Possibilistic C-means Clustering Research Articles

Suppressed possibilistic fuzzy c-means clustering based on shadow sets for noisy data with imbalanced sizes

Possibilistic fuzzy c-means clustering (PFCM) algorithm generates fewer overlapping clustering centers than the possibilistic c-means clustering (PCM) algorithm and possesses better noise immunity than fuzzy c-means clustering (FCM) algorithm. However, with the increasing noise intensity and number of clusters, PFCM still faces the problem of getting partially overlapping clustering centers or mislocated centers in noise regions. Moreover, the sample-size imbalance increasingly intensifies the difficulty of positioning centers of small clusters. To solve the above problems, a suppressed possibilistic fuzzy c-means clustering algorithm based on shadow sets (S-SPFCM) is proposed by introducing the shadow set theory and the "suppressed competitive learning" strategy. Firstly, KL divergence is introduced in the objective function of PFCM to increase the anti-noise robustness of fuzzy memberships against long-range noise and outliers. Secondly, to reduce the number of overlapping centers caused by possibilistic memberships, the shadow set theory is introduced to divide each class adaptively into three regions (core, shadow, and exclusion regions) by an uncertainty balance method. The suppressed competitive learning method is extended by modifying the memberships of points within the three regions, thus artificially guiding the iterative track of clustering centers. Meanwhile, to further reduce the influence of imbalanced sizes, a scheme to reset mislocated centers in the core and shadow regions is also designed. In addition, to improve the segmentation performance of S-SPFCM for noisy images, a suppressed possibilistic fuzzy c-means clustering algorithm based on shadow sets and local information (SL-SPFCM) is also proposed. The SL-SPFCM first improves the Euclidean distance by a distance filtering scheme. Then SL-SPFCM introduces the local median membership of each pixel into the KL divergence of the objective function. Finally, experiments on synthetic datasets and color images which are characteristic of imbalanced sizes and noise injection demonstrate the proposed S-SPFCM and SL-SPFCM algorithms achieve smaller center deviations and higher clustering accuracy compared with several state-of-the-art clustering algorithms.

Mahalanobis-Kernel Distance-Based Suppressed Possibilistic C-Means Clustering Algorithm for Imbalanced Image Segmentation

Mahalanobis-Kernel Distance-Based Suppressed Possibilistic C-Means Clustering Algorithm for Imbalanced Image Segmentation

Semi-supervised possibilistic c-means clustering algorithm based on feature weights for imbalanced data

The possibilistic c-means clustering (PCM) algorithm improves the robustness of fuzzy c-means clustering (FCM) to noise and outliers by releasing the probabilistic constraint of memberships. The semi-supervised possibilistic c-means clustering (SSPCM) algorithm improves the clustering effect on datasets with imbalanced sizes by introducing a small amount of label information. However, the traditional semi-supervised algorithm still faces the problem of low utilization of supervision information for datasets with large differences in sample sizes. Moreover, the Euclidean distance, which treats features equally, cannot handle feature-imbalanced data. Therefore, this paper proposes a semi-supervised possibilistic c-means clustering algorithm based on feature weights (FW-SSPCM) by introducing the ideas of supervised centers. First, the algorithm introduces the supervised center into the objective function of the SSPCM to improve the utilization rate of supervision information and thus guide the center iteration of small clusters. Second, the feature weighting strategy is introduced in the objective function to adaptively assign feature weights according to the importance of different features in different clusters, thus improving the adaptability of the algorithm to feature-imbalanced datasets. In addition, to improve the robustness of the antinoise effect and retain additional image details, a new image segmentation algorithm based on FW-SSPCM and local information (LFW-SSPCM) is proposed by introducing local spatial information obtained by bilateral filtering. Finally, through clustering experiments on synthetic data, UCI datasets and on color images characteristic of multiple features, including imbalanced sizes, imbalanced features and strong noise injection, the clustering performances of the proposed FW-SSPCM and LFW-SSPCM proposed in this paper are significantly better than those of several related clustering algorithms.

A feature-weighted suppressed possibilistic fuzzy c-means clustering algorithm and its application on color image segmentation

The possibilistic fuzzy c-means clustering (PFCM) algorithm is a hybridization of possibilistic c-means clustering (PCM) and fuzzy c-means clustering (FCM) algorithms. However, there are two main problems in PFCM. One is that the Euclidean distance employed in PFCM always disregards the imbalance among sample features because it treats all features of data equally, which easily causes misclassification for feature-imbalanced multidimensional data. The other is that PFCM always produces significant center deviations and overlapping centers for multiclass datasets with strong noise injection, due to the difficulty of PFCM in the membership-weight parameter setting and the lack of between-class relationships in possibilistic memberships. Therefore, a feature-weighted suppressed possibilistic fuzzy c-means clustering (FW-S-PFCM) algorithm is presented by introducing a feature-weighted method and “suppressed competitive learning” strategy into the PFCM algorithm in this paper. First, the FW-S-PFCM algorithm introduces a feature-weight matrix into the objective function that can automatically assign feature-weight values to different features and different clusters according to the distribution of samples, thus overcoming the influence of feature imbalance and improving clustering effects for noisy multidimensional datasets. Second, combined with the feature-weight matrix, a “suppressed competitive learning” strategy is designed to resolve the center-overlapping problem in noisy multiclass dataset clustering. Specifically, partial crucial points of each class near the center are selected according to a cluster core generated by a cross-section of a threshold on the possibilistic membership surface. Third, their possibilistic memberships participate in the suppressed learning process to overcome the lack of between-class relationships. Last, a segmentation algorithm for noisy color images based on FW-S-PFCM is proposed combined with the feature-weight method and noise-identification ability of possibilistic memberships. Experiments on synthetic data, UCI data and color image segmentation demonstrate that the proposed FW-S-PFCM algorithm can overcome the partial center-overlapping problem and improve clustering performance on complex datasets with feature imbalance and strong noise injection. The proposed algorithm can also reduce the iteration number, sensitivity to membership weights, and initializations of PFCM.

Double-suppressed possibilistic fuzzy Gustafson–Kessel clustering algorithm

Possibilistic fuzzy c-means clustering (PFCM) is an unsupervised hybrid clustering algorithm, which can partly inherit the stability of fuzzy c-means clustering (FCM) algorithm and the noise robustness of possibilistic c-means clustering (PCM) algorithm. However, there are still several limitations in the PFCM when clustering complex data with multiple characteristics: sensitivity to strong noise, coincident clustering problem in multi-class clustering, and disability to deal with strong correlations of feature components. Therefore, a double-suppressed possibilistic fuzzy Gustafson–Kessel​ clustering algorithm (DS-PFGK) is presented. Firstly, we design a new objective function with a modified Mahalanobis distance and an improved weight parameter setting method based on the stability of fuzzy memberships and the anti-noise ability of possibilistic memberships. Moreover, combined with the absolute attribute of possibilistic memberships and the covariance matrix in the modified Mahalanobis distance, an ellipsoidal cluster core which can depict the distribution of sample data is generated to divide each cluster into different regions for selecting appropriate learning objects and identifying noisy data adaptively. Then, a “double-suppressed competitive learning” strategy is designed for the selected learning objects to solve the coincident clustering problem in multi-class clustering by suppressing the nonwinner possibilistic memberships, and to reduce the iteration number by suppressing nonwinner fuzzy memberships and rewarding winner fuzzy memberships. Finally, a segmentation algorithm on noisy color images based on the DS-PFGK is proposed based on the generated cluster cores. Experiments on synthetic datasets, real datasets, and color images show the good performance of the proposed methods compared with several classical and state-of-the-art clustering algorithms.

Generalized possibilistic c-means clustering with double weighting exponents

Considering that the improved possibilistic c-means (PCM) algorithms are sensitive to noise while addressing the issue of consistency clustering in PCM, this paper proposes the generalized possibilistic c-means clustering with double weighting exponents. Firstly, double weighting exponents are introduced into the PCM algorithm, and the generalized possibilistic c-means clustering model is established. Secondly, the difference between the double weighting exponents in the generalized possibilistic clustering model is set to 1 or −1; two improved single-exponent possibilistic clustering algorithms called IPCM1 and IPCM2 are proposed, and their local convergence is strictly proven by the Zangwill theorem. Finally, the reasonable range of the weighting exponent in IPCM1 and IPCM2 algorithms is determined by mathematical optimization. Experimental results indicate that IPCM1 and IPCM2 outperform existing PCM-related algorithms; they achieve excellent clustering performance, significantly improve the robustness to noise, and decrease the sensitivity to the weighting exponent. The work of this paper has far-reaching significance for promoting the development of the possibilistic c-means clustering theory.

Total-aware suppressed possibilistic c-means clustering

Cutset-type possibilistic c-means (CPCM) is an improved version of possibilistic c-means (PCM), and it addresses the issue of consistency clustering in PCM. However, the clustering performance has not significantly improved, and its convergence speed is still slow. Hence, a total-aware suppressed possibilistic c-means (TSPCM) clustering is proposed in this paper. Firstly, from a global perspective, the typicality values of all the non-winners of samples inside the cluster core are decreased by the suppressed factor while increasing the typicality values of all the winners of samples in the same core. Meanwhile, the typicality values of samples outside the cluster core remain unchanged. The corrected typicality values are used to update the clustering centers, and the modified clustering centers are again used to renew the typicality values alternately until the algorithm converges. Secondly, the objective function of the proposed TSPCM is constructed, and Zangwill's theorem firmly establishes its convergence. Finally, two robust total-aware suppressed algorithms are presented when TSPCM is used for the clustering of numerical data with noise and the segmentation of noisy images. Experimental results show that the proposed TSPCM and its robust algorithms are obviously superior to existing state-of-the-art PCM-related algorithms.

An improved fuzzy C-means clustering algorithm using Euclidean distance function

The fuzzy c-mean (FCM) clustering algorithm is a typical algorithm using Euclidean distance for data clustering and it is also one of the most popular fuzzy clustering algorithms. However, FCM does not perform well in noisy environments due to its possible constraints. To improve the clustering accuracy of item varieties, an improved fuzzy c-mean (IFCM) clustering algorithm is proposed in this paper. IFCM uses the Euclidean distance function as a new distance measure which can give small weights to noisy data and large weights to compact data. FCM, possibilistic C-means (PCM) clustering, possibilistic fuzzy C-means (PFCM) clustering and IFCM are run to compare their clustering effects on several data samples. The clustering accuracies of IFCM in five datasets IRIS, IRIS3D, IRIS2D, Wine, Meat and Apple achieve 92.7%, 92.0%, 90.7%, 81.5%, 94.2% and 88.0% respectively, which are the highest among the four algorithms. The final simulation results show that IFCM has better robustness, higher clustering accuracy and better clustering centers, and it can successfully cluster item varieties.

Sparse possibilistic c-means clustering with Lasso

Krishnapuram and Keller first proposed possibilistic c-means (PCM) clustering in 1993. Afterward, PCM was widely studied with various extensions. The PCM algorithm and its extensions always treat feature components under equal importance, but, in real applications, different features may better have different weights. Recently, Yang and Benjamin in 2021 proposed a feature-weighted PCM clustering with feature reduction. Although Yang and Benjamin (2021) can reduce feature dimensions, it still encounters the curse of dimensionality for high dimensional data. One possible way to address this problem is to conduct a sparse clustering technique. In this paper, we further study the PCM clustering by incorporating the idea of sparsity with different feature weights. We propose two approaches that use the PCM clustering with the least absolute shrinkage and selection operator (Lasso). The first one is the sparse PCM subject to a Lasso constraint of feature weights, called S-PCM1. The second is the sparse PCM by adding a Lasso penalty term of feature weights in the objective function, called S-PCM2. We show that S-PCM1 and S-PCM2 are theoretically the same, and both can induce sparsity in features, but they use different procedures in algorithms. Synthetic and real data sets are used to compare S-PCM1 and S-PCM2 with some existing sparsity clustering algorithms. Experimental results and comparisons demonstrate the effectiveness and usefulness of the proposed S-PCM1 and S-PCM2 clustering algorithms.

Possibilistic c-means clustering based on the nearest-neighbour isolation similarity

Clustering is widely used in data mining and machine learning. The possibilistic c-means clustering (PCM) method loosens the constraint of the fuzzy c-means clustering (FCM) method to solve the problem of noise sensitivity of FCM. But there is also a new problem: overlapping cluster centers are not suitable for clustering non-cluster distribution data. We propose a novel possibilistic c-means clustering method based on the nearest-neighbour isolation similarity in this paper. All samples are taken as the initial cluster centers in the proposed approach to obtain k sub-clusters iteratively. Then the first b samples farthest from the center of each sub-cluster are chosen to represent the sub-cluster. Afterward, sub-clusters are mapped to the distinguishable space by using these selected samples to calculate the nearest-neighbour isolation similarity of the sub-clusters. Then, adjacent sub-clusters can be merged according to the presented connecting strategy, and finally, C clusters are obtained. Our method proposed in this paper has been tested on 15 UCI benchmark datasets and a synthetic dataset. Experimental results show that our proposed method is suitable for clustering non-cluster distribution data, and the clustering results are better than those of the comparison methods with solid robustness.

Retracted: Deep Possibilistic C-means Clustering Algorithm on Medical Datasets.

[This retracts the article DOI: 10.1155/2022/3469979.].

SPCM: Efficient semi-possibilistic c-means clustering algorithm

The required division and exponentiation operations needed per iteration for the possibilistic c-means (PCM) clustering algorithm complicate its implementation, especially on homomorphically-encrypted data. This paper presents a novel efficient soft clustering algorithm based on the possibilistic paradigm, termed SPCM. It aims at easing future applications of PCM to encrypted data. It reduces the required exponentiation and division operations at each iteration by restricting the membership values to an ordered set of discrete values in [0,1], resulting in a better performance in terms of runtime and several other performance indices. At each iteration, distances to the new clusters’ centers are determined, then the distances are compared to the initially computed and dynamically updated range of values, that divide the entire range of distances associated with each cluster center into intervals (bins), to assign appropriate soft memberships to objects. The required number of comparisons is O(log the number of discretization levels). Thus, the computation of centers and memberships is greatly simplified during execution. Also, the use of discrete values for memberships allows soft modification (increment or decrement) of the soft memberships of identified outliers and core objects instead of rough modification (setting to zero or one) in related algorithms. Experimental results on synthetic and standard test data sets verified the efficiency and effectiveness of the proposed algorithm. The average percent of the achieved reduction in runtime is 35% and the average percent of the achieved increase in v-measure, adjusted mutual information, and adjusted rand index is 6% on five datasets compared to PCM. The larger the dataset, the higher the reduction in runtime. Also, SPCM achieved a comparable performance with less computational complexity compared to variants of related algorithms.

A novel interval-valued data driven type-2 possibilistic local information c-means clustering for land cover classification

In the process of land cover classification, existing fuzzy clustering is not enough to describe the high-order fuzzy uncertainty, while possibilistic clustering has serious parameter dependence and cluster consistency, which makes them unable to effectively deal with the phenomena of “different objects with the same spectrum” and “different objects with the same spectrum”. Hence, this paper proposes a robust type-2 possibilistic C-means clustering with local information and interval-valued data model for remote sensing land cover classification. Firstly, according to the local neighborhood variance, remote sensing information is modeled as interval-valued data. Secondly, existing possibilistic C-means clustering is modified and an enhanced possibilistic C-means clustering is obtained. Once again, it is used to clustering interval-valued data and a single weighting exponent type-2 possibilistic C-means clustering with double distance measures is constructed. Finally, to further improve the robustness of clustering method, local information is embedded into the objective function of this enhanced type-2 possibilistic C-means clustering and a novel robust possibilistic clustering-related algorithm for remote sensing information classification is proposed. Experimental results show that the proposed algorithm outperforms existing state of the art type-2 clustering-related algorithms, and is of great significance to the interpretation of remote sensing images.

Deep Possibilistic C-means Clustering Algorithm on Medical Datasets.

In the past, the possibilistic C-means clustering algorithm (PCM) has proven its superiority on various medical datasets by overcoming the unstable clustering effect caused by both the hard division of traditional hard clustering models and the susceptibility of fuzzy C-means clustering algorithm (FCM) to noise. However, with the deep integration and development of the Internet of Things (IoT) as well as big data with the medical field, the width and height of medical datasets are growing bigger and bigger. In the face of high-dimensional and giant complex datasets, it is challenging for the PCM algorithm based on machine learning to extract valuable features from thousands of dimensions, which increases the computational complexity and useless time consumption and makes it difficult to avoid the quality problem of clustering. To this end, this paper proposes a deep possibilistic C-mean clustering algorithm (DPCM) that combines the traditional PCM algorithm with a special deep network called autoencoder. Taking advantage of the fact that the autoencoder can minimize the reconstruction loss and the PCM uses soft affiliation to facilitate gradient descent, DPCM allows deep neural networks and PCM's clustering centers to be optimized at the same time, so that it effectively improves the clustering efficiency and accuracy. Experiments on medical datasets with various dimensions demonstrate that this method has a better effect than traditional clustering methods, besides being able to overcome the interference of noise better.

A New Cutset-type Kernelled Possibilistic C-means Clustering Segmentation Algorithm Based on SLIC Super-pixels

: The kernelled possibilistic C-means clustering algorithm (KPCM) can effectively cluster hyper-sphere data with noise and outliers by introducing the kernelled method to the possibilistic C-means clustering (PCM) algorithm. However, the KPCM still suffers from the same coincident clustering problem as the PCM algorithm due to the lack of between-class relationships. Therefore, this paper introduces the cut-set theory into the KPCM and modifies the possibilistic memberships in the iterative process. Then a cutset-type kernelled possibilistic C-means clustering (CKPCM) algorithm is proposed to overcome the coincident clustering problem of the KPCM. Simultaneously a adaptive method of estimating the cut-set threshold is also given by averaging inter-class distances. Additionally, a cutset-type kernelled possibilistic C-means clustering segmentation algorithm based on the SLIC super-pixels (SS-C-KPCM) is also proposed to improve the segmentation quality and efficiency of the color images. Several experimental results on artificial data sets and image segmentation simulation results prove the excellent performance of the proposed algorithms in this paper.

Cutset-type Possibilistic C-means Clustering Algorithms Based on Semi-supervised Information

Cutset-type Possibilistic C-Means clustering (C-PCM) algorithm can significantly reduce the coincident clustering phenomenon of the Possibilistic C-Means clustering (PCM) algorithm by introducing the cut-set concept into the PCM. The C-PCM also has strong robustness to noise and outliers. However, the C-PCM still suffers from the center migration problem for datasets with small targets. In order to solve this problem, a Semi-Supervised Cutset-type Possibility C-Means (SS-C-PCM) clustering algorithm is proposed by introducing the semi-supervised learning mechanism into the objective function of the C-PCM and utilizing some prior information to guide the clustering process. Meanwhile, in order to improve the segmentation efficiency and accuracy of color images, a differential evolutionary superpixel-based Semi-Supervised Cutset-type Possibilistic C-Means (desSS-C-PCM) clustering algorithm is proposed. In the desSS-C-PCM, the Differential Evolutionary Superpixel(DES) algorithm is used to obtain the spatial neighborhood information of an image, which is integrated into the objective function of the semi-supervised C-PCM to improve the segmentation quality. Simultaneously, the color histogram is used to reconstruct the new objective function to reduce the computational complexity of the algorithm. Several experiments of artificial data clustering and color image segmentation show that the proposed algorithm can effectively improve the clustering effect of datasets with small targets and the execution efficiency compared with several related algorithms.

Weighted Multiview Possibilistic C-Means Clustering With L2 Regularization

Since social media, virtual communities and networks rapidly grow, multiview data become more popular. In general, multiview data always contain different feature components in different views. Although these data are extracted in different ways (views) from diverse settings and domains, they are used to describe the same samples, which make them highly related. Hence, applying (single-view) clustering methods for multiview data poses difficulty in achieving desirable clustering results. Thus, multiview clustering methods should be developed that will utilize available multiview information. Most of multiview clustering techniques currently use k-means due to its conceptual simplicity, and use fuzzy c-means (FCM) that the datapoints can belong to more than one cluster based on their membership degrees from 0 to 1. However, the use of k-means or FCM may degrade its performance due to the presence of noise and outliers, especially on large or high-dimensional datasets. The constraint imposed on the membership degrees of k-means and FCM tends to assign a corresponding high membership value to an outlier or a noisy data point. To address these drawbacks, possibilistic c-means (PCM) relaxes the membership constraint of k-means and FCM so that outliers and noisy datapoints can be properly identified. On the other hand, there are various extensions of k-means and FCM for multiview data, but no extension of PCM for multiview data was made in the literature. Thus, we use PCM in our proposed multiview clustering model. In this article, we propose novel weighted multiview PCM algorithms designed for clustering multiview data as well as view and feature weights on PCM approaches, called W-MV-PCM and W-MV-PCM with L2 regularization (W-MV-PCM-L2). In multiview clustering, different views may vary with respect to its importance and each view may contain some irrelevant features. In the proposed algorithms, a learning scheme is constructed to compute for the view weights, and feature weights within each view. This scheme will be able to identify the importance of each view and, at the same time, it will also identify and select relevant features in each view. Comparisons of W-MV-PCM-L2 with existing multiview clustering algorithms are made on both synthetic and real datasets. The experimental results are evaluated using accuracy rate (AR) and external validity indexes, such as Rand index (RI) and normalized mutual information (NMI). The proposed W-MV-PCM-L2 algorithm with comparisons of existing algorithms under criteria of AR, RI, and NMI shows that it is a feasible and effective multiview clustering algorithm.

Pet dog disease pre-diagnosis system for caregiver with possibilistic C-means clustering and disease database

<p>While the population of pet dogs and veterinary clinics are increasing, there is no reliable and useful software for pet owners/caregivers who have limited knowledge on the pet diseases. In this paper, we propose a pre-diagnosis system working on the mobile platform that the pet owner can take a pre-diagnosis from his/her observation of pet dog’s abnormality. Technically, the system needs a reliable databases for disease-symptom association thus we provide it based on the textbook and encyclopedia. Then, we apply Possibilistic C-Means algorithm that is an unsupervised machine learning algorithm to form the connections between disease and symptoms from database. The system outputs five most probable diseases from the observed symptoms of pet dog. The utility of this system is to alert the owner’s attention on the pet dog’s abnormal behavior and try to find the diseases as soon as possible.</p>

An Efficient Automatic Intrusion Detection in Cloud Using Optimized Fuzzy Inference System

Security incidents such as denial of service (DoS), scanning, malware code injection, viruses, worms, and password cracking are becoming common in a cloud environment that affects companies and may produce a financial loss if not detected in time. Such problems are handled by presenting an intrusion detection system (IDS) into the cloud. The existing cloud IDSs affect low detection accuracy, high false detection rate, and execution time. To overcome this problem, in this article, a gravitational search algorithm-based fuzzy inference system (GSA-FIS) is developed as intrusion detection. In this approach, fuzzy parameters are optimized using GSA. The proposed consist of two modules namely; possibilistic fuzzy c-means (PFCM) based clustering, training based on the GSA-FIS, and testing process. Initially, the incoming data is pre-processed and clustered with the help of PFCM. PFCM detects the noise of fuzzy c-means clustering (FCM), then conquers the coincident cluster problem of possibilistic fuzzy c-means (PCM) and eradicate the row sum constraints of fuzzy possibilistic c-means clustering (FPCM). After the clustering process, the clustered data is given to the optimized fuzzy inference system (OFIS). Here, normal and abnormal data are identified by the fuzzy score, while the training is done by the GSA through optimizing the entire fuzzy system. In this approach, four types of abnormal data are detected namely- probe, remote to local (R2L), user to root (U2R), and DoS. Simulation results show that the performance of the proposed GSA-FIS based IDS outperforms that of the different schemes in terms of precision, recall and F-measure.

An Intelligence EEG Signal Recognition Method via Noise Insensitive TSK Fuzzy System Based on Interclass Competitive Learning.

Epilepsy is an abnormal function disease of movement, consciousness, and nerve caused by abnormal discharge of brain neurons in the brain. EEG is currently a very important tool in the process of epilepsy research. In this paper, a novel noise-insensitive Takagi–Sugeno–Kang (TSK) fuzzy system based on interclass competitive learning is proposed for EEG signal recognition. First, a possibilistic clustering in Bayesian framework with interclass competitive learning called PCB-ICL is presented to determine antecedent parameters of fuzzy rules. Inherited by the possibilistic c-means clustering, PCB-ICL is noise insensitive. PCB-ICL learns cluster centers of different classes in a competitive relationship. The obtained clustering centers are attracted by the samples of the same class and also excluded by the samples of other classes and pushed away from the heterogeneous data. PCB-ICL uses the Metropolis–Hastings method to obtain the optimal clustering results in an alternating iterative strategy. Thus, the learned antecedent parameters have high interpretability. To further promote the noise insensitivity of rules, the asymmetric expectile term and Ho–Kashyap procedure are adopted to learn the consequent parameters of rules. Based on the above ideas, a TSK fuzzy system is proposed and is called PCB-ICL-TSK. Comprehensive experiments on real-world EEG data reveal that the proposed fuzzy system achieves the robust and effective performance for EEG signal recognition.