduction in network latency can help to scale the network effectively. A Fuzzy C-Means approach is used for placement of controller in optimized manner to improve the network latency. A topology-zoo network data-set, such as OS3E and Chinanet, were used to validate the proposed FCMCP. This technique offers faster response time than K-Clustering methods such as K-Center, K-Mean, etc. Finally, the Fuzzy C-Means method reduces latency by 18% when compared to the K-Clustering methods. [ABSTRACT FROM AUTHOR]

In a recent paper published in this very journal, the "Bounded fuzzy possibilistic method" (BFPM) was proposed. We point out that there are some critical flaws in the said algorithm, which makes the results presented therein highly questionable. In particular, the method does not generate meaningful cluster membership degrees and fails to converge when run on some well-known benchmark data sets. [ABSTRACT FROM AUTHOR]

Recently, smart data has attracted great attention in the smart city community since it can provide valuable information to support intelligent services such as planning, monitoring, and decision making. However, it imposes a big challenge to explore smart data from big data gathered from smart city with various advanced fusion and analysis approaches. This paper proposes an incremental tensor-based fuzzy c-means approach (IT-FCM) for obtaining smart data from continuously generated big data. Specifically, a weighted version of the tensor-based fuzzy c-means approach (T-FCM) is firstly proposed to cluster the dataset that combines the previous cluster centroids and the new generated data. Aiming to improve the clustering efficiency, the old data objects are represented by the centroids to avoid repeat clustering. Furthermore, this paper presents an edge-cloud-aided clustering scheme to fuse big data from different sources and perspectives and further to implement co-clustering on the fused datasets for exploring smart data. Finally, the proposed IT-FCM approach is evaluated by comparing with T-FCM regarding clustering accuracy and efficiency on two different datasets in the experiments. The results state that IT-FCM outperforms T-FCM in clustering streaming big data in terms of accuracy and efficiency for obtaining smart data. • An edge-cloud-aided computing system for co-clustering is presented. • An edge-cloud-aided computing system for co-clustering is presented. • Experiments are conducted to evaluate the presented approach. [ABSTRACT FROM AUTHOR]

The efficient segmentation of customers of an enterprise is categorized into groups of similar behavior based on the RFM (Recency, Frequency and Monetary) values of the customers. The transactional data of a company over is analyzed over a specific period. Segmentation gives a good understanding of the need of the customers and helps in identifying the potential customers of the company. Dividing the customers into segments also increases the revenue of the company. It is believed that retaining the customers is more important than finding new customers. For instance, the company can deploy marketing strategies that are specific to an individual segment to retain the customers. This study initially performs an RFM analysis on the transactional data and then extends to cluster the same using traditional K-means and Fuzzy C- Means algorithms. In this paper, a novel idea for choosing the initial centroids in K- Means is proposed. The results obtained from the methodologies are compared with one another by their iterations, cluster compactness and execution time. [ABSTRACT FROM AUTHOR]

Semi-supervised clustering aims to guide the clustering by utilizing auxiliary information about the class labels. Among the semi-supervised clustering categories, the constraint-based approach uses the available pairwise constraints in some steps of the clustering procedure, usually by adding new terms to the objective function. Considering this category, Semi-supervised FCM (SSFCM) is a semi-supervised version of the fuzzy c -means algorithm, which takes advantage of fuzzy logic and auxiliary class distribution knowledge. Despite the performance enhancement caused by incorporating this extra knowledge in the clustering process, semi-supervised fuzzy approaches still suffer from some problems. All the data attributes in the feature space are assumed to have equal importance in the cluster formation, while some features may be more informative than others. Thus the feature importance issue is not addressed in the semi-supervised category. This paper proposes a novel Semi-Supervised Fuzzy c -means approach, which is designed based on Feature-Weight, and Cluster-Weight learning, named SSFCM-FWCW. Inspired by the SSFCM, a fuzzy objective function is presented, which is composed of (1) a semi-supervised term representing the external class knowledge; (2) a feature weighting; and (3) a cluster weighting. Both feature weights and cluster weights are determined adaptively during the clustering. Considering these two techniques leads to insensitivity to the initial center selection, insensitivity to noise, and consequently helps to form an optimal clustering structure. Experimental comparisons are carried out on several benchmark datasets to evaluate the proposed approach's performance, and promising results are achieved. The Matlab implementation source code of the proposed method is publicly accessible at https://github.com/Amin-Golzari-Oskouei/SSFCM-FWCW. • This paper proposes a novel Semi-Supervised Fuzzy C-means approach based on Feature-Weight and Cluster-Weight learning. • An adaptive weight for each feature in each cluster applies based on its importance in forming the clusters. • The weight of the clusters is calculated dynamically to decrease cluster center initialization sensitivity. • Considering the conjunction of feature and cluster weighting helps form an optimal clustering structure. [ABSTRACT FROM AUTHOR]

Brain-computer interface (BCI) is a domain, in which a person can send information without using any exterior nerve or muscles, just using their brain signal, called electroencephalography (EEG) signal. Multiview learning or data integration or data fusion from a different set of features is an emerging way in machine learning to improve the generalized performance by considering the knowledge with multiple views. Multiview learning has made rapid progress and development in recent years and is also facing many new challenges. This method can be used in the BCI domain, as the meaningful representation of the EEG signal in plenty of ways. This study utilized the multiview ensemble learning (MEL) approach for the binary classification of five mental tasks on the six subjects individually. In this study, we used a well-known EEG database (Keirn and Aunon database). The EEG signal has been decomposed using by methods i.e wavelet transform (WT), empirical mode decomposition (EMD), empirical wavelet transform (EWT), and fuzzy C-means followed by EWT (FEWT). After that, the feature coding technique is applied using parametric feature formation from the decomposed signal. Hence, we had four views to learn four same type of independent base classifiers and predictions are made in an ensemble manner. The study is performed independently with three types of base classifiers, i.e., K-nearest neighbor (KNN), support vector machine (SVM) with linear and non-linear kernels The performance validation of the ten combinations of mental tasks was performed by three MEL based classifiers, i.e., K-nearest neighbor (KNN), support vector machine (SVM) with linear and non-linear kernels. For reliability of the obtained results of the classifiers, 10-fold cross-validation was used. The proposed algorithm shows a promising accuracy of 80 % to 100 % for binary pair-wise classification of mental tasks. [ABSTRACT FROM AUTHOR]

Magnetic Resonance Imaging (MRI) is a medical imaging modality that is commonly employed for the analysis of different diseases. However, these images come with several problems such as noise and other imaging artifacts added during acquisition process. The researchers have actual challenges for segmentation under the consideration of these effects. In medical images, a well-known clustering approach like Fuzzy C-Means widely used for segmentation. The performance of FCM algorithm is fast in noise-free images; however, this method did not consider the spatial context of the image due to which its performance suffers when images corrupted with noise and other imaging relics. In this paper, a weighted spatial Fuzzy C-Means (wsFCM) segmentation method is proposed that considered the spatial information of image. Moreover, a spatial function is also developed that integrate a membership function. In order assess this function, a neighborhood window is established around a pixel and more weights have been assigned to those pixels which have greater correlation with central pixel in local neighborhood. By integration of this spatial function in membership function, the modified membership function strengthens the original membership function in handling the noise and intensity inhomogeneity, which has the ability to preserves and maintains structural information like edges. A comprehensive set of experimentation is performed on publicly accessible simulated and real standard brain MRI datasets. The performance of the proposed method has been compared with existing state-of-the-art methods. The results show that the performance of the proposed method is better and robust in handling noise and intensity inhomogeneity than of the existing works. [ABSTRACT FROM AUTHOR]

This work explores the implementation of an energy supply chain considering the analysis of photovoltaic, biogas, biomass and conventional grid energy systems to satisfy electricity demand minimizing costs, greenhouse gas emissions, water consumption and maximizing energy security. To address this problem, a multi-criteria decision-making environment was implemented that takes into consideration priorities over economic, environmental and energy security objectives obtaining a compromise solution that minimizes stakeholder dissatisfaction and conflicts and, in addition, possible alliances between stakeholders are analyzed using fuzzy C-means clustering. The compromise solution of multi-objective optimization shows the optimal configuration of the electric power and biomass distribution network, the sizing, behavior, installation and location of the technologies. A case study of the Patzcuaro lake region in Mexico is used to evaluate the performance of the proposed methodology. The results indicate that the implementation of this type of methodology leads to attractive solutions for stakeholders, who are the main influencers in the design and implementation of energy supply chains. The compromise solution found reduces emissions by 73.5% and water consumption by 71.8% compared to grid power and achieves economic returns in most locations of up to $517,000 per year. In addition, the compromise solution satisfies on average 70% of the stakeholders either individually or in alliance. [Display omitted] • Water-energy‑carbon nexus and energy security are considered. • Conflict resolution strategy is presented using a multi-objective approach. • Compromise solutions are proposed for reaching trade-offs among multiple criteria. • Alliances among stakeholders are analyzed through fuzzy C-means clustering. [ABSTRACT FROM AUTHOR]

Adaptive-network-based fuzzy inference system (ANFIS) is a well-known neuro-fuzzy system, which is widely implemented in nonlinear system approximation, prediction, control, and pattern classification. However, either too many fuzzy sets or fuzzy rules are indispensable to establish an accurate ANFIS for a high-dimensional system, which increases the complexity and limits the widespread application of the ANFIS. In this paper, an approach to simplify the ANFIS is developed based on importance-confidence-similarity (ICS) measures. The simplification process consists of selection of fuzzy rules with large importance-confidence (IC) values and reduction of similar fuzzy rules. The importance is defined as the average normalized firing strength of the rule. The confidence which reflects the approximation performance of a T-S fuzzy rule is estimated by the weighted orthogonal distance from the output data to the rule hyperplane (the consequent of a linear T-S fuzzy rule). The IC measures provide a comprehensive basis for the selection of the appropriate fuzzy rules. Furthermore, to the best of our knowledge, an approach to measure similarities of the T-S fuzzy rules including the rule premises and consequents is first proposed in this paper. We also develop a direct and simple method to remove the similar fuzzy rules based on a hierarchical tree and the IC measures. The proposed simplification approach is applied to Mackey-Glass chaotic time series prediction problem and the strip temperature increment prediction problem of the indirect-fired furnace of the annealing heating line. The results show that our proposed method achieves a balance between simplicity and accuracy of the ANFIS for the high-dimensional system. [ABSTRACT FROM AUTHOR]

Addressing the Water–Energy–Food Nexus has become the main point of many studies due to the necessity of finding a solution that fits the demands while considering the strong interdependence among the nexus elements and taking care of their sustainable security. However, managing the elements of the nexus is also a matter of making decisions in a multi-stakeholder environment, where the final solution should ensure the security of the nexus for all the participants. In this sense, we present a multi-stakeholder approach for the optimal management of resources and the mitigation of conflicts among stakeholders. The nexus security is modeled by sustainability indicators to measure the availability, accessibility and sufficiency of water, energy and food. Soft-clustering and multi-objective strategies, as well as the concept of ideological distance, are used for performing a similarity analysis in multi-criteria and multi-stakeholder environments to forecast alliances among participants and mitigate conflicts. For testing these ideas, the supply chain of water, energy and food utilities in a state in the northern part of Mexico, where there is strong competition for resources, is presented as a case study. This study indicates that it is possible to reduce the discussion among several stakeholders to a few groups, facilitating consensus. [Display omitted] • Water–Energy–Food nexus is addressed using a security approach. • Ideological distance is used to address similarities among the interests of stakeholders. • The Fuzzy C-means algorithm is used for defining potential alliances among stakeholders. • Trade-off solutions are computed for different alliances of stakeholders. [ABSTRACT FROM AUTHOR]

Monitoring of environmental change can benefit from the increasing availability of multitemporal satellite imagery, and efficient and effective analysis tools are needed to generate relevant spatio-temporal land cover datasets. We present a data driven approach for automatic training sample selection to support supervised spatio-temporal mapping of seasonally burned areas in the semi-arid savannas of Southern Africa. Our approach leveraged the distinctive spectral-temporal trajectories associated with areas on the landscape burned at different times or areas remaining unburned over time. Using fuzzy c-means clustering, we extracted distinctive trajectories from the multitemporal mid-infrared burn index (MIRBI) data derived from Landsat data and characterized them based on empirically developed labeling rules. The selected training trajectories captured both the burn condition (burned or unburned) and if burned, the timeframe of the burn event. We assessed the approach by training a Random Forests model using over 2500 automatically selected training data and validated the model against ground truth for years 2009 and 2014. Based on over 1000 validation points in each year, we obtained overall accuracies above 90% showing reliable and consistent training data were supplied by our automatic training sample selection approach. The method provides a data driven and automatic approach which can reduce the time-consuming and expensive training task, enabling quicker generation of relevant burned area information that can support fire monitoring programs and climate change research. [ABSTRACT FROM AUTHOR]

• This research introduces the hybrid optimization of both CPU and GPU for image processing. • A novel 3D medical volume segmentation is proposed. • Modified FCM versions are used to increase the accuracy of volume segmentation. • Volumetric neighborhood has been considered to validate the actual 3D FCM. In the past, 2D models were the main models for medical image processing applications, whereas the wide adoption of 3D models has appeared only in recent years. The 2D Fuzzy C-Means (FCM) algorithm has been extensively used for segmenting medical images due to its effectiveness. Various extensions of it were proposed throughout the years. In this work, we propose a modified version of FCM for segmenting 3D medical volumes, which has been rarely implemented for 3D medical image segmentation. We present a parallel implementation of the proposed algorithm using Graphics Processing Unit (GPU). Researchers state that efficiency is one of the main problems of using FCM for medical imaging when dealing with 3D models. Thus, a hybrid parallel implementation of FCM for extracting volume objects from medical files is proposed. The proposed algorithm has been validated using real medical data and simulated phantom data. Segmentation accuracy of predefined datasets and real patient datasets were the key factors for the system validation. The processing times of both the sequential and the parallel implementations are measured to illustrate the efficiency of each implementation. The acquired results conclude that the parallel implementation is 5X faster than the sequential version of the same operation. [ABSTRACT FROM AUTHOR]

• A diverse fuzzy c -means is introduced for better accomplishing image clustering. • Diversity term makes the image cluster centers to cover as many clusters as possible. • A smooth relaxation is used to replace the non-smooth and non-convex diversity term. Image clustering is a key technique for better accomplishing image annotation and searching in large image repositories. Fuzzy c -means and its variations have achieved excellent performance on image clustering because they allow each image to belong to more than one cluster. However, these methods neglect the relations between different image clusters, and hence often suffer from the "cluster one-sidedness" problem that redundant centers are learned to characterize the same or similar image clusters. To this issue, we propose a diverse fuzzy c -means for image clustering via introducing a novel diversity regularization into the traditional fuzzy c -means objective. This diversity regularization guarantees the learned image cluster centers to be different from each other and to fill the image data space as much as possible. An efficient optimization algorithm is exploited to address the diverse fuzzy c -means objective, which is proved to converge to local optimal solutions and has a satisfactory time complexity. Experiments on synthetic and six image datasets demonstrate the effectiveness of the proposed method as well as the necessity of the diversity regularization. [ABSTRACT FROM AUTHOR]

Fuzzy clustering validation of high-dimensional datasets is only possible using a reliable cluster validity index (CVI). A good CVI must correctly recognize a data structure and its validations must be independently of any parameter of a clustering algorithm or data property. However, some classical fuzzy CVIs as Partition Coefficient (PC), Partition Entropy (PE) and Fukuyama-Sugeno (FS) have the monotonic tendency in function of the number of clusters. Although the literature presents extensive investigations about such tendency, they were conducted for low-dimensional data, in which such data property does not affect the clustering behavior. In order to investigate how such aspects affect the fuzzy clustering results of high-dimensional data, in this work we have clustered objects of thirteen real datasets, using the Fuzzy c-Means algorithm. The fuzzy partitions were validated by PC, PE, FS and some proposed improvements of them to lead with the monotonic tendency, totaling eight fuzzy CVIs analyzed. Besides the analysis made about the number of clusters selected by the CVIs, the Mann-Kendall test was performed to verify statistically the monotonic trend of the CVIs results. From the two analysis made, the Modified Partition Coefficient and Scaled Partition Entropy indices were successful in respectively improving the PC and PE indices. [ABSTRACT FROM AUTHOR]

Intuitionistic based Fuzzy clustering is a popular method in the field of image segmentation. The widely used Intuitionistic Fuzzy C-means (IFCM) based image segmentation is sensitive to noise since it uses only distance criterion in the feature space to segment the images. To overcome this, an enhanced spatial intuitionistic fuzzy c-means clustering algorithm is proposed that uses:- (i) an intuitionistic fuzzification of image to simplify the representation of the image (ii) an improved method to calculate the hesitation degree in the images. (iii) the spatial property of an image in order to make segmentation more robust and effective. The performance of the proposed method is evaluated for synthetic and real images. The result indicates the effectiveness of the proposed methodology over existing methodologies. [ABSTRACT FROM AUTHOR]

• Acquire real data from a distillation column. • Propose direct monitoring approach based on ANFIS combined with FCM. • Estimate the degradation path of a distillation column. • Determine an accurate Remaining Useful Life (RUL). • Calculate the lifetime percentage of the system. The maintenance, repair, and rehabilitation of industrial reactors are expensive and time-consuming. Sudden interruptions may adversely affect the production process and may lead to harmful effects and disastrous results. Therefore, lifetime prediction is extremely important to prevent catastrophic breakdowns leading to complete cessation of production. This paper aims to propose a prognosis reliable method that can be used to estimate the degradation path of a distillation column and calculate the lifetime percentage of this system. The work presents a direct monitoring approach based on the technique of adaptive neuro-fuzzy inference system (ANFIS) combined with fuzzy C-means algorithm (FCM). At the beginning, ANFIS is used to detect the small variations in the signal over time. Secondly, a new strategy is proposed to find the system degradation path. Thirdly, ANFIS is combined with FCM to predict the future path and calculate the lifetime percentage of the system. The methodology is tested on real experimental data obtained from a distillation column. Results demonstrate the validity of the proposed technique to achieve the needed objectives with a high-level accuracy, especially the ability to determine a more accurate Remaining Useful Life (RUL) when it applied on the automated distillation process in the chemical industry. [ABSTRACT FROM AUTHOR]

• Effective strategies for noisy image segmentation using adaptive wavelet shrinkage. • Edge enhancement in wavelet domain improve the results. • Significantly better performance than other methods on severely noisy images. • No parameter-tuning required for different noise levels and types • Very consistent results even when the noise level has a large variation. Noisy image segmentation is a hot topic in natural, medical, and remote sensing image processing. It is among the non-trivial problems of computer vision having to address denoising and segmentation at the same time. Fuzzy C-means (FCM) is a clustering algorithm that has been shown to be effective at dealing with both segmentation-oriented denoising and segmentation at the same time. Moreover, with a high level of noise and other imaging artifacts, FCM loses its ability to perform image segmentation effectively. This paper introduces a Particle Swarm Optimization (PSO)-based feature enhancement approach in the wavelet domain for noisy image segmentation. This approach applies adaptive wavelet shrinkage using FCM clustering performance as an evaluation mechanism and also as the segmentation algorithm. The PSO-based process helps to enhance intensity features for clustering-based denoising, and also provides adaptivity for the system that performs well on a range of real, synthetic, and simulated noisy images with different noise levels and range/spatial properties. Furthermore, the algorithm applies edge enhancement based on Canny edge detector in order to further improve accuracy. Experiments are presented using three different datasets each degraded with different types of common noise. The presented algorithms show effective and consistent performance over a range of severe noise levels without the need for any parameter tuning. [ABSTRACT FROM AUTHOR]