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Information granulation theory has been widely used in short-term time-series forecasting research and holds significant weight. However, the error accumulation due to the lack of granular accuracy, along with information redundancy or deficiency in predictions, significantly affects short-term prediction accuracy. To compensate for these shortcomings, this paper proposes a double-level optimal fuzzy association rules prediction model for short-term time-series forecasting, which can strengthen the performance of information granulation in prediction. Firstly, this paper proposes a concept of breakpoints, which can accurately segment complex linear trends in time series and thus obtain a granular time series with highly accurate linear fuzzy information granules (LFIGs). Secondly, a improved distance is proposed to more accurately reflect the similarity between LFIGs by addressing counter-intuitive problems in the original distance. Theoretical analysis shows that the improved distance can effectively reduce errors in granular calculation. Then, a granule-suited fuzzy c-means algorithm is proposed for clustering LFIGs. Finally, this paper proposes a double-level optimal fuzzy association rules prediction model, which establishes the optimal rules for each cluster and selects the optimal two rules for prediction by the contribution of the clusters. The experimental results show that the prediction method effectively avoids the problems of information redundancy and information deficiency, and increases forecast accuracy. The model's exceptional performance is demonstrated through comparative analysis with existing models in experimental investigations. • A new concept of breakpoints is proposed to partition time series linear trends. • A DTW-iL1 distance is proposed to measure the similarity between granules. • DTW-iL1 Fuzzy C-Means(DFCM) is proposed for clustering granules. • Propose double-level optimal fuzzy association rules prediction model based on DFCM. [ABSTRACT FROM AUTHOR]

In the field of data mining, outlier detection is an important and challenging task. This paper focuses on studying the impacts of outliers on the performance of models learned from large-scale datasets while it is unknown whether a data point is outlier or not. In the proposed approach, a fuzzy c-means clustering algorithm is applied and outliers are defined as those that have greater membership values in the cluster and are located further away from the cluster centroid. Ideally, the sample with a higher membership value should be located closer to the cluster centroid. In this context, we calculate the weight of each sample using the AdaBoost algorithm, where a weight determines the representativeness of each sample within the data distribution. Additionally, in this study, the impact of weighted loss functions in different situations are discussed in detail. At last, our method is evaluated on 12 UCI datasets and the accuracy of our method is greater than 95% on some datasets, such as banknote 99.99%, biodeg 99.01%, optdigits 99.19%, and letters 97.37%. The experimental results show the efficiency and effectiveness of the proposed approach. • Outlier impact is investigated in a classification context. • Outliers are identified as having higher membership and found outside cluster center. • Different weighted loss functions are also discussed in detail in various situations. • The efficiency and effectiveness of the proposed method are verified experimentally. [ABSTRACT FROM AUTHOR]

At present, high-dimensional data clustering has become a vital research field in machine learning. Traditional clustering algorithms cannot perform well on high-dimensional data, where the clustering task is usually divided into two stages: dimensionality reduction first and clustering later. In general, the existing high-dimensional clustering methods usually have the following shortcomings: (1) the two-stage strategy splits the connection between clustering and dimensionality reduction; (2) these algorithms do not consider the impact of anomalous instances in high-dimensional data on clustering performance. Therefore, to address these problems, a projected fuzzy c -means clustering algorithm with instance penalty (PCIP) is proposed. Firstly, we construct an instance penalty matrix and assign an instance penalty coefficient to each sample. Secondly, a model for clustering high-dimensional data is constructed by integrating fuzzy c -means clustering (FCM) and principal component analysis (PCA). The proposed model can perform dimensionality reduction and clustering simultaneously. In addition, the time complexity of the proposed algorithm is linearly related to the number of samples n , which can efficiently deal with large data sets. The proposed PCIP algorithm is verified by experiments using clustering accuracy and normalized mutual information (NMI) as evaluation metrics. The experimental results on 10 image datasets show that the average accuracy and average NMI of the PCIP algorithm are improved by 0.0375 and 0.0275, respectively, compared to the second-ranked algorithm. • The proposed PCIP accomplishes both dimensionality reduction and clustering. • The instance penalty matrix is used to identify and handle the abnormal samples. • We propose an iterative algorithm to solve PCIP and its convergence is proved. • The time complexity of PCIP is linearly related to the number of samples. • Extensive experiments have demonstrated the effectiveness of PCIP. [ABSTRACT FROM AUTHOR]

Computerized assessment of brain tumor identification and discrimination process from magnetic resonance imaging is of immense concern for improved investigation, growth rate prediction, treatment planning and monitoring of clinical trials. Due to extensive diversification of tumors and complex outline interactions between sub-regions, it is of a great challenge to extract significant features. The proposed approach starts with Grey Wolf Optimization based Gabor Filtering for enhancement process and spatial fuzzy c-means clustering algorithm for segmentation purpose. Following this, we apply non-sub-sampled shearlet transformation to investigate multi-scale space-frequency representation of tumor data. In order to measure the hierarchical correlation pattern of tumors, interlayer cross spectral coherence function is analyzed in terms of some significant indices such as fundamental global mean, secondary mean pair, span of secondary mean pair, percentage of samples having values greater than upper secondary mean pair and percentage of samples having values smaller than lower secondary mean pair. Additionally, topological profile of tumor getsassessed from its phase spectrum distribution pattern. Regarding this, some phase spectrum distribution-based quantifiers such as phase-sign change counter, phase change frequency, figure of merit and standard deviation of phase sign change location are introduced as the significant indices. These feature quantifiers have been fed to a deep neural network model and hybrid AdaBoost classifier to discriminate the state of benignancy/malignancy of tumors. Experimental results demonstrate that the overall accuracy attained by the proposed model are 99.67 %, 98.92 %, 96.89 %, 97.82 %, 96.98 %, 99.54 %for the datasets of Harvard University, BraTS −2018, −2019, −2020, −2021 and Kaggle respectively. Apart from this, promising sensitivity rate of the model helps us to avoid the risk of false negativity. Altogether, these qualities make the proposed model superior to the state of art techniques. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel clustering approach that eliminates the need for predefined cluster centres and cluster counts, addressing common limitations in traditional clustering algorithms. We achieve this by allowing each data point within the problem space to serve as a potential cluster centre, determined by the presence of nearby data points. Three distinct algorithms are introduced: i) Identifying valid data points for clustering by assessing their presence within the specified vicinity of each potential cluster centre, allowing data points to belong to multiple clusters, ii) Calculating the fuzzy membership of shared data points among the clusters and iii) Retaining shared data points in the cluster with the highest membership and removing them from others. A comprehensive evaluation of this method using synthetic data and benchmark datasets from well-known problems demonstrates promising performance. Our approach offers increased flexibility, ease of use, and enhances the fidelity of cluster centres to the underlying data distribution. [ABSTRACT FROM AUTHOR]

This paper proposes a new model for creating fuzzy time series and conducting future forecasts using the Bi-directional Long Short-term Memory model (Bi-LSTM). This study contributes by using both classical machine learning and deep learning techniques. Firstly, a self-updating clustering algorithm is used to determine the optimal number of clusters for time series. Secondly, the study describes a method for determining the fuzzy relationship between elements of time series and the identified clusters. Thirdly, the developed model creates the fuzzy time series based on the established rules. Finally, forecasting for the future value using the Bi-LSTM model with some improvement in optimizing the parameters and increasing the accuracy of forecasting result. The steps of the proposed model are clearly illustrated by a numerical example. Moreover, this model also tested on various datasets, including M3, M4, and M5 datasets. By evaluating its performance using parameters such as sMAPE and RMSSE, the proposed model has shown significant enhancements when compared to existing models. Additionally, the model's effectiveness is further demonstrated through its successful application in forecasting the VN index stock in Vietnam. [ABSTRACT FROM AUTHOR]

The practical applicability of smart control systems suffers from the existence of uncertainty in the physical parameters, sensor measurements and external excitations. Effective methods and its ease of implementation are required in the real-time active control strategies. To this end, in this research, we introduce an overlapping clusters and Multilayer Extreme Learning Machine (ML-ELM)-aided interval type-2 Takagi-Sugeno fuzzy inference system for vibration mitigation of smart structures. The combined Fuzzy C-Means (FCM) and imperialist competitive algorithm (ICA) with respect to degree of fuzzy overlap between clusters was utilized for characterizing the upper and lower membership functions forming the antecedent part. Furthermore, indeterminacy was modeled as footprint of uncertainty (FOU) and automatically formed based on statistical characteristics of soft clusters. The consequent parameters were adjusted by hybridization of ML-ELM and overlapping clusters, then the adaptivity was guaranteed. The predictive accuracy and generalization capability of the proposed method were demonstrated over the estimation of active control effort. Finally, to prove the practicability of the implemented framework, it was applied to four high-rise, mid-rise and low-rise benchmark building structures equipped with active mass damper (AMD), active tendon and active bracing system (ABS). The obtained results demonstrated the higher predictive accuracy and generalization ability of the presented data-driven control scheme compared to the other standard technical machine learning strategies. This practical guideline is easy to implement and automates control engineering tasks in real-time applications, solving one of the most challenging aspects of smart control systems. [ABSTRACT FROM AUTHOR]

Battery is the core component of new energy vehicles. The choice of proper battery supplier is crucial for new energy vehicle companies since it directly affects the market share and core competitiveness. Some criteria of battery suppliers cannot be evaluated in the short period and need to be continuously evaluated at different periods (or time). Decision makers (DMs) may present some hesitancy when giving their evaluations. Thus, this paper formulates the battery supplier selection as a type of time-series based multi-criteria large-scale group decision making (LSGDM) with intuitionistic fuzzy information. A novel method is proposed to effectively resolve the battery supplier selection. Firstly, considering the importance of different periods, the comprehensive time weights are determined by combining the exponential decay model and the maximal entropy ordered weighted averaging (OWA) operator weights determining model. Secondly, DMs are divided into different clusters by using the proposed intuitionistic fuzzy Hamming distance-based fuzzy c-means (FCM) algorithm on each criterion. Combining the confidence levels of DMs and the corresponding clustering results, the DMs' weights with respect to each criterion are determined. Then, the comprehensive criteria weights are obtained by integrating the intuitionistic fuzzy entropy and the constructed multi-objective programming model. Thirdly, the individual consensus level and group consensus degree at each period are defined, respectively. Then, a new identification approach is proposed to identify DMs to be adjusted. Subsequently, a total adjustment minimization model is built to adjust these DMs' evaluation information. The optimal alternative is generated according to the collective global overall evaluations. Finally, a real example of batter supplier selection is demonstrated to verify the feasibility and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

Highlights • Analysis of virus trend using hybrid clustering. • Combining the K-means, Fuzzy C-means, and hierarchical clustering. • Processing DNA data into unsupervised learning methods. • DNA Micro Array data processing. Abstract Every single strand of DNA consists of 10 sequences of nucleotides. These sequences cannot be separated or randomly arranged because each sequence of DNA contains a certain genomic encoding. When a virus mutates, a drug or vaccine for that virus that has been given to a patient will become useless. Therefore, there is a need for a method of analysing the likely direction of DNA mutation so that preventative measures can be adapted more quickly. RNA-type viruses are able to alter the patterns of infected DNA, which is one way for such a virus to defend itself. In this paper, we propose a new hybrid clustering method that combines K-means, fuzzy C-means, and hierarchical clustering to predict the direction of DNA mutation trends. We have combined these three different approaches in a hybrid clustering method and tested it on two data sets of 1000 isolated positive hepatitis C virus (HCV)-infected and non-infected DNA strands with 37 HCV primers. We compare the results with those of eight other clustering methods, and the comparison shows that our method achieves sensitivity and specificity values of 0.998. The level of precision of cluster division is also 0.004 higher than that of the next highest among the eight methods considered for comparison. From this study, the primer trends that most often appear in isolated DNA can be found, and the origins of these trends in isolated DNA can be inferred. [ABSTRACT FROM AUTHOR]

Highlights • An improved FFCM clustering algorithm based on CSA is proposed for PA. • CSA-FFCM is able to avoid difficulties in the identification of vegetation. • The aim of CSA is to find best cluster centroids and avoids stuck in local minima. • CSA has strong ability of the global optimization with fewer parameters. • The proposed approach obtains better results in comparison with other methods. Abstract In this article is introduced an improved version of Fast Fuzzy C-Means (FFCM) by using the Crow Search optimization Algorithm (CSA) for the task of data clustering. In the proposed version of the FFCM the CSA is employed to find the centroids of the clusters that provide more accurate results in the clustering process. In this sense, the CSA avoids that the FFCM get stuck in local minima and increases the computational performance. The main feature of the CSA is its ability to find the global solution in complex optimization problems with the calibration of a reduced amount of parameter. This fact reduces the sensibility in the iterative process and permits the FFCM use the best centroids. To verify the efficiency of the proposed FFCM in a real problem, it is applied for the identification of maize plants in images from crop fields. The process starts using the adaptive colour histogram equalization to enhance the contrast and adjusts the intensities of crop images. The next task consists in to obtain the green index that is used by the CSA to compute the centroids for the FFCM algorithm. To evaluate the performance of the presented approach, it has been tested over a set of images from maize fields with different degrees of complexity, captured by different cameras and with a different perspective of the scene. Different metrics and a statistical analysis evidence that the proposed algorithm obtains better segmentation results in comparison with other methods. The experimental results proved that the proposed approach is capable of finding the optimal centroid values of the FFCM and avoids the local optima problem. Moreover, the FFCM based on CSA method can locate crop rows with the maximum accuracy as possible in digital images. [ABSTRACT FROM AUTHOR]

Highlights • To introduce an Integrated Fuzzy Clustering Cooperative Game DEA. • To provide a clustering technique to deal with lack of homogeneity among DMUs. • To provide a framework for measuring hospitals in different provinces. • Use of Core and Shapley values for ranking efficient DMUs in DEA. Abstract Hospitals are the main sub-section of health care systems and evaluation of hospitals is one of the most important issue for health policy makers. Data Envelopment Analysis (DEA) is a nonparametric method that has recently been used for measuring efficiency and productivity of Decision Making Units (DMUs) and commonly applied for comparison of hospitals. However, one of the important assumption in DEA is that DMUs must be homogenous. The crucial issue in hospital efficiency is that hospitals are providing different services and so may not be comparable. In this paper, we propose an integrated fuzzy clustering cooperative game DEA approach. In fact, due to the lack of homogeneity among DMUs, we first propose to use a fuzzy C-means technique to cluster the DMUs. Then we apply DEA combined with the game theory where each DMU is considered as a player, using Core and Shapley value approaches within each cluster. The procedure has successfully been applied for performances measurement of 288 hospitals in 31 provinces of Iran. Finally, since the classical DEA model is not capable to distinguish between efficient DMUs, efficient hospitals within each cluster, are ranked using combined DEA model and cooperative game approach. The results show that the Core and Shapley values are suitable for fully ranking of efficient hospitals in the healthcare systems. [ABSTRACT FROM AUTHOR]

This paper presents an approach to fault diagnosis with online detection of novel faults and automatic learning using fuzzy clustering techniques. In the off-line learning stage, the classifier is trained to diagnose the known faults and the normal operation state using the Density Oriented Fuzzy C-Means and the Kernel Fuzzy C-Means algorithms. In this stage, the historical data previously selected by experts, are firstly pre-processed to eliminate outliers and reduce the confusion in the classification process by using the Density Oriented Fuzzy C-Means algorithm. Later on, the Kernel Fuzzy C-Means algorithm is used for achieving greater separability among the classes and reducing the classification errors. Finally, the optimization of the two parameters used by these algorithms in the training stage is developed by using a bio-inspired optimization algorithm, namely the differential evolution. After the training, the classifier is used online (online diagnosis stage) in order to classify the new observations that are collected from the process. In this stage, the detection of novel faults based on density by using the DOFCM algorithm is applied. The algorithm analyzes the observations belonging to a window of time which were not classified into the known classes and it is determined if they are a new class or outliers. If a new class is identified, a procedure is developed to incorporate it to the known classes set. The proposed approach was validated using the Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems (DAMADICS) benchmark. The results obtained indicate the feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

Big data has increasingly become predominant in many research fields affecting human knowledge, including medicine and engineering. Cluster analysis, or clustering, is widely recognized as one of the most effective processes to deal with various types of data, especially big data. There has been considerable interest in Fuzzy C-Means (FCM) as a method for clustering data using a short-distance approach in data mining. However, despite its simplicity, this method is not suitable for clustering large data sets due to their complex structure. In particular, FCM is sensitive to cluster center initialization, and an improper initialization can result in slow or non-optimal convergence. In order to solve the FCM convergence problem and find more appropriate cluster centers, optimization methods are generally used. In this study, a whale optimization algorithm is applied to solve the problem. As a solution to the problem of big data clustering, random sampling, clustering on samples, and extending the clustering results to all data are proposed. The proposed algorithm is implemented on several large data sets, both artificial and real, with many features after normalization and standardization. To verify the validity and correctness of the performance of the proposed algorithm, the same data sets have been clustered with other known algorithms, and the results compared using several valid fuzzy indices. Based on the comparison results, it can be concluded that the proposed algorithm is more powerful and efficient than other algorithms and, hence, can be used to effectively cluster large data sets. Our study can benefit organizations and managers who have a large amount of data and are unable to classify or make use of them properly. Using big data takes a lot of time. The features of the proposed algorithm would be of great help to managers allowing them to make better decisions and improve the quality of their work. [ABSTRACT FROM AUTHOR]

The learning algorithm for multivariable data analysis (LAMDA) is a learning method to group or classify quantitative and qualitative historical data. LAMDA can be applied for self-learning and directed learning. Considering self-learning, LAMDA groups historical data through the global membership degrees of a sample with respect to a class, considering the contribution of all features for each sample. Such contribution is called marginal adequacy degree (MAD). To mix all MADs, several aggregation functions such as linear and geometrical connectives are used. The aggregation function calculates the global adequacy degree (GAD) of a sample with respect to a class. This procedure avoids assigning the class number as initial parameter due to that LAMDA applies an automatic threshold called non-informative class (NIC) which finds the best assignment of a portion of data to one class. One improvement for the LAMDA algorithm is the use of a full reinforcement operator called Yager–Rybalov Triple Pi , which can reduce the number of classes. However, this kind of solution ignores the degree to which one sample belongs to one class relative to all samples. Another limitation is that the classes reduction is not controlled by a parameter or an algorithm, which removes some classes required by a human expert. Such removed classes can be useful for the human expert in the data analysis of complex processes or for intelligent systems when the searching of additional information is required in decision-making. In this paper, the typicality degree and the intuitionistic fuzzy sets (IFSs) are used to propose one improvement of the LAMDA method in order to develop a strategy that avoids the loss of significant classes. This paper shows two functions: global typicality degree (GTD) and intuitionistic global adequacy degree (IGAD). By integrating both functions, a new function called typicality and intuitionistic global adequacy degree (TIGAD) is proposed. The proposal is applied in three study cases. The results show an improvement of clustering which were validated by the human expert and the information of data. Furthermore, the impact of the research is focused on data analysis, where the expert should make the best decision. [ABSTRACT FROM AUTHOR]

Sensory data are generally associated with imprecision and uncertainty, and consequently, it becomes difficult to extract useful information from them. The problem becomes even more difficult to handle, when the data are collected using multiple sensors. Realizing the ability of fuzzy sets to deal with imprecision and uncertainty, a multi-sensors data fusion technique was developed in this study by using fuzzy clustering and predictive tools. The data were first clustered based on their similarity using an entropy-based fuzzy C-means clustering technique and the obtained clusters were utilized to develop a fuzzy reasoning-based predictive tool. The novelty of this study lies with the application of a clustering algorithm, which can ensure both compactness and distinctness of the developed clusters, and development of a reasoning tool utilizing the information of obtained clusters. Two types of multi-sensors data were used to test the performance of the proposed algorithm. Results were compared with those available in the literature, and the developed technique was found to perform better than the previous approaches on both the data sets. The better performance of the proposed algorithm could be due to its in-depth search of the data set through similarity-based fuzzy clustering followed by the development of fuzzy reasoning tool utilizing the information of obtained clusters. [ABSTRACT FROM AUTHOR]

In the last years, many clustering techniques dealing with time course data have been proposed due to recent interests in studying phenomena that change over time. A new clustering method suitable for time series applications has been recently proposed by exploiting the properties of the P-splines approach. This semi-parametric tool has several advantages, i.e. it facilitates the removal of noise from time series and it ensures a computational time saving. In this paper, we propose to use this clustering approach on financial data with the aim of building a financial portfolio. Our proposal works directly on time series without any pre-processing, except for the computation of the spline coefficients and, eventually, normalizing the series. We show that our strategy is useful to support the investment decisions of financial practitioners. [ABSTRACT FROM AUTHOR]

Clustering analysis is one of the major topics in unsupervised machine learning. A recent study proposes a novel density-based clustering algorithm called the Density Peaks. It is based on two intuitive assumptions: that cluster centers have a higher density than those of their neighbors, and that they also have a relatively large distance from other points with a higher density. To see whether a distance is relatively large, we should make a comparison of it and another one. However, such comparison is not explicitly modeled in the algorithm. Therefore, we propose the Comparative Density Peaks algorithm which takes the comparison into the design of the method. Furthermore, we give our analysis of Density Peaks from the perspective of the tree structure, and summarize two sufficient conditions that contribute to a good clustering performance under the Density Peaks framework. Extensive experiments show that our proposed algorithm significantly outperforms the original Density Peaks clustering algorithm. [ABSTRACT FROM AUTHOR]

Segmentation of brain MR image tissues has been a challenge because of the embedded nonlinear bias field acquired during the image acquisition process. This problem is further compounded due to the presence of noise. In order to deal with such issues, we have proposed a Variable Variance Adaptive Mean-Shift (VVAMS) algorithm which not only removes noise but also reinforces the clustering attribute by its mode seeking ability. We have formulated the problem for jointly estimating the bias field, tissue class labels and noise free pixels. Since, all the parameters are unknown and interdependent it is hard to obtain optimal estimates. In this regard, we have proposed a recursive framework to obtain the estimates of the parameters, which are partial optimal ones. In the first step of the recursion, the possibilistic fuzzy clustering algorithms has been applied to determine different clusters and bias field. These clusters are noisy and hence in the second step of the recursion, VVAMS algorithm has been applied on each cluster to eliminate noise and reinforce the modes of the clusters. These two steps constitute one combined iteration. Theoretically, the recursive framework is supposed to converge after large number of recursions but in practice it converges after a few iterations. This proposed scheme has successfully been tested with 50 biased noisy slices from Brainweb database and some real brain MR image data from IBSR database. The results have been quantitatively evaluated by percentage of misclassification, Rand Index, t -test, fuzzy partition coefficient ( V pc ), fuzzy partition entropy ( V pe ) and Tanimoto index. The quantitative evaluations of the tissue class labels demonstrate the superiority of proposed scheme over the existing methods. [ABSTRACT FROM AUTHOR]

Over the last few decades, the advance of new technologies in computer equipment, cameras and medical devices became a starting point for the shape of medical imaging systems. Since then, many new medical devices, e.g. the X-Ray machines, computed tomography scans, magnetic resonance imaging, etc., accompanied with operational algorithms inside has contributed greatly to successful diagnose of clinical cases. Enhancing the accuracy of segmentation, which plays an important role in the recognition of disease patterns, has been the focus of various researches in recent years. Segmentation using advanced fuzzy clustering to handle the problems of common boundaries between clusters would tackle many challenges in medical imaging. In this paper, we propose a new fuzzy clustering algorithm based on the neutrosophic orthogonal matrices for segmentation of dental X-Ray images. This algorithm transforms image data into a neutrosophic set and computes the inner products of the cutting matrix of input. Pixels are then segmented by the orthogonal principle to form clusters. The experimental validation on real dental datasets of Hanoi Medical University Hospital, Vietnam showed the superiority of the proposed method against the relevant ones in terms of clustering quality. [ABSTRACT FROM AUTHOR]

Data clustering is a very useful data mining technique to find groups of similar objects present in the dataset. Scalability to handle immense volumes, robustness to intrinsic outlier data and validity of clustering results are the main challenges of any data clustering approach. In order to address these challenges, a fuzzy weighted clustering approach which is comprehensibly parallel and distributed in every phase, is proposed in this research. Although the proposed method can be used for various data clustering purposes, it has been applied in gene expression clustering to reveal functional relationships of genes in a biological process. Conforming to MapReduce, the proposed method also presents a novel similarity measure which benefits from combining ordered weighted averaging and Spearman correlation coefficient. In the proposed method, density reachable genes were joined to establish subclusters. Afterwards, final cluster results were obtained by merging these subclusters. A voting system detects the best weights and consequently the most valid clusters among all possible results for each distinct dataset. The whole algorithm is implemented on a distributed processing platform and it is scalable to process any size of data stored in cloud infrastructures. Precision of resulting clusters were evaluated using some of the well-known cluster validity indexes in the literature. Also, the efficiency of the proposed method in scalability and robustness was compared with recently published similar researches. In all the mentioned comparisons, the proposed method outperformed recent works on the same datasets. [ABSTRACT FROM AUTHOR]

In this study, we introduce novel fuzzy neural networks designed with the aid of linear function prototype-driven fuzzy clustering (LFPFC) and layer reconstruction-based network design strategy to deal with the regression problem. The LFPFC constitutes a new clustering technique inspired by the fuzzy c-regression model (FCRM) clustering unlike fuzzy c-means (FCM) clustering LFPFC represents the prototypes of clusters as linear functions, and this can lead to more reliable data analysis of complex regression problems. We propose two types of LFPFC such as an estimated output-based LFPFC and a distance-based LFPFC. The estimated output-based LFPFC uses the output estimated on a basis of the simple model instead of the target output to calculate the centroid of LFPFC. A centroid of distance-based LFPFC is computed through the Euclidean distance between input data and the centroid of the cluster. By using two kinds of LFPFC approaches, we propose three different types of fuzzy neural networks: i) the fuzzy neural networks through layer reconstruction-based network design strategy consists of two models. The first model serves as an estimate of the desired output and the estimated output is used in the LFPFC of the second model. ii) In the fuzzy neural networks applied to the basic architecture of distance-based LFPFC, the hidden layer using the membership function changes to basic distance-based LFPFC, and the partition matrix obtained from LFPFC is used as the output of the hidden layer. iii) in the fuzzy neural network with the advanced architecture of distance-based LFPFC, an additional auxiliary layer is considered between the hidden and output layers to estimate the membership function of output space through LFPFC. In the experiments, we evaluate the performance index of the proposed models using publicly available machine learning datasets. The superiority of the proposed fuzzy neural networks designed by using LFPFC is demonstrated through the comparative analysis with the diverse regression models offered in the Weka data mining software. By conducting the Friedman test we show that the proposed model exhibits visible competitiveness from the viewpoint of performance. In addition, a real-world Portland cement dataset is dealt with to demonstrate the superiority of the models designed with the aid of LFPFC and reinforced layer reconstruction-based network design strategy. [ABSTRACT FROM AUTHOR]

A data driven Fuzzy Inference System (FIS) employs Membership Functions (MFs) with adjustable parameters in its IF part to fuzzify the input data. The input space is partitioned simply by dividing universe of discourse of each input variable into some fuzzy subspaces. The MFs are then defined on the fuzzy subspaces of the input variables. Parameters of the MFs are tuned for maximum accuracy of the system (which demands high runtime) without considering the data structure which impairs interpretability of the FIS and degenerates the system into a black-box tool. Such a FIS does not represent actual structure of the data and its MFs are not necessarily in accord with the data distribution in the input space. In addition, the FIS suffers from exponential complexity of order O ( T r ) where T is number of linguistic terms (number of subspaces on the universe of discourse of input variables) and r is number of input variables. This article presents a novel Multiple-Input and Multiple-Output Clustering based Fuzzy Inference System (MIMO CFIS) which is made directly from a class of fuzzy clustering algorithms to overcome these shortcomings. CFIS identifies dense regions of the input data using fuzzy clustering and then places a cluster on each of these regions. These fuzzy clusters represent actual structure of the data and serve as fuzzy rules in the rule base of CFIS and provide MFs that exactly fit the dense regions of the data that makes the system more interpretable and avoids redundant rules. These MFs are normal, convex, and continuous and have no parameter to be tuned (which makes CFIS much faster than other FISs) and fuzzify the input data according to their membership in the clusters. THEN part of CFIS is generalized form of THEN part of Takagi-Sugeno (TS) fuzzy system which accommodates any function of input variables. Despite less number of adjustable parameters, testing error of CFIS is less than that of TS system and its modified versions. Moreover, number of fuzzy rules in CFIS rule base is the same as the number of linguistic terms (or fuzzy clusters) and consequently its complexity is of order O(T). Also, CFIS is a MIMO system and avoids inconsistent (contradictory) rules by generating well-separated fuzzy clusters whereas TS system is MISO and never guarantees generation of consistent rules. In addition, CFIS satisfies most of the interpretability criteria of FISs. [ABSTRACT FROM AUTHOR]

A wind power system has diverse operating characteristics as its operations depend on many factors such as wind power, machinery ageing and breakdowns, etc. Knowledge of the operating behavior of the wind power system is helpful for monitoring its status and for isolating harmful elements when malfunctions occur. To investigate the operating status and behavior of the system, the fuzzy clustering method is introduced to classify the system's operating points. Relative distance indices of the cluster centers are defined to describe the operating behavior. With those, the location and operating behavior of the operating point are identified in relation to the cluster centers. [ABSTRACT FROM AUTHOR]

Large graphs are scale free and ubiquitous having irregular relationships. Clustering is used to find existent similar patterns in graphs and thus help in getting useful insights. In real-world, nodes may belong to more than one cluster thus, it is essential to analyze fuzzy cluster membership of nodes. Traditional centralized fuzzy clustering algorithms incur high communication cost and produce poor quality of clusters when used for large graphs. Thus, scalable solutions are obligatory to handle huge amount of data in less computational time with minimum disk access. In this paper, we proposed a parallel fuzzy clustering algorithm named ‘PGFC’ for handling scalable graph data. It will be advantageous from the viewpoint of expert systems to develop a clustering algorithm that can assure scalability along with better quality of clusters for handling large graphs.The algorithm is parallelized using bulk synchronous parallel (BSP) based Pregel model. The cluster centers are initialized using degree centrality measure, resulting in lesser number of iterations. The performance of PGFC is compared with other state of art clustering algorithms using synthetic graphs and real world networks. The experimental results reveal that the proposed PGFC scales up linearly to handle large graphs and produces better quality of clusters when compared to other graph clustering counterparts. [ABSTRACT FROM AUTHOR]

Multi-view data clustering refers to categorizing a data set by making good use of related information from multiple representations of the data. It becomes important nowadays because more and more data can be collected in a variety of ways, in different settings and from different sources, so each data set can be represented by different sets of features to form different views of it. Many approaches have been proposed to improve clustering performance by exploring and integrating heterogeneous information underlying different views. In this paper, we propose a new multi-view fuzzy clustering approach called MinimaxFCM by using minimax optimization based on well-known Fuzzy c means. In MinimaxFCM the consensus clustering results are generated based on minimax optimization in which the maximum disagreements of different weighted views are minimized. Moreover, the weight of each view can be learned automatically in the clustering process. In addition, there is only one parameter to be set besides the fuzzifier. The detailed problem formulation, updating rules derivation, and the in-depth analysis of the proposed MinimaxFCM are provided here. Experimental studies on nine multi-view data sets including real world image and document data sets have been conducted. We observed that MinimaxFCM outperforms related multi-view clustering approaches in terms of clustering accuracy, demonstrating the great potential of MinimaxFCM for multi-view data analysis. [ABSTRACT FROM AUTHOR]

In data clustering fuzzy predicates act as cluster descriptors providing linguistically expressed knowledge which indicates how features are related to each cluster. Fuzzy predicates directly and automatically obtained from data enable discovering knowledge inside clusters, even when there is no prior-information about the clustering problem. In this work a new method for automatic discovering of interval type-2 fuzzy predicates in data clustering is proposed, called Type-2 Data-based Fuzzy Predicate Clustering (T2-DFPC). In a first stage, a data analysis is performed by making a random partition of the original data and running a clustering scheme that automatically determines the suitable number of clusters. From this stage, interval type-2 fuzzy predicates are discovered. Results obtained on very different clustering datasets show that the T2-DFPC method was consistently one of the best in terms of accuracy. The method preserves all known advantages of the interval type-2 FL to deal with problems with vagueness, quantifying the degree of truth of the fuzzy predicates and modelling the variability of the data inside the clusters. The proposed method is a fast, useful, general, and unsupervised approach for interpretable data clustering, being the knowledge-extracting capabilities one of the main contributions. Linguistic expressions can be easily adapted to match the terminology used in the field the data are related to. The predicates are able to generalize the knowledge for new cases (new data), as an intelligent system. This new approach might be surprisingly useful in contexts where, besides the clustering partition, summary information from data is of interest. [ABSTRACT FROM AUTHOR]

Automated computer vision-based fire detection has gained popularity in recent years, as every fire detection needs to be fast and accurate. In this paper, a new fire detection method using image processing techniques is proposed. We explore how to create a fire flame-based colour space via a linear multiplication of a conversion matrix and colour features of a sample image. We show how the matrix multiplication can result in a differentiating colour space, in which the fire part is highlighted and the non-fire part is dimmed. Particle Swarm Optimization (PSO) and sample pixels from an image are used to obtain the weights of the colour-differentiating conversion matrix, and K-medoids provides a fitness metric for the PSO procedure. The obtained conversion matrix can be used for fire detection on different fire images without performing the PSO procedure. This allows a fast and easy implementable fire detection system. The empirical results indicate that the proposed method provides both qualitatively and quantitatively better results when compared to some of the conventional and state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

The performance of supervised classification algorithms is highly dependent on the quality of training data. Ambiguous training patterns may misguide the classifier leading to poor classification performance. Further, the manual exploration of class labels is an expensive and time consuming process. An automatic method is needed to identify noisy samples in the training data to improve the decision making process. This article presents a new classification technique by combining an unsupervised learning technique (i.e. fuzzy c-means clustering (FCM)) and supervised learning technique (i.e. back-propagation artificial neural network (BPANN)) to categorize benign and malignant tumors in breast ultrasound images. Unsupervised learning is employed to identify ambiguous examples in the training data. Experiments were conducted on 178 B-mode breast ultrasound images containing 88 benign and 90 malignant cases on MATLAB® software platform. A total of 457 features were extracted from ultrasound images followed by feature selection to determine the most significant features. Accuracy, sensitivity, specificity, area under the receiver operating characteristic curve (AUC) and Mathew's correlation coefficient (MCC) were used to access the performance of different classifiers. The result shows that the proposed approach achieves classification accuracy of 95.862% when all the 457 features were used for classification. However, the accuracy is reduced to 94.138% when only 19 most relevant features selected by multi-criterion feature selection approach were used for classification. The results were discussed in light of some recently reported studies. The empirical results suggest that eliminating doubtful training examples can improve the decision making performance of expert systems. The proposed approach show promising results and need further evaluation in other applications of expert and intelligent systems. [ABSTRACT FROM AUTHOR]

Abdominal Aortic Aneurism is a disease related to a weakening in the aortic wall that can cause a break in the aorta and the death. The detection of an unusual dilatation of a section of the aorta is an indicative of this disease. However, it is difficult to diagnose because it is necessary image diagnosis using computed tomography or magnetic resonance. An automatic diagnosis system would allow to analyze abdominal magnetic resonance images and to warn doctors if any anomaly is detected. We focus our research in magnetic resonance images because of the absence of ionizing radiation. Although there are proposals to identify this disease in magnetic resonance images, they need an intervention from clinicians to be precise and some of them are computationally hard. In this paper we develop a novel approach to analyze magnetic resonance abdominal images and detect the lumen and the aortic wall. The method combines different algorithms in two stages to improve the detection and the segmentation so it can be applied to similar problems with other type of images or structures. In a first stage, we use a spatial fuzzy C-means algorithm with morphological image analysis to detect and segment the lumen; and subsequently, in a second stage, we apply a graph cut algorithm to segment the aortic wall. The obtained results in the analyzed images are pretty successful obtaining an average of 79% of overlapping between the automatic segmentation provided by our method and the aortic wall identified by a medical specialist. The main impact of the proposed method is that it works in a completely automatic way with a low computational cost, which is of great significance for any expert and intelligent system. [ABSTRACT FROM AUTHOR]

In this paper, a new fast incremental fuzzy partitioning algorithm able to find either a fuzzy globally optimal partition or a fuzzy locally optimal partition of the set A ⊂ R n close to the global one is proposed. This is the main impact of the paper, which could have an important role in applied research. Since fuzzy k -optimal partitions with k = 2 , 3 , ⋯ , k m a x clusters are determined successively in the algorithm, it is possible to calculate corresponding validity indices for every obtained partition. The number k max is defined in such a way that the objective function value of optimal partition with k max clusters is relatively very close to the objective function value of optimal partition with ( k m a x − 1 ) clusters. Before clustering, the data are normalized and afterwards several validity indices are applied to partitions of the normalized data. Very simple relationships between used validity indices on normalized and original data are given as well. Hence, the proposed algorithm is able to find optimal partitions with the most appropriate number of clusters. The algorithm is tested on numerous synthetic data sets and several real data sets from the UCI data repository. [ABSTRACT FROM AUTHOR]

Traditional Importance–Performance Analysis assumes the distribution of a given set of attributes in four sets, “Keep up the good work”, “Concentrate here”, “Low priority” and “Possible overkill” , corresponding to the four possibilities, high–high, low–high, low–low and high–low, of the pair performance–importance. This can lead to ambiguities, contradictions or non-intuitive results, especially because the most real-world classes are fuzzy rather than crisp. The fuzzy clustering is an important tool to identify the structure in data, therefore we apply the Fuzzy C -Means Algorithm to obtain a fuzzy partition of a set of attributes. A membership degree of every attribute to each of the sets mentioned above is determined, against to the forcing categorization in traditional Importance–Performance Analysis. The main benefit is related with the deriving of the managerial decisions which become more refined due to the fuzzy approach. In addition, the development priorities and the directions in which the effort of an economic or non-economic entity would be useless or even dangerous are identified on a rigorous basis and taking into account only the internal structure of the input data. [ABSTRACT FROM AUTHOR]

Clustering aims to classify different patterns into groups called clusters . Many algorithms for both hard and fuzzy clustering have been developed to deal with exploratory data analysis in many contexts such as image processing, pattern recognition, etc. However, we are witnessing the era of big data computing where computing resources are becoming the main bottleneck to deal with those large datasets. In this context, sequential algorithms need to be redesigned and even rethought to fully leverage the emergent massively parallel architectures. In this paper, we propose a parallel implementation of the fuzzy minimals clustering algorithm called Parallel Fuzzy Minimal (PFM). Our experimental results reveal linear speed-up of PFM when compared to the sequential counterpart version, keeping very good classification quality. [ABSTRACT FROM AUTHOR]

Design space exploration and metamodeling techniques have gained rapid dominance in complex engineering design problems. It is observed that the modeling efficiency and accuracy are directly associated with the design space. In order to reduce the complexity of the design space and improve modeling accuracy, a multi-stage design space reduction and metamodeling optimization methodology based on self-organizing maps and fuzzy clustering is proposed in this paper. By using the proposed three-stage optimization approach, the design space is systematically reduced to a relatively small promising region. Self-organizing maps are introduced to act as the preliminary reduction approach through analyzing the underlying mapping relations between design variables and system responses within the original samples. GK (Gustafson & Kessel) clustering algorithm is employed to determine the proper number of clusters by utilizing clustering validity indices, and sample points are clustered using fuzzy c-means (FCM) clustering method with the known number of clusters, so that the search can focus on the most promising area and be better supported by the constructed kriging metamodel. Empirical studies on benchmark problems with multi-humps and two practical nonlinear engineering design problems show the accurate results can be obtained within the reduced design space, which improve the overall efficiency significantly. [ABSTRACT FROM AUTHOR]

Dental X-ray image segmentation (DXIS) is an indispensable process in practical dentistry for diagnosis of periodontitis diseases from an X-ray image. It has been said that DXIS is one of the most important and necessary steps to analyze dental images in order to get valuable information for medical diagnosis support systems and other recognition tools. Specialized data mining methods for DXIS have been investigated to achieve high accuracy of segmentation. However, traditional image processing and clustering algorithms often meet challenges in determining parameters or common boundaries of teeth samples. It was shown that performance of a clustering algorithm is enhanced when additional information provided by users is attached to inputs of the algorithm. In this paper, we propose a new cooperative scheme that applies semi-supervised fuzzy clustering algorithms to DXIS. Specifically, the Otsu method is used to remove the Background area from an X-ray dental image. Then, the FCM algorithm is chosen to remove the Dental Structure area from the results of the previous steps. Finally, Semi-supervised Entropy regularized Fuzzy Clustering algorithm (eSFCM) is opted to clarify and improve the results based on the optimal result from the previous clustering method. The proposed framework is evaluated on a real collection of dental X-ray image datasets from Hanoi Medical University, Vietnam. Experimental results have revealed that clustering quality of the cooperative framework is better than those of the relevant ones. The findings of this paper have great impact and significance to researches in the fields of medical science and expert systems. It has been the fact that medical diagnosis is often an experienced and case-based process which requests long time practicing in real patients. In many situations, young clinicians do not have chance for such the practice so that it is necessary to utilize a computerized medical diagnosis system which could simulate medical processes from previous real evidences. By learning from those cases, clinicians would improve their experience and responses for later ones. In the view of expert systems, this paper made uses of knowledge-based algorithms for a practical application. This shows the advantages of such the algorithm in the conjunction domain between expert systems and medical informatics. The findings also suggested the most appropriate configuration of the algorithm and parameters for this problem that could be reused by other researchers in similar applications. The usefulness and significance of this research are clearly demonstrated within the extent of real-life applications. [ABSTRACT FROM AUTHOR]

Clustering structures are one of the most important aspects of complex networks. Minimum spanning tree (MST), the tree that connects all vertices with minimum total weight, can be considered as a fundamental unit of original weighted graphs. There are different types of algorithms that identify clusters in a network, but the existing theories and algorithms for searching trees have not been investigated for uncertain scenarios. This paper tackles the situations where network parameters may be uncertain. Rather, we permit the parameters to take the form of Pythagorean fuzzy numbers (PFNs). Moreover, to represent qualitative aspects of uncertainty, the use of linguistic variables (LVs) has effective means for experts in expressing their views. The current study proposes a graph theory-based agglomerative hierarchical clustering technique for Pythagorean fuzzy sets. We first define generalized Pythagorean fuzzy numbers (GPFNs) and LR-type PFNs. Then we compute the PF distance between two GPFNs and also LR-type PFNs, and formulate the expressions for PF similarity measure. This paper mainly examines the use of PF distance and similarity measures in a minimum spanning tree agglomerative hierarchical clustering method by considering PFLVs. Since the structural and functional systems of brain are characterized by complex networks, we apply the proposed algorithm on a functional brain network to prove its practicality and efficiency. We discuss the hierarchical clustering consequences of the proposed algorithm in the shape of a dendrogram. Finally, we compare the clustering results obtained by different similarity measures. • The paper tackles the situations where network parameters may be uncertain. • We let the network parameters to take the form of Pythagorean fuzzy (PF) numbers. • We propose a graph theory-based agglomerative hierarchical clustering technique. • A minimum spanning tree agglomerative hierarchical clustering method is used. • A functional brain network is used to prove its practicality and efficiency. [ABSTRACT FROM AUTHOR]

Fuzzy clustering has become an important research field with many applications to real world problems. Among fuzzy clustering methods, fuzzy c-means (FCM) is one of the best known for its simplicity and efficiency, although it shows some weaknesses, particularly its tendency to fall into local minima. To tackle this shortcoming, many optimization-based fuzzy clustering methods have been proposed in the literature. Some of these methods are based solely on a metaheuristic optimization, such as particle swarm optimization (PSO) whereas others are hybrid methods that combine a metaheuristic with a traditional partitional clustering method such as FCM. It is demonstrated in the literature that methods that hybridize PSO and FCM for clustering have an improved accuracy over traditional partitional clustering approaches. On the other hand, PSO-based clustering methods have poor execution time in comparison to partitional clustering techniques. Another problem with PSO-based clustering is that the current PSO algorithms require tuning a range of parameters before they are able to find good solutions. In this paper we introduce two hybrid methods for fuzzy clustering that aim to deal with these shortcomings. The methods, referred to as FCM–IDPSO and FCM2–IDPSO, combine FCM with a recent version of PSO, the IDPSO, which adjusts PSO parameters dynamically during execution, aiming to provide better balance between exploration and exploitation, avoiding falling into local minima quickly and thereby obtaining better solutions. Experiments using two synthetic data sets and eight real-world data sets are reported and discussed. The experiments considered the proposed methods as well as some recent PSO-based fuzzy clustering methods. The results show that the methods introduced in this paper provide comparable or in many cases better solutions than the other methods considered in the comparison and were much faster than the other state of the art PSO-based methods. [ABSTRACT FROM AUTHOR]

The health care support system is a special type of recommender systems that play an important role in medical sciences nowadays. This kind of systems often provides the medical diagnosis function based on the historic clinical symptoms of patients to give a list of possible diseases accompanied with the membership values. The most acquiring disease from that list is then determined by clinicians’ experience expressed through a specific defuzzification method. An important issue in the health care support system is increasing the accuracy of the medical diagnosis function that involves the cooperation of fuzzy systems and recommender systems in the sense that uncertain behaviors of symptoms and the clinicians’ experience are represented by fuzzy memberships whilst the determination of the possible diseases is conducted by the prediction capability of recommender systems. Intuitionistic fuzzy recommender systems (IFRS) are such the combination, which results in better accuracy of prediction than the relevant methods constructed on either the traditional fuzzy sets or recommender system only. Based upon the observation that the calculation of similarity in IFRS could be enhanced by the integration with the information of possibility of patients belonging to clusters specified by a fuzzy clustering method, in this paper we propose a novel hybrid model between picture fuzzy clustering and intuitionistic fuzzy recommender systems for medical diagnosis so-called HIFCF (Hybrid Intuitionistic Fuzzy Collaborative Filtering). Experimental results reveal that HIFCF obtains better accuracy than IFCF and the standalone methods of intuitionistic fuzzy sets such as De, Biswas & Roy, Szmidt & Kacprzyk, Samuel & Balamurugan and recommender systems, e.g. Davis et al. and Hassan & Syed. The significance and impact of the new method contribute not only the theoretical aspects of recommender systems but also the applicable roles to the health care support systems. [ABSTRACT FROM AUTHOR]

A High–order algorithm for Multi-Variable Fuzzy Time Series (HMV-FTS) is presented based on fuzzy clustering to eliminate some well-known problems with the existing FTS algorithms. High-order algorithms can handle only one-variable FTS and multi-variable algorithms can handle only one-order FTS. HMV-FTS does both tasks simultaneously. FTS algorithms cannot incorporate existing information about future value of a variable in the forecasting process while HMV-FTS can. Defuzzification of the fuzzy value of a forecast to cluster centers or midpoint of intervals and use of intervals are other controversial problems with the existing FTS algorithms. These are eliminated by constructing fuzzy sets from partition matrices and letting each data point to contribute in defuzzification based on its membership grade in the fuzzy sets. In multi-variable FTS algorithms, one variable is considered as main variable which is forecasted and the other variables are secondary; while HMV-FTS treats all variables equally and more than one variable can be forecasted at the same time. It is shown that HMV-FTS is suitable for system identification, forecasting and interpolation. This algorithm is more accurate than popular FTS algorithms and other forecasting tools and systems such as ANFIS, Type II fuzzy model and ARIMA model. [ABSTRACT FROM AUTHOR]

Accessibility and accurate estimation of the tropospheric delay plays a crucial role in meteorological studies and weather forecasts as well as improving positioning accuracy. We propose to employ an adaptive neuro fuzzy inference system (ANFIS) to build estimation and prediction models for zenith path delay (ZPD). Five selected stations over Antarctica were used to examine the applicability of ANFIS. GPS ZPD data of 2010 with five-minute resolution was used as the target output. A fuzzy clustering algorithm is adopted to enhance the performance of the models, which is able to minimize the number of membership functions and rules for better efficiency in the models. To investigate the accuracy of models developed, a combination of the surface pressure ( P ), temperature ( T ) and relative humidity ( H ) is performed to obtain the best estimation of ZPD. The results demonstrated that ANFIS models with three inputs network ( P , T and H ) agreed very well with ZPD obtained from GPS than separated input only coming from P or T , or P and T , or P and H . Finally, the input network ( P , T and H ) is selected in developing the ZPD predictive models. The prediction resulted from one-step to eight-step ahead development, demonstrated that the high-resolution of data used in training process will increase the accuracy of the predictive model. [ABSTRACT FROM AUTHOR]

Fuzzy clustering is considered as an important tool in pattern recognition and knowledge discovery from a database; thus has been being applied broadly to various practical problems. Recent advances in data organization and processing such as the cloud computing technology which are suitable for the management, privacy and storing big datasets have made a significant breakthrough to information sciences and to the enhancement of the efficiency of fuzzy clustering. Distributed fuzzy clustering is an efficient mining technique that adapts the traditional fuzzy clustering with a new storage behavior where parts of the dataset are stored in different sites instead of the centralized main site. Some distributed fuzzy clustering algorithms were presented including the most effective one – the CDFCM of Zhou et al. (2013). Based upon the observation that the communication cost and the quality of results in CDFCM could be ameliorated through the integration of a distributed picture fuzzy clustering with the facilitator model, in this paper we will present a novel distributed picture fuzzy clustering method on picture fuzzy sets so-called DPFCM. Experimental results on various datasets show that the clustering quality of DPFCM is better than those of CDFCM and relevant algorithms. [ABSTRACT FROM AUTHOR]

Time series data are commonly clustered based on their distributional characteristics. The moments play a central role among such characteristics because of their relevant informative content. This paper aims to develop a novel approach that faces still open issues in moment-based clustering. First of all, we deal with a very general framework of time-varying moments rather than static quantities. Second, we include in the clustering model high-order moments. Third, we avoid implicit equal weighting of the considered moments by developing a clustering procedure that objectively computes the optimal weight for each moment. As a result, following a fuzzy approach, two weighted clustering models based on both unconditional and conditional moments are proposed. Since the Dynamic Conditional Score model is used to estimate both conditional and unconditional moments, the resulting framework is called weighted score-driven clustering. We apply the proposed method to financial time series as an empirical experiment. • The paper proposes a new method for time series clustering. • The procedure is based on an optimal combination of conditional and unconditional moments. • The clustering procedure includes fuzziness. • The clustering method is applied to financial time series. [ABSTRACT FROM AUTHOR]

Highlights: [•] Interval attribute weights are proposed and introduced for fuzzy clustering. [•] Genetic mechanism and gradient-based iteration constitute optimization strategy. [•] Data partition and weights can be obtained by minimizing the objective function. [•] Reasonable clustering results can be achieved more easily. [ABSTRACT FROM AUTHOR]

Highlights: [•] A weighted multivariate fuzzy clustering method for interval-valued data is introduced. [•] Weights measure importance of each variable to compute membership degree by cluster. [•] This method is robust to ambiguous cluster membership assignment. [•] An application with interval-valued scientific production data is described. [ABSTRACT FROM AUTHOR]

Abstract: In this study, we propose an enhanced fuzzy clustering algorithm related to α-cut interval descriptions of fuzzy numbers and a new cluster validity index, which occurs by α-cut intervals and adding two ad hoc functions in the compactness and separability measures. As an application, we use the enhanced fuzzy clustering algorithm and its proposed validity index to rank supplier firms of a Turkish Machinery Corporation by design alternatives. In addition, the rankings of supplier firms are determined with a proposed decision measure. [Copyright &y& Elsevier]

Abstract: In recent years, time series forecasting studies in which fuzzy time series approach is utilized have got more attentions. Various soft computing techniques such as fuzzy clustering, artificial neural networks and genetic algorithms have been used in fuzzy time series method to improve the method. While fuzzy clustering and genetic algorithms are being used for fuzzification, artificial neural networks method is being preferred for using in defining fuzzy relationships. In this study, a hybrid fuzzy time series approach is proposed to reach more accurate forecasts. In the proposed hybrid approach, fuzzy c-means clustering method and artificial neural networks are employed for fuzzification and defining fuzzy relationships, respectively. The enrollment data of University of Alabama is forecasted by using both the proposed method and the other fuzzy time series approaches. As a result of comparison, it is seen that the most accurate forecasts are obtained when the proposed hybrid fuzzy time series approach is used. [Copyright &y& Elsevier]

Abstract: As it is known, fuzzy clustering is a kind of soft clustering method and primarily based on idea of segmenting data by using membership degrees of cases which are computed for each cluster. However, most of the current fuzzy clustering modules packaged in both open source and commercial products have lack of enabling users to explore fuzzy clusters deeply and visually in terms of investigation of different relations among clusters. Furthermore, without a decision maker or an expert, it is hard to decide the number of clusters in fuzzy clustering studies. Therefore, in this study, a desktop software, namely FUAT, is developed to analyze, explore and visualize different aspects of obtained fuzzy clusters which are segmented by fuzzy c-means algorithm. Moreover, to obtain and inform possible natural cluster number, FUAT is equipped with Expectation Maximization algorithm. [Copyright &y& Elsevier]

Abstract: Geo-Demographic Analysis (GDA) is an important tool to explore the underlying rules that regulate our world, and therefore, it has been widely applied to the development of effective socio-economic policies through the analysis of data generated from Geographic Information Systems (GIS). In GDA applications, clustering plays a major role however, the current state-of-the-art algorithms, namely the Fuzzy Geographically Weighted Clustering (FGWC), have demonstrated several limitations both in terms of speed and in terms of quality of the achieved results. Accordingly, in this paper, we propose a novel clustering algorithm for GDA application, based on recent results regarding intuitionistic fuzzy sets and the possibilistic fuzzy C-means, that aims at overcoming some of the limitations of the existing methods. [Copyright &y& Elsevier]

Abstract: Increasing our understanding of typhoon movements remains a priority in the western North Pacific. In this study, the trajectories of typhoons that affected Taiwan between 1986 and 2010 are used for clustering, where each trajectory consists of 6-hourly latitude-longitude positions over two days. We compare the performance of four statistical clustering methods, namely, k-means clustering, fuzzy c-means (FCM) clustering, hierarchical clustering, and normalized cut techniques. The results show that the FCM technique provides sufficient cluster efficiency with a relatively high degree of goodness of fit. FCM identifies six clusters according to the minimum coefficients of variation (CV). The hotspots of the typhoon centers in each cluster are determined by kernel density estimation (KDE). Moreover, the typhoon track belongs to six clusters with different membership degrees in FCM. The typhoon track density map is estimated by combining the KDE hotspot maps associated with the FCM weights. The information could be used in planning for disaster management. [Copyright &y& Elsevier]

Abstract: Clustering is a well known technique in identifying intrinsic structures and find out useful information from large amount of data. One of the most extensively used clustering techniques is the fuzzy c-means algorithm. However, computational task becomes a problem in standard objective function of fuzzy c-means due to large amount of data, measurement uncertainty in data objects. Further, the fuzzy c-means suffer to set the optimal parameters for the clustering method. Hence the goal of this paper is to produce an alternative generalization of FCM clustering techniques in order to deal with the more complicated data; called quadratic entropy based fuzzy c-means. This paper is dealing with the effective quadratic entropy fuzzy c-means using the combination of regularization function, quadratic terms, mean distance functions, and kernel distance functions. It gives a complete framework of quadratic entropy approaching for constructing effective quadratic entropy based fuzzy clustering algorithms. This paper establishes an effective way of estimating memberships and updating centers by minimizing the proposed objective functions. In order to reduce the number iterations of proposed techniques this article proposes a new algorithm to initialize the cluster centers. In order to obtain the cluster validity and choosing the number of clusters in using proposed techniques, we use silhouette method. First time, this paper segments the synthetic control chart time series directly using our proposed methods for examining the performance of methods and it shows that the proposed clustering techniques have advantages over the existing standard FCM and very recent ClusterM-k-NN in segmenting synthetic control chart time series. [Copyright &y& Elsevier]

• Extension of fuzzy k-means to generate feature subspaces. • Generation of input clusterings from feature subspace. • Ensemble method for ensemble clustering. • Results generation from cancer data. • Interpretation of the results. Clustering analysis is a significant research topic in discovering cancer using different profiles of gene expression, which is very important to successfully diagnose and treat the cancer decease. Many ensemble clustering methods have been developed to perform clustering using tumor data. Only few of them incorporates a significant number of input clusterings, the optimal number of clusters in each input clustering, and an appropriate ensemble method to combine input clusterings into a final clustering. In this paper, we introduce two new steps in the standard fuzzy k -means algorithm to determine the optimal number of input clusterings, and the optimal number of clusters in each clustering for ensemble clustering. The first one is to incorporate a penalty term for making the algorithm insensitive to the initialization of cluster centroids. The second one is to automate a clustering process for iteratively updating the feature weights. This step addresses the noise values in the dataset. We propose an ensemble clustering method, which combines a set of input clusterings into a final clustering having better overall quality. Experiments on real cancer gene expression profiles illustrate that the proposed algorithm outperformed the well-known clustering algorithms. [ABSTRACT FROM AUTHOR]