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Representing data in different spaces becomes more powerful and suitable for solving downstream learning tasks. The membership degrees obtained through fuzzy C -means (FCM) clustering cannot capture data structures sufficiently, as they represent samples from a single Euclidean geometrical perspective. To address this issue, we propose a novel fuzzy clustering model guided by spectral rotation and scaling (FCSR). In FCSR, both spectral embeddings and membership degrees are considered as new representations of data. They can complement each other from different perspectives which enables the model to engage more structural properties of the data. The process of solving the problem of membership degrees not only inherits the merits of traditional FCM but also preserves data neighborhood structures revealed by the spectral decomposition based on an affinity matrix. Furthermore, to improve the adaptability and extensibility of FCSR, the projected and kernel versions of FCSR (FCSR-P and FCSR-K) are formed. We demonstrate that FCSR-P is suitable for high-dimensional scenarios and FCSR-K can improve the linear separability among data. Extensive experiments conducted on various well-known data sets illustrate the validity of the proposed ideas.

A novel fuzzy adaptive knowledge-based inference neural network (FAKINN) is proposed in this study. Conventional fuzzy cluster-based neural networks (FCBNNs) suffer from the challenge of a direct extraction of fuzzy rules that can capture and represent the interclass heterogeneity and intraclass homogeneity when the data possess complex structures. Moreover, the capability of the cluster-based rule generator in FCBNNs may decrease with the increase of data dimensionality. These drawbacks impede the generation of desired fuzzy rules, and affect the inference results depending on the fuzzy rules, thereby limiting their generalization ability. To address these drawbacks, an adaptive knowledge generator (AKG), consisting of the observation paradigm (OP) and clustering strategy (CS), is effectively designed to improve the generalization ability in FAKINN. The OP distills the characteristic information (CI) from data to highlight the homogeneity and heterogeneity of objects, and the CS, viz., the weighted condition-driven fuzzy clustering method (WCFCM), is proposed to summarize the CI to construct fuzzy rules. Moreover, the feedback between the OP and CS can control the dimensionality of CI, which endows FAKINN with the potential to tackle high-dimensional data. The main originality of the study focuses on the AKG and WCFCM that are proposed to develop the structural design methodology of FNNs. The performance of FAKINN is evaluated on various benchmarks with 27 comparative methods, and two real-world problems are adopted to validate its effectiveness. Experimental results show that FAKINN outperforms the comparison methods.

This article reports a novel consensus model where a group of internal and external experts evaluate alternatives under multiple attributes and provide mutual evaluations. First, different from previous studies, the cognitive and interest conflicts of internal and external experts are considered simultaneously. But interest conflict is emphasized for internal experts, and cognitive conflict is mainly considered for external experts. Second, we explore the categorization and management methods of noncooperative behaviors (NCBs) of experts. The relative projection-based indexes are proposed for the first time to measure the degrees of cognitive and interest conflicts by using multiattribute preference matrices (MAPMs) and the weight vectors of attributes. A group of experts are divided into three categories and the corresponding management strategies are developed. Third, we investigate the consensus mechanism among experts with cognitive and interest conflicts. For reaching an acceptable consensus level, an adjustment process is proposed to revise some local entries in MAPMs and mutual evaluation matrix (MEM). A penalty mechanism is further established to dynamically update the weights of experts. An algorithm is designed to capture the consensus reaching process in multiattribute group decision making, where internal and external experts are distinguished by proposing a parameter. Finally, the high-performance battery supplier selection of new energy vehicle is studied to illustrate the proposed model. The results reveal that the efficiency of reaching consensus can be enhanced by using the developed model with effective management of NCBs.

A coupled multimodal emotional feature analysis (CMEFA) method based on broad-deep fusion networks, which divide multimodal emotion recognition into two layers, is proposed. First, facial emotional features and gesture emotional features are extracted using the broad and deep learning fusion network (BDFN). Considering that the bi-modal emotion is not completely independent of each other, canonical correlation analysis (CCA) is used to analyze and extract the correlation between the emotion features, and a coupling network is established for emotion recognition of the extracted bi-modal features. Both simulation and application experiments are completed. According to the simulation experiments completed on the bimodal face and body gesture database (FABO), the recognition rate of the proposed method has increased by 1.15% compared to that of the support vector machine recursive feature elimination (SVMRFE) (without considering the unbalanced contribution of features). Moreover, by using the proposed method, the multimodal recognition rate is 21.22%, 2.65%, 1.61%, 1.54%, and 0.20% higher than those of the fuzzy deep neural network with sparse autoencoder (FDNNSA), ResNet-101 + GFK, C3D + MCB + DBN, the hierarchical classification fusion strategy (HCFS), and cross-channel convolutional neural network (CCCNN), respectively. In addition, preliminary application experiments are carried out on our developed emotional social robot system, where emotional robot recognizes the emotions of eight volunteers based on their facial expressions and body gestures.

Unsupervised feature selection (UFS) aims to learn an indicator matrix relying on some characteristics of the high-dimensional data to identify the features to be selected. However, traditional unsupervised methods perform only at the feature level, i.e., they directly select useful features by feature ranking. Such methods do not pay any attention to the interaction information with other tasks such as classification, which severely degrades their feature selection performance. In this article, we propose an UFS method which also takes into account the classification level, and selects features that perform well both in clustering and classification. To achieve this, we design a bi-level spectral feature selection (BLSFS) method, which combines classification level and feature level. More concretely, at the classification level, we first apply the spectral clustering to generate pseudolabels, and then train a linear classifier to obtain the optimal regression matrix. At the feature level, we select useful features via maintaining the intrinsic structure of data in the embedding space with the learned regression matrix from the classification level, which in turn guides classifier training. We utilize a balancing parameter to seamlessly bridge the classification and feature levels together to construct a unified framework. A series of experiments on 12 benchmark datasets are carried out to demonstrate the superiority of BLSFS in both clustering and classification performance.

Airway segmentation is crucial for the examination, diagnosis, and prognosis of lung diseases, while its manual delineation is unduly burdensome. To alleviate this time-consuming and potentially subjective manual procedure, researchers have proposed methods to automatically segment airways from computerized tomography (CT) images. However, some small-sized airway branches (e.g., bronchus and terminal bronchioles) significantly aggravate the difficulty of automatic segmentation by machine learning models. In particular, the variance of voxel values and the severe data imbalance in airway branches make the computational module prone to discontinuous and false-negative predictions, especially for cohorts with different lung diseases. The attention mechanism has shown the capacity to segment complex structures, while fuzzy logic can reduce the uncertainty in feature representations. Therefore, the integration of deep attention networks and fuzzy theory, given by the fuzzy attention layer, should be an escalated solution for better generalization and robustness. This article presents an efficient method for airway segmentation, comprising a novel fuzzy attention neural network (FANN) and a comprehensive loss function to enhance the spatial continuity of airway segmentation. The deep fuzzy set is formulated by a set of voxels in the feature map and a learnable Gaussian membership function. Different from the existing attention mechanism, the proposed channel-specific fuzzy attention addresses the issue of heterogeneous features in different channels. Furthermore, a novel evaluation metric is proposed to assess both the continuity and completeness of airway structures. The efficiency, generalization, and robustness of the proposed method have been proved by training on normal lung disease while testing on datasets of lung cancer, COVID-19, and pulmonary fibrosis.

Fuzzy min-max neural network (FMNN) is one kind of three-layer models based on hyperboxes that are constructed in a sequential way. Such a sequential mechanism inevitably leads to the input order and overlap region problem. In this study, we propose a deep FMNN (DFMNN) based on initialization and optimization operation to overcome these limitations. Initialization operation that can solve the input order problem is to design hyperboxes in a simultaneous way, and side parameters have been proposed to control the size of hyperboxes. Optimization operation that can eliminate overlap region problem is realized by means of deep layers, where the number of layers is immediately determined when the overlap among hyperboxes is eliminated. In the optimization process, each layer consists of three sections, namely, the partition section, combination section, and union section. The partition section aims to divide the hyperboxes into a nonoverlapping hyperbox set and an overlapping hyperbox set. The combination section eliminates the overlap problem of overlapping hyperbox set. The union section obtains the optimized hyperbox set in the current layer. DFMNN is evaluated based on a series of benchmark datasets. A comparative analysis illustrates that the proposed DFMNN model outperforms several models previously reported in the literature.

Fuzzy clustering-based neural networks (FCNNs) based on information granulation techniques have been shown to be effective Takagi-Sugeno (TS)-type fuzzy models. However, the existing FCNNs could not cope well with sequential learning tasks. In this study, we introduce incremental FCNNs (IFCNNs), which could dynamically update themselves whenever new learning data (e.g., single datum or block data) are incorporated into the dataset. Specifically, we employ dynamic (incremental) fuzzy C-means (FCMs) clustering algorithms to reveal a structure in data and divide the entire input space into several subregions. In the aforementioned partition, the dynamic FCM adaptively adjusts the position of its prototypes by using sequential data. Due to the time-sharing arrival of training data, compared with batch learning models, incremental learning methods may lose classification (prediction) accuracy. In order to tackle this challenge, we utilize quasi-fuzzy local models (QFLMs) based on modified Schmidt neural networks to replace the popular linear functions in TS-type fuzzy models to refine and enhance the ability to represent the behavior of fuzzy subspaces. Meanwhile, the recursive least square error (LSE) estimation is utilized to update the weights of QFLMs from one-by-one or block-by-block (fixed or varying block size) learning data. In addition, the L 2 regularization is considered to ameliorate the deterioration of generalization abilities caused by potential overfitting when carrying out weight estimation. The proposed method leads to the construction of FCNNs in a new way, which can effectively deal with incremental data as well as deliver sound generalization capability. Extensive machine-learning datasets and a real-world application are employed to show the validity and performance of the presented methods. From the experimental results, we show that the proposal can maintain sound classification accuracy when effectively processing sequential data.

Objective: Convolutional neural network (CNN), a classical structure in deep learning, has been commonly deployed in the motor imagery brain-computer interface (MIBCI). Many methods have been proposed to evaluate the vulnerability of such CNN models, primarily by attacking them using direct temporal perturbations. In this work, we propose a novel attacking approach based on perturbations in the frequency domain instead., Methods: For a given natural MI trial in the frequency domain, the proposed approach, called frequency domain channel-wise attack (FDCA), generates perturbations at each channel one after another to fool the CNN classifiers. The advances of this strategy are two-fold. First, instead of focusing on the temporal domain, perturbations are generated in the frequency domain where discriminative patterns can be extracted for motor imagery (MI) classification tasks. Second, the perturbing optimization is performed based on differential evolution algorithm in a black-box scenario where detailed model knowledge is not required., Results: Experimental results demonstrate the effectiveness of the proposed FDCA which achieves a significantly higher success rate than the baselines and existing methods in attacking three major CNN classifiers on four public MI benchmarks., Conclusion: Perturbations generated in the frequency domain yield highly competitive results in attacking MIBCI deployed by CNN models even in a black-box setting, where the model information is well-protected., Significance: To our best knowledge, existing MIBCI attack approaches are all gradient-based methods and require details about the victim model, e.g., the parameters and objective function. We provide a more flexible strategy that does not require model details but still produces an effective attack outcome.

The highly dimensional characteristic of time series brings many challenges on direct mining time series, such as high cost in time and space. Granular computing provides a potential strategy for representing and dealing with time series at a higher level of abstraction. In this study, we propose an information granulation-based weighted fuzzy C -means (wFCM) method to realize time-series clustering, which could avoid high dimensionality processing and provide a concise and visible granular prototype for each cluster. In this method, each time series is first transformed into a series of information granules with trend following the principle of justifiable granularity. The formed granular time series can well capture the main features lying in the original time series and help realize dimensionality reduction. Then, the wFCM method is developed to complete time-series clustering in the granular space. Here, the dynamic time warping (DTW) is extended to capture the similarity for trend-based granular time series. Furthermore, the weighted DTW barycenter averaging is introduced to derive prototypes presented in a granular format, capturing the level, the fluctuation, and the changing trend, which are meaningful and understandable clustering results. The experiments conducted on real-world datasets coming from the UCR time-series database and Chinese stocks are presented to illustrate the effectiveness and practicality of the designed time-series clustering model.

Since a noisy image has inferior characteristics, the direct use of Fuzzy C -Means (FCM) to segment it often produces poor image segmentation results. Intuitively, using its ideal value (noise-free image) benefits FCM's robustness enhancement. Therefore, the realization of accurate noise estimation in FCM is a new and important task. To date, only two noise-estimation-based FCM algorithms have been proposed for image segmentation, that is: 1) deviation-sparse FCM (DSFCM) and 2) our earlier proposed residual-driven FCM (RFCM). In this article, we make a thorough comparative study of DSFCM and RFCM. We demonstrate that an RFCM framework can realize more accurate noise estimation than DSFCM when different types of noise are involved. It is mainly thanks to its utilization of noise distribution characteristics instead of noise sparsity used in DSFCM. We show that DSFCM is a particular case of RFCM, thus signifying that they are the same when only impulse noise is involved. With a spatial information constraint, we demonstrate RFCM's superior effectiveness and efficiency over DSFCM in terms of supporting experiments with different levels of single, mixed, and unknown noise.

In this study, we establish a new design methodology of granular models realized by augmenting the existing numeric models through analyzing and modeling their associated prediction error. Several novel approaches to the construction of granular architectures through augmenting existing numeric models by incorporating modeling errors are proposed in order to improve and quantify the numeric models' prediction abilities. The resulting construct arises as a granular model that produces granular outcomes generated as a result of the aggregation of the outputs produced by the numeric model (or its granular counterpart) and the corresponding error terms. Three different architectural developments are formulated and analyzed. In comparison with the numeric models, which strive to achieve the highest accuracy, granular models are developed in a way such that they produce comprehensive prediction outcomes realized as information granules. In virtue of the granular nature of results, the coverage and specificity of the constructed information granules express the quality of the results of prediction in a more descriptive and comprehensive manner. The performance of the granular constructs is evaluated using the criteria of coverage and specificity, which are pertinent to granular outputs produced by the granular models.

Information granularity and information granules are fundamental concepts that permeate the entire area of granular computing. With this regard, the principle of justifiable granularity was proposed by Pedrycz, and subsequently a general two-phase framework of designing information granules based on Fuzzy C-means clustering was successfully developed. This design process leads to information granules that are likely to intersect each other in substantially overlapping clusters, which inevitably leads to some ambiguity and misperception as well as loss of semantic clarity of information granules. This limitation is largely due to imprecise description of boundary-overlapping data in the existing algorithms. To address this issue, the rough k -means clustering is introduced in an innovative way into Pedrycz's two-phase information granulation framework, together with the proposed local boundary fuzzy metric. To further strengthen the characteristics of support and inhibition of boundary-overlapping data, an augmented parametric version of the principle is refined. On this basis, a local boundary fuzzified rough k -means-based information granulation algorithm is developed. In this manner, the generated granules are unique and representative whilst ensuring clearer boundaries. The validity and performance of this algorithm are demonstrated through the results of comparative experiments.

Thanks to the efficient retrieval speed and low storage consumption, learning to hash has been widely used in visual retrieval tasks. However, the known hashing methods assume that the query and retrieval samples lie in homogeneous feature space within the same domain. As a result, they cannot be directly applied to heterogeneous cross-domain retrieval. In this article, we propose a generalized image transfer retrieval (GITR) problem, which encounters two crucial bottlenecks: 1) the query and retrieval samples may come from different domains, leading to an inevitable domain distribution gap and 2) the features of the two domains may be heterogeneous or misaligned, bringing up an additional feature gap. To address the GITR problem, we propose an asymmetric transfer hashing (ATH) framework with its unsupervised/semisupervised/supervised realizations. Specifically, ATH characterizes the domain distribution gap by the discrepancy between two asymmetric hash functions, and minimizes the feature gap with the help of a novel adaptive bipartite graph constructed on cross-domain data. By jointly optimizing asymmetric hash functions and the bipartite graph, not only can knowledge transfer be achieved but information loss caused by feature alignment can also be avoided. Meanwhile, to alleviate negative transfer, the intrinsic geometrical structure of single-domain data is preserved by involving a domain affinity graph. Extensive experiments on both single-domain and cross-domain benchmarks under different GITR subtasks indicate the superiority of our ATH method in comparison with the state-of-the-art hashing methods.

Fuzzy utility (FU) pattern mining with an advantage in human reasoning has become one of the interesting topics in studies of knowledge discovery. The discovered information in FU pattern mining from real-life quantitative databases with item profits is suitable for interpreting data from a human perspective because it is not expressed using numerical values but linguistic terms which consist of natural languages. State-of-the-art approaches in this literature provide extended results by considering temporal factors, such as seasons, which can be influential in real-life situations. However, they still suffer from scalability issues because they are based on level-wise approaches which generate a number of candidates. In this article, we propose a scalable and efficient approach with a novel data structure for mining high temporal FU patterns without generating candidates. Efficient pruning techniques and algorithms are presented to improve the performance of the proposed approach. Performance experiments on both real and synthetic datasets show that the suggested algorithm has better performance than the state-of-the-art algorithms in terms of runtime, memory usage, and scalability.

The introduction of domain knowledge opens new horizons to fuzzy clustering. Then knowledge-driven and data-driven fuzzy clustering methods come into being. To address the challenges of inadequate extraction mechanism and imperfect fusion mode in such class of methods, we propose the Knowledge-induced Multiple Kernel Fuzzy Clustering (KMKFC) algorithm. First, to extract knowledge points better, the Relative Density-based Knowledge Extraction (RDKE) method is proposed to extract high-density knowledge points close to cluster centers of real data structure, and provide initialized cluster centers. Moreover, the multiple kernel mechanism is introduced to improve the adaptability of clustering algorithm and map data to high-dimensional space, so as to better discover the differences between the data and obtain superior clustering results. Second, knowledge points generated by RDKE are integrated into KMKFC through a knowledge-influence matrix to guide the iterative process of KMKFC. Third, we also provide a strategy of automatically obtaining knowledge points, and thus propose the RDKE with Automatic knowledge acquisition (RDKE-A) method and the corresponding KMKFC-A algorithm. Then we prove the convergence of KMKFC and KMKFC-A. Finally, experimental studies demonstrate that the KMKFC and KMKFC-A algorithms perform better than thirteen comparison algorithms with regard to four evaluation indexes and the convergence speed.

This article aims to design a trend-oriented-granulation-based fuzzy C -means (FCM) algorithm that can cluster a group of time series at an abstract (granular) level. To achieve a better trend-oriented granulation of a time series, l 1 trend filtering is firstly carried out to result in segments which are then optimized by the proposed segment merging algorithm. By constructing a linear fuzzy information granule (LFIG) on each segment, a granular time series which well reflects the linear trend characteristic of the original time series is produced. With the novel designed distance that can well measure the trend similarity of two LFIGs, the distance between two granular time series is calculated by the modified dynamic time warping (DTW) algorithm. Based on this distance, the LFIG-based FCM algorithm is developed for clustering time series. In this algorithm, cluster prototypes are iteratively updated by the specifically designed granule splitting and merging algorithm, which allows the lengths of prototypes to change in the process of iteration. This overcomes the serious drawback of the existing approaches, where the lengths of prototypes cannot be changed. Experimental studies demonstrate the superior performance of the proposed algorithm in clustering time series with different shapes or trends.

In this brief, we investigate the problem of incremental learning under data stream with emerging new classes (SENC). In the literature, existing approaches encounter the following problems: 1) yielding high false positive for the new class; i) having long prediction time; and 3) having access to true labels for all instances, which is unrealistic and unacceptable in real-life streaming tasks. Therefore, we propose the k -Nearest Neighbor ENSemble-based method (KNNENS) to handle these problems. The KNNENS is effective to detect the new class and maintains high classification performance for known classes. It is also efficient in terms of run time and does not require true labels of new class instances for model update, which is desired in real-life streaming classification tasks. Experimental results show that the KNNENS achieves the best performance on four benchmark datasets and three real-world data streams in terms of accuracy and F1-measure and has a relatively fast run time compared to four reference methods. Codes are available at https://github.com/Ntriver/KNNENS.

Dominance-based rough approximation discovers inconsistencies from ordered criteria and satisfies the requirement of the dominance principle between single-valued domains of condition attributes and decision classes. When the ordered decision system (ODS) is no longer single-valued, how to utilize the dominance principle to deal with multivalued ordered data is a promising research direction, and it is the most challenging step to design a feature selection algorithm in interval-valued ODS (IV-ODS). In this article, we first present novel thresholds of interval dominance degree (IDD) and interval overlap degree (IOD) between interval values to make the dominance principle applicable to an IV-ODS, and then, the interval-valued dominance relation in the IV-ODS is constructed by utilizing the above two developed parameters. Based on the proposed interval-valued dominance relation, the interval-valued dominance-based rough set approach (IV-DRSA) and their corresponding properties are investigated. Moreover, the interval dominance-based feature selection rules based on IV-DRSA are provided, and the relevant algorithms for deriving the interval-valued dominance relation and the feature selection methods are established in IV-ODS. To illustrate the effectiveness of the parameters variation on feature selection rules, experimental evaluation is performed using 12 datasets coming from the University of California-Irvine (UCI) repository.

Recent studies on heterogeneous information network (HIN) embedding-based recommendations have encountered challenges. These challenges are related to the data heterogeneity of the associated unstructured attribute or content (e.g., text-based summary/description) of users and items in the context of HIN. In order to address these challenges, in this article, we propose a novel approach of semantic-aware HIN embedding-based recommendation, called SemHE4Rec. In our proposed SemHE4Rec model, we define two embedding techniques for efficiently learning the representations of both users and items in the context of HIN. These rich-structural user and item representations are then used to facilitate the matrix factorization (MF) process. The first embedding technique is a traditional co-occurrence representation learning (CoRL) approach which aims to learn the co-occurrence of structural features of users and items. These structural features are represented for their interconnections in terms of meta-paths. In order to do that, we adopt the well-known meta-path-based random walk strategy and heterogeneous Skip-gram architecture. The second embedding approach is a semantic-aware representation learning (SRL) method. The SRL embedding technique is designed to focus on capturing the unstructured semantic relations between users and item content for the recommendation task. Finally, all the learned representations of users and items are then jointly combined and optimized while integrating with the extended MF for the recommendation task. Extensive experiments on real-world datasets demonstrate the effectiveness of the proposed SemHE4Rec in comparison with the recent state-of-the-art HIN embedding-based recommendation techniques, and reveal that the joint text-based and co-occurrence-based representation learning can help to improve the recommendation performance.

A visible trend in representing knowledge through information granules manifests in the developments of information granules of higher type and higher order, in particular, type-2 fuzzy sets and order-2 fuzzy sets. All these constructs are aimed at the formalization and processing data at a certain level of abstraction. Along the same line, in the recent years, we have seen intensive developments in fuzzy clustering, which are not surprising in light of a growing impact of clustering on fundamentals of fuzzy sets (as supporting ways to elicit membership functions) as well as algorithms (in which clustering and clusters form an integral functional component of various fuzzy models). In this study, we investigate order-2 information granules (fuzzy sets) by analyzing their formal description and properties to cope with structural and hierarchically organized concepts emerging from data. The design of order-2 information granules on a basis of available experimental evidence is discussed and a way of expressing similarity (resemblance) of two order-2 information granules by engaging semantically oriented distance is discussed. In the sequel, the study reported here delivers highly original contributions in the realm of order-2 clustering algorithms. Formally, the clustering problem under discussion is posed as follows: given is a finite collection of reference information granules. Determine a structure in data defined over the space of such granules. Conceptually, this makes a radical shift in comparison with data defined in the p -dimensional space of real numbers Rp. In this situation, expressing distance between two data deserves prudent treatment so that such distance properly captures the semantics and consequently, the closeness between any two information granules to be determined in cluster formation. Following the proposal of the semantically guided distance (and its ensuing design process), we develop an order-2 variant of the fuzzy C-means (FCM), discuss its detailed algorithmic steps, and deliver interpretation of the obtained clustering results. Several relevant applied scenarios of order-2 FCM are identified for spatially and temporally distributed data, which deliver interesting motivating arguments and underline the practical relevance of this category of clustering. Experimental studies are provided to further elicit the performance of the clustering method and discuss essential ways of interpreting results.

The existing clustering validity indexes (CVIs) show some difficulties to produce the correct cluster number when some cluster centers are close to each other, and the separation processing mechanism appears simple. The results are imperfect in case of noisy data sets. For this reason, in this study, we come up with a novel CVI for fuzzy clustering, referred to as the triple center relation (TCR) index. The originality of this index is twofold. On the one hand, a new fuzzy cardinality is built on the strength of the maximum membership degree, and a novel compactness formula is constructed by combining it with the within-class weighted squared error sum. On the other hand, starting from the minimum distance between different cluster centers, the mean distance as well as the sample variance of cluster centers in the statistical sense are further integrated. These three factors are combined by means of product to form a triple characterization of the relationship between cluster centers, and hence a 3-D expression pattern of separability is formed. Subsequently, the TCR index is put forward by combining the compactness formula with the separability expression pattern. By virtue of the degenerate structure of hard clustering, we show an important property of the TCR index. Finally, based on the fuzzy C -means (FCMs) clustering algorithm, experimental studies were conducted on 36 data sets (incorporating artificial and UCI data sets, images, the Olivetti face database). For comparative purposes, 10 CVIs were also considered. It has been found that the proposed TCR index performs best in finding the correct cluster number, and has excellent stability.

In this article, we propose the concept of random polynomial neural networks (RPNNs) realized based on the architecture of polynomial neural networks (PNNs) with random polynomial neurons (RPNs). RPNs exhibit generalized polynomial neurons (PNs) based on random forest (RF) architecture. In the design of RPNs, the target variables are no longer directly used in conventional decision trees, and the polynomial of these target variables is exploited here to determine the average prediction. Unlike the conventional performance index used in the selection of PNs, the correlation coefficient is adopted here to select the RPNs of each layer. When compared with the conventional PNs used in PNNs, the proposed RPNs exhibit the following advantages: first, RPNs are insensitive to outliers; second, RPNs can obtain the importance of each input variable after training; third, RPNs can alleviate the overfitting problem with the use of an RF structure. The overall nonlinearity of a complex system is captured by means of PNNs. Moreover, particle swarm optimization (PSO) is exploited to optimize the parameters when constructing RPNNs. The RPNNs take advantage of both RF and PNNs: it exhibits high accuracy based on ensemble learning used in the RF and is beneficial to describe high-order nonlinear relations between input and output variables stemming from PNNs. Experimental results based on a series of well-known modeling benchmarks illustrate that the proposed RPNNs outperform other state-of-the-art models reported in the literature.

A fuzzy cognitive map (FCM) is a graph-based knowledge representation model wherein the connections of the nodes (edges) represent casual relationships between the knowledge items associated with the nodes. This model has been applied to solve various modeling tasks including forecasting time series. In the original FCM-based forecasting model, causal relationships among concepts of the FCM remain unchanged. However, causal relationships may change in time. Therefore, we propose a new learning method for training an FCM resulting in an adaptive FCM which consists of several sub-FCMs. It can select different sub-FCMs at different moments. In an active processing scenario, in which we deal with a large-scale time series with new data being continuously generated, a forecasting model built on the old data should be updated when the new data arrive. Furthermore, retraining an FCM from scratch entails increasing computing overhead that will become a serious obstacle in many practical scenarios. To overcome the above-mentioned shortcomings, this study offers an original design setting in which the FCM is updated by knowledge-guidance learning mechanism for the first time. Compared with the existing classical forecasting models, the proposed model shows higher accuracy and efficiency. Its increased performance is demonstrated through a series of reported experimental studies.

A key issue in social network group decision making (SNGDM) is to determine the weights (i.e., social influences) of individuals. Notably, in some SNGDM scenarios, the social influences of individuals may evolve over time. Meanwhile, consensus reaching is another important issue in SNGDM. In this article, we are dedicated to disclosing the natural evolution process of social influence, and further to discussing the consensus reaching issue in SNGDM. First, we establish the social influence evolution model, where the individual's social influence is obtained by combining his/her intrinsic influence and network influence. Afterward, we design the consensus reaching process based on social influence evolution (CRP-SIE) to assist the individuals to reach a consensus. Furthermore, we use a hypothetical application to show the applicability of the proposed CRP-SIE. Finally, simulation analysis is adopted to investigate the effects of social influence evolution on consensus reaching in SNGDM, and comparative analysis is conducted to demonstrate the advantages of our proposal.

Network embedding which aims to learn a low dimensional representation of nodes is a powerful technique for network analysis. While network embedding for networks with complete attributes has been widely investigated, in many real-world applications the attributes of partial nodes are unobserved (i.e., missing) due to privacy concern or resource limit. Very recently, several network embedding methods have been proposed for attribute-missing networks. They first complete the missing attributes and then use the complemented network to learn network embedding. The parameters of these two processes cannot be adjusted by each other, resulting in compromised results. To address this problem, we propose a unified model in which the process of completing missing attributes and the process of learning embedding are not separated but closely intertwined. Being specific, completing missing attributes is under the guidance of learning network representation via mutual information maximization, and the complemented attributes directly enter network representation module which will generate further feedback for completing missing attributes. We further impose attribute-structure relationship constraint for completing missing attributes by designing a new generative adversarial networks (GANs) model. To the best of our knowledge, this is the first unified model for attribute-missing network embedding. Empirical results on real-world datasets show the superiority of our new method over other state-of-the-art methods on four network analysis tasks, including node classification, node clustering, link prediction, and network visualization.

Consensus reaching process (CRP) is a key topic in the area of group decision making (GDM). When the consensus level is not high enough, it becomes necessary to adjust the original opinions of decision makers (DMs). To offer the adjustment reference for DMs, we build the programming models to determine the minimum modification to be carried out from the individual and global perspectives. Meanwhile, all DMs are divided into two subgroups: DMs with acceptable and unacceptable consensus levels. If some DMs with unacceptable consensus level do not accept the relevant modifications, the Nash bargaining game-based programming model is built for the fairness and efficiency of modifications. When some DMs refuse to make any modifications or tend to modify the opinions in their way, with respect to different group consensus situations, we make the minimum hybrid penalty mechanism by the Nash bargaining game-based programming models. For each case, we determine the corresponding optimal modification mechanism in view of the fixed individual total modification and the maximum consensus level. Furthermore, we study the arrangements of weights of DMs according to their cardinal and ordinal consensus contributions. Based on these results, we present a new algorithm and illustrate its application by a numerical example. Moreover, we carry out the sensitivity and comparison analysis. We summarize the conclusions and future research directions in the end. The main originality of the new method includes: the fairness and efficiency of modifications, and the determination of the hybrid penalty mechanism.

Current fully supervised facial landmark detection methods have progressed rapidly and achieved remarkable performance. However, they still suffer when coping with faces under large poses and heavy occlusions for inaccurate facial shape constraints and insufficient labeled training samples. In this article, we propose a semisupervised framework, that is, a self-calibrated pose attention network (SCPAN) to achieve more robust and precise facial landmark detection in challenging scenarios. To be specific, a boundary-aware landmark intensity (BALI) field is proposed to model more effective facial shape constraints by fusing boundary and landmark intensity field information. Moreover, a self-calibrated pose attention (SCPA) model is designed to provide a self-learned objective function that enforces intermediate supervision without label information by introducing a self-calibrated mechanism and a pose attention mask. We show that by integrating the BALI fields and SCPA model into a novel SCPAN, more facial prior knowledge can be learned and the detection accuracy and robustness of our method for faces with large poses and heavy occlusions have been improved. The experimental results obtained for challenging benchmark datasets demonstrate that our approach outperforms state-of-the-art methods in the literature.

Recently, granular models have been highlighted in system modeling and applied to many fields since their outcomes are information granules supporting human-centric comprehension and reasoning. In this study, a design method of granular model driven by hyper-box iteration granulation is proposed. The method is composed mainly of partition of input space, formation of input hyper-box information granules with confidence levels, and granulation of output data corresponding to input hyper-box information granules. Among them, the formation of input hyper-box information granules is realized through performing the hyper-box iteration granulation algorithm governed by information granularity on input space, and the granulation of out data corresponding to input hyper-box information granules is completed by the improved principle of justifiable granularity to produce triangular fuzzy information granules. Compared with the existing granular models, the resulting one can yield the more accurate numeric and preferable granular outcomes simultaneously. Experiments completed on the synthetic and publicly available datasets demonstrate the superiority of the granular model designed by the proposed method at granular and numeric levels. Also, the impact of parameters involved in the proposed design method on the performance of ensuing granular model is explored.

Task prioritization is one of the most researched areas in software development. Given the huge number of papers written on the topic, it might be challenging for IT practitioners-software developers, and IT project managers-to find the most appropriate tools or methods developed to date to deal with this important issue. The main goal of this work is therefore to review the current state of research and practice on task prioritization in the Software Engineering domain and to individuate the most effective ranking tools and techniques used in the industry. For this purpose, we conducted a systematic literature review guided and inspired by the Preferred Reporting Items for Systematic Reviews and Meta-Analyses, otherwise known as the PRISMA statement. Based on our analysis, we can make a number of important observations for the field. Firstly, we found that most of the task prioritization approaches developed to date involve a specific type of prioritization strategy-bug prioritization. Secondly, the most recent works we review investigate task prioritization in terms of "pull request prioritization" and "issue prioritization," (and we speculate that the number of such works will significantly increase due to the explosion of version control and issue management software systems). Thirdly, we remark that the most frequently used metrics for measuring the quality of a prioritization model are f-score, precision, recall, and accuracy., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2023 Bugayenko et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

The automatic segmentation of COVID-19 pneumonia from a computerized tomography (CT) scan has become a major interest for scholars in developing a powerful diagnostic framework in the Internet of Medical Things (IoMT). Federated deep learning (FDL) is considered a promising approach for efficient and cooperative training from multi-institutional image data. However, the nonindependent and identically distributed (Non-IID) data from health care remain a remarkable challenge, limiting the applicability of FDL in the real world. The variability in features incurred by different scanning protocols, scanners, or acquisition parameters produces the learning drift phenomena during the training, which impairs both the training speed and segmentation performance of the model. This paper proposes a novel FDL approach for reliable and efficient multi-institutional COVID-19 segmentation, called MIC-Net. MIC-Net consists of three main building modules: the down-sampler, context enrichment (CE) module, and up-sampler. The down-sampler was designed to effectively learn both local and global representations from input CT scans by combining the advantages of lightweight convolutional and attention modules. The contextual enrichment (CE) module is introduced to enable the network to capture the contextual representation that can be later exploited to enrich the semantic knowledge of the up-sampler through skip connections. To further tackle the inter-site heterogeneity within the model, the approach uses an adaptive and switchable normalization (ASN) to adaptively choose the best normalization strategy according to the underlying data. A novel federated periodic selection protocol (FED-PCS) is proposed to fairly select the training participants according to their resource state, data quality, and loss of a local model. The results of an experimental evaluation of MIC-Net on three publicly available data sets show its robust performance, with an average dice score of 88.90% and an average surface dice of 87.53%., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2022 Elsevier Inc. All rights reserved.)

The recycling of retired new energy vehicle power batteries produces economic benefits and promotes the sustainable development of environment and society. However, few attentions have been paid to the design and optimization of sustainable reverse logistics network for the recycling of retired power batteries. To this end, we develop a six-level sustainable dynamic reverse logistics network model from the perspectives of economy, environment, and society. We solve the multi-objective combinatorial optimization model to explore the layout of the sustainable reverse logistics network for retired new energy vehicle power batteries recycling. A case study is implemented to verify the effectiveness of the proposed model. The results show that (a) the facility nodes near the front of the network fluctuate more by opening and closing; (b) the dynamic reverse logistics network is superior to its static counterpart; and (c) cooperation cost changes affect the transaction volume between third-party and cooperative enterprises and total network cost., (© 2023. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

This article proposes a new multiattribute group decision-making (MAGDM) method with probabilistic linguistic information that considers the following three aspects: an allocation of ignorance information, a realization of group consensus, and an aggregation of assessments. To allocate ignorance information, an optimization model based on minimizing the distances among experts is developed. To measure the consensus degree, a consensus index that considers the information granules of linguistic terms (LTs) is defined. On this basis, a suitable optimization model is established to realize the group consensus adaptively by optimizing the allocation of information granules of LTs with the particle swarm optimization (PSO) algorithm. With an objective to reduce the information loss during aggregation phases, the process of generating comprehensive assessments of alternatives with the evidential reasoning (ER) algorithm is presented. Therefore, a new method is developed based on the adaptive consensus reaching (ACR) model and the ER algorithm. Finally, the applicability of the proposed method is demonstrated by solving a selection problem of a financial technology company. Comparative analyses are conducted to show the advantages of the proposed method.

Designing effective and efficient classifiers is a challenging task given the facts that data may exhibit different geometric structures and complex intrarelationships may exist within data. As a fundamental component of granular computing, information granules play a key role in human cognition. Therefore, it is of great interest to develop classifiers based on information granules such that highly interpretable human-centric models with higher accuracy can be constructed. In this study, we elaborate on a novel design methodology of granular classifiers in which information granules play a fundamental role. First, information granules are formed on the basis of labeled patterns following the principle of justifiable granularity. The diversity of samples embraced by each information granule is quantified and controlled in terms of the entropy criterion. This design implies that the information granules constructed in this way form sound homogeneous descriptors characterizing the structure and the diversity of available experimental data. Next, granular classifiers are built in the presence of formed information granules. The classification result for any input instance is determined by summing the contents of the related information granules weighted by membership degrees. The experiments concerning both synthetic data and publicly available datasets demonstrate that the proposed models exhibit better prediction abilities than some commonly encountered classifiers (namely, linear regression, support vector machine, Naïve Bayes, decision tree, and neural networks) and come with enhanced interpretability.

In artificial intelligence systems, a question on how to express the uncertainty in knowledge remains an open issue. The negation scheme provides a new perspective to solve this issue. In this paper, we study quantum decisions from the negation perspective. Specifically, complex evidence theory (CET) is considered to be effective to express and handle uncertain information in a complex plane. Therefore, we first express CET in the quantum framework of Hilbert space. On this basis, a generalized negation method is proposed for quantum basic belief assignment (QBBA), called QBBA negation. In addition, a QBBA entropy is revisited to study the QBBA negation process to reveal the variation tendency of negation iteration. Meanwhile, the properties of the QBBA negation function are analyzed and discussed along with special cases. Then, several multisource quantum information fusion (MSQIF) algorithms are designed to support decision making. Finally, these MSQIF algorithms are applied in pattern classification to demonstrate their effectiveness. This is the first work to design MSQIF algorithms to support quantum decision making from a new perspective of "negation", which provides promising solutions to knowledge representation, uncertainty measure, and fusion of quantum information.

Domain adaptation (DA) is a popular strategy for pattern recognition and classification tasks. It leverages a large amount of data from the source domain to help train the model applied in the target domain. Supervised domain adaptation (SDA) approaches are desirable when only few labeled samples from the target domain are available. They can be easily adopted in many real-world applications where data collection is expensive. In this study, we propose a new supervision signal, namely center transfer loss (CTL), to efficiently align features under the SDA setting in the deep learning (DL) field. Unlike most previous SDA methods that rely on pairing up training samples, the proposed loss is trainable only using one-stream input based on the mini-batch strategy. The CTL exhibits two main functionalities in training to increase the performance of DL models, i.e., domain alignment and increasing the feature's discriminative power. The hyper-parameter to balance these two functionalities is waived in CTL, which is the second improvement from the previous approaches. Extensive experiments completed on well-known public datasets show that the proposed method performs better than recent state-of-the-art approaches., Competing Interests: Conflict of InterestsThe authors declare that they have no conflict of interest., (© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023, Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.)

A frequent cause of auto accidents is disregarding the proximal traffic of an ego-vehicle during lane changing. Presumably, in a split-second-decision situation we may prevent an accident by predicting the intention of a driver before her action onset using the neural signals data, meanwhile building the perception of surroundings of a vehicle using optical sensors. The prediction of an intended action fused with the perception can generate an instantaneous signal that may replenish the driver's ignorance about the surroundings. This study examines electromyography (EMG) signals to predict intention of a driver along perception building stack of an autonomous driving system (ADS) in building an advanced driving assistant system (ADAS). EMG are classified into left-turn and right-turn intended actions and lanes and object detection with camera and Lidar are used to detect vehicles approaching from behind. A warning issued before the action onset, can alert a driver and may save her from a fatal accident. The use of neural signals for intended action prediction is a novel addition to camera, radar and Lidar based ADAS systems. Furthermore, the study demonstrates efficacy of the proposed idea with experiments designed to classify online and offline EMG data in real-world settings with computation time and the latency of communicated warnings.

Under the assumption of rational economics, the opinions of decision makers should exhibit some transitivity properties. It is an important issue on how to measure the transitivity properties of the provided preference relations over a set of alternatives. In this study, we report the methods for measuring weak consistency (w-consistency) and weak transitivity (w-transitivity) of pairwise comparison matrices (PCMs) originating from the analytic hierarchy process (AHP). First, some interesting properties of PCMs with w-consistency and w-transitivity are studied. Second, novel methods are proposed to construct the quantification indices of w-consistency and w-transitivity of PCMs, respectively. Some comparisons with the existing methods are offered to illustrate the novelty of the proposed ones. Third, an optimization model is put forward to modify a PCM without any transitivity property to a new one with w-consistency and w-transitivity, respectively. The particle swarm optimization (PSO) algorithm is adopted to solve the nonlinear optimization problems. A novel decision-making model is established by considering the w-transitivity as the minimum requirement. Some numerical examples are carried out to illustrate the developed methods and models. It is observed that the proposed indices can be computed efficiently and reflect the inherent relations of the entries in a PCM with w-consistency and w-transitivity, respectively.

For practical motor imagery (MI) brain-computer interface (BCI) applications, generating a reliable model for a target subject with few MI trials is important since the data collection process is labour-intensive and expensive. In this paper, we address this issue by proposing a few-shot learning method called temporal episode relation learning (TERL). TERL models MI with only limited trials from the target subject by the ability to compare MI trials through episode-based training. It can be directly applied to a new user without being re-trained, which is vital to improve user experience and realize real-world MIBCI applications. We develop a new and effective approach where, unlike the original episode learning, the temporal pattern between trials in each episode is encoded during the learning to boost the classification performance. We also perform an online evaluation simulation, in addition to the offline analysis that the previous studies only conduct, to better understand the performance of different approaches in real-world scenario. Extensive experiments are completed on four publicly available MIBCI datasets to evaluate the proposed TERL. Results show that TERL outperforms baseline and recent state-of-the-art methods, demonstrating competitive performance for subject-specific MIBCI where few trials are available from a target subject and a considerable number of trials from other source subjects.

High occupancy pattern mining has been recently studied as an improved method for frequent pattern mining. It considers the proportion of each pattern in the transactions where the pattern occurred. The results of high occupancy pattern mining can be employed for automated control systems in order to make decisions. Meanwhile, the features of the databases have changed, because information technology has advanced. In real-world databases, new transactions are inserted in real time. However, the state-of-the-art approach to high occupancy pattern mining cannot handle incremental databases. Moreover, the existing method also requires a large amount of memory space, because it adopted a BFS-based search in order to find patterns. In this paper, we propose an approach, which is called HOMI (High Occupancy pattern Mining on Incremental databases), that uses a DFS-based search in order to detect patterns, and it mines high occupancy patterns on incremental databases. The performance analysis for both real and synthetic datasets indicates that HOMI has better performance than the state-of-the-art approaches and related algorithms., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022 ISA. Published by Elsevier Ltd. All rights reserved.)

In this study, a novel promotive particle swarm optimizer with double hierarchical structures is proposed. It is inspired by successful mechanisms present in social and biological systems to make particles compete fairly. In the proposed method, the swarm is first divided into multiple independent subpopulations organized in a hierarchical promotion structure, which protects subpopulation at each hierarchy to search for the optima in parallel. A unidirectional communication strategy and a promotion operator are further implemented to allow excellent particles to be promoted from low-hierarchy subpopulations to high-hierarchy subpopulations. Furthermore, for the internal competition within each subpopulation of the hierarchical promotion structure, a hierarchical multiscale optimum controlled by a tiered architecture of particles is constructed for particles, in which each particle can synthesize a set of optima of its different scales. The hierarchical promotion structure can protect particles that just fly to promising regions and have low fitness from competing with the entire swarm. Also, the double hierarchical structures increase the diversity of searching. Numerical experiments and statistical analysis of results reported on 30 benchmark problems show that the proposed method improves the accuracy and convergence speed especially in solving complex problems when compared with several variations of particle swarm optimization.

Most exiting results for impulsive switched systems (ISSs) are mainly built on the synchronous switching and impulses case; however, the impulses can not only occur in switched interval including switched instants but also the switched signals may exist between two impulsive points in practical instants. Under asynchronous impulses and switching signals, the main objective of this article is to study the exponential stability of fractional-order hybrid systems. In order to better characterize stability, some novel criteria are presented by adopting the mode-dependent average impulsive interval and induction method. The obtained impulsive switched criteria lead to a tradeoff between fractional-order α and impulsive strength. Especially, the impulsive effects (positive or negative) with the order α are also discussed in detail, which extends the previous integer order results. Moreover, numerical examples are given to interpret and verify the effectiveness of the obtained criteria.

Sintering is the preproduction process of ironmaking, whose products are the basis of ironmaking. How to improve the operating performance of the iron ore sintering process has always been a problem that operators are committed to solve. An operating performance improvement method based on prediction and grade assessment is presented in this article. First, considering the data distribution characteristics of the process, a performance index prediction model based on the Gaussian process regression is built, in which the mutual information analysis method is used to select the inputs of the performance index prediction model. Then, the operating performance grade is assessed by a threshold division method. Next, the operating performance grade guides the control of the burn-through point to improve the operating performance. Finally, experimental verification is performed based on the actual running data. The results show that the proposed method has high prediction accuracy, and it is also significant in improving the operating performance. Therefore, this approach provides an effective solution to predict and improve operating performance.

For preventing the outbreaks of Covid-19 infection in different countries, many organizations and governments have extensively studied and applied different kinds of quarantine isolation policies, medical treatments as well as organized massive/fast vaccination strategy for over-18 citizens. There are several valuable lessons have been achieved in different countries this Covid-19 battle. These studies have presented the usefulness of prompt actions in testing, isolating confirmed infectious cases from community as well as social resource planning/optimization through data-driven anticipation. In recent times, many studies have demonstrated the effectiveness of short/long-term forecasting in number of new Covid-19 cases in forms of time-series data. These predictions have directly supported to effectively optimize the available healthcare resources as well as imposing suitable policies for slowing down the Covid-19 spreads, especially in high-populated cities/regions/nations. There are several progresses of deep neural architectures, such as recurrent neural network (RNN) have demonstrated significant improvements in analyzing and learning the time-series datasets for conducting better predictions. However, most of recent RNN-based techniques are considered as unable to handle chaotic/non-smooth sequential datasets. The consecutive disturbances and lagged observations from chaotic time-series dataset like as routine Covid-19 confirmed cases have led to the low performance in temporal feature learning process through recent RNN-based models. To meet this challenge, in this paper, we proposed a novel dual attention-based sequential auto-encoding architecture, called as: DAttAE. Our proposed model supports to effectively learn and predict the new Covid-19 cases in forms of chaotic and non-smooth time series dataset. Specifically, the integration between dual self-attention mechanism in a given Bi-LSTM based auto-encoder in our proposed model supports to directly focus the model on a specific time-range sequence in order to achieve better prediction. We evaluated the performance of our proposed DAttAE model by comparing with multiple traditional and state-of-the-art deep learning-based techniques for time-series prediction task upon different real-world datasets. Experimental outputs demonstrated the effectiveness of our proposed attention-based deep neural approach in comparing with state-of-the-art RNN-based architectures for time series based Covid-19 outbreak prediction task., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2022 Elsevier Ltd. All rights reserved.)

Granular computing has been an intense research area over the past two decades, focusing on acquiring, processing, and interpreting information granules. In this study, we focus on the granulation of time series and discover the overall structure of the original time series by clustering the granular time series. During the granulation process, when time series exhibit some trend (up trend, equal trend, or down trend) or consist of a variety of tendencies, the trend is essential to be involved to construct the granular time series. Following the principle of justifiable granularity, we propose to form a series of trend-based information granules to describe the original time series and effectively reduce its dimensionality. Then, the similarity measure between trend-based information granules is provided, and considering the dynamic feature of time-series data, dynamic time warping (DTW) distance is generalized to measure the distance for granular time series. In sum, we show here a novel way of forming trend-based granular time series and the corresponding similarity measure, then based on this, the hierarchical clustering of granular time series is realized. The proposed approach can capture the main essence of time series and help to reduce the computing overhead. Experimental results show that the designed approach can reveal meaningful trend-based information granules, and provide promising clustering results on UCR and real-world datasets.

In this article, we elaborate on a Kullback-Leibler (KL) divergence-based Fuzzy C -Means (FCM) algorithm by incorporating a tight wavelet frame transform and morphological reconstruction (MR). To make membership degrees of each image pixel closer to those of its neighbors, a KL divergence term on the partition matrix is introduced as a part of FCM, thus resulting in KL divergence-based FCM. To make the proposed FCM robust, a filtered term is augmented in its objective function, where MR is used for image filtering. Since tight wavelet frames provide redundant representations of images, the proposed FCM is performed in a feature space constructed by tight wavelet frame decomposition. To further improve its segmentation accuracy (SA), a segmented feature set is reconstructed by minimizing the inverse process of its objective function. Each reconstructed feature is reassigned to the closest prototype, thus modifying abnormal features produced in the reconstruction process. Moreover, a segmented image is reconstructed by using tight wavelet frame reconstruction. Finally, supporting experiments coping with synthetic, medical, and real-world images are reported. The experimental results exhibit that the proposed algorithm works well and comes with better segmentation performance than other peers. In a quantitative fashion, its average SA improvements over its peers are 4.06%, 3.94%, and 4.41%, respectively, when segmenting synthetic, medical, and real-world images. Moreover, the proposed algorithm requires less time than most of the FCM-related algorithms.

We present adversarial event prediction (AEP), a novel approach to detecting abnormal events through an event prediction setting. Given normal event samples, AEP derives the prediction model, which can discover the correlation between the present and future of events in the training step. In obtaining the prediction model, we propose adversarial learning for the past and future of events. The proposed adversarial learning enforces AEP to learn the representation for predicting future events and restricts the representation learning for the past of events. By exploiting the proposed adversarial learning, AEP can produce the discriminative model to detect an anomaly of events without complementary information, such as optical flow and explicit abnormal event samples in the training step. We demonstrate the efficiency of AEP for detecting anomalies of events using the UCSD-Ped, CUHK Avenue, Subway, and UCF-Crime data sets. Experiments include the performance analysis depending on hyperparameter settings and the comparison with existing state-of-the-art methods. The experimental results show that the proposed adversarial learning can assist in deriving a better model for normal events on AEP, and AEP trained by the proposed adversarial learning can surpass the existing state-of-the-art methods.

Rule-based fuzzy models play a dominant role in fuzzy modeling and come with extensive applications in the system modeling area. Due to the presence of system modeling error, it is impossible to construct a model that fits exactly the experimental evidence and, at the same time, exhibits high generalization capabilities. To alleviate these problems, in this study, we elaborate on a realization of granular outputs for rule-based fuzzy models with the aim of effectively quantifying the associated modeling errors. Through analyzing the characteristics of modeling errors, an error model is constructed to characterize deviations among the estimated outputs and the expected ones. The resulting granular model comes into play as an aggregation of the regression model and the error model. Information granularity plays a central role in the construction of granular outputs (intervals). The quality of the produced interval estimates is quantified in terms of the coverage and specificity criteria. The optimal allocation of information granularity is determined through a combined index involving these two criteria pertinent to the evaluation of interval outputs. A series of experimental studies is provided to demonstrate the effectiveness of the proposed approach and show its superiority over the traditional statistical-based method.

Fuzzy rule-based models (FRBMs) are sound constructs to describe complex systems. However, in reality, we may encounter situations, where the user or owner of a system only owns either the input or output data of that system (the other part could be owned by another user); and due to the consideration of data privacy, he/she could not obtain all the needed data to build the FRBMs. Since this type of situation has not been fully realized (noticed) and studied before, our objective is to come up with some strategy to address this challenge to meet the specific privacy consideration during the modeling process. In this study, the concept and algorithm of the collaborative fuzzy clustering (CFC) are applied to the identification of FRBMs, describing either multiple-input-single-output (MISO) or multiple-input-multiple-output (MIMO) systems. The collaboration between input and output spaces based on their structural information (conveyed in terms of the corresponding partition matrices) makes it possible to build FRBMs when input and output data could not be collected and used in unison. Surprisingly, on top of this primary pursuit, with the collaboration mechanism the input and output spaces of a system are endowed with an innovative way to comprehensively share, exchange, and utilize the structural information between each other, which results in their more relevant structures that guarantee better model performance compared with performance produced by some state-of-the-art modeling strategies. The effectiveness of the proposed approach is demonstrated by experiments on a series of synthetic and publicly available datasets.

In the analytic hierarchy process (AHP), the reciprocal matrix is generated based on the pairwise comparisons completed among all the alternatives or attributes under consideration. To ensure reliability and validity of the decision solution, a certain modification of entries of the matrix is usually needed to improve the consistency of the reciprocal matrix. This study aims to present a consistency improvement method by admitting some level of information granularity in the evaluation process. This gives rise to a granular rather than numeric matrix of pairwise comparisons. First, with a given average level of information granularity, we present an optimal granularity model that is characterized by maximal consistency. One can maximize the consistency degree by invoking a process of allocation of information granularity across the corresponding modifications of the reciprocal matrix. Based on the optimal granularity model, an interactive consistency improvement process is presented with the involvement of the decision maker. Then, an adaptive differential evolution algorithm is applied to optimize entries of the modified reciprocal matrix. Detailed experiments along with a thorough comparative analysis are completed to demonstrate the effectiveness of the proposed method.