Clustering provides a powerful technique for data analysis and data interpretation in the current complex background. Fuzzy clustering has gained significant attention in both research and applications due to its effectiveness in capturing the inherent uncertainty of real-world data. Among these methods, fuzzy C-means (FCM) stands out as one of the most representative and widely used approaches. This study develops a novel nonlinear transformation strategy to restructure data in order to improve the classification performance of FCM, and the transformed data structure, achieved through the developed nonlinear techniques, exhibits highly effective in enhancing the performance of FCM-based classifiers. In the proposed scheme, the original dataset is first partitioned into multiple subsets (matrix blocks) based on the original labels, with distinct weights assigned to each feature within these subsets. This process constructs a more separable dataset, referred to as the "expected high-performance dataset." Then, multiple nonlinear transformation models are constructed for the original dataset and for each feature of the constructed "expected high-performance dataset" with the support vector regression (SVR) method. During these operations, weight optimization is performed using particle swarm optimization (PSO), ultimately enhancing intraclass compactness by amplifying the similarity among samples within the same class. A comprehensive analysis of the proposed method was conducted, and experimental results on public datasets demonstrate its effectiveness and feasibility. The classification accuracy of the proposed method on multiple datasets has been improved by varying degrees compared with FCM, with an average improvement of 16.029% and a maximum improvement of 57.365%.

Granular computing (GrC) embraces a spectrum of concepts, methodologies, methods, and applications, which dwells upon information granules and their processing. Fuzzy C-means (FCM) based encoding and decoding (granulation-degranulation) mechanism plays a visible role in granular computing. Fuzzy decoding mechanism, also known as the reconstruction (degranulation) problem, has become an intensively studied category in recent years. This study mainly focuses on the improvement of the fuzzy decoding mechanism, and an augmented version achieved through constructing perturbation matrices of prototypes is put forward. Particle swarm optimization is employed to determine a group of optimal perturbation matrices to optimize the prototype matrix and obtain an optimal partition matrix. A series of experiments are carried out to show the enhancement of the proposed method. The experimental results are consistent with the theoretical analysis and demonstrate that the developed method outperforms the traditional FCM-based decoding mechanism.

Most of the existing consensus reaching approaches for group decision-making (GDM) need decisionmakers to reevaluate alternatives multiple times or require additional external interventions, which results in great time and labor consumption. To this end, automatic consensus reaching approaches have been developed to improve effectiveness and efficiency. However, in the existing automatic consensus reaching approaches, preference adjustment willingness (PAW) is overlooked and consistency/consensus thresholds cannot be guaranteed to be reached, which may lead to an unacceptable collective decision. This study proposes a new automatic consensus reaching approach with PAW for GDM. First, under the paradigm of interval information granularity, PAW is formally defined by considering both the amount and sensitivity of preference adjustment. Levels of interval information granularity are adaptively determined by an algorithm with achievement of the consistency threshold. Then, we propose an automatic preference adjustment model where the weighted average of PAW, group consensus, and individual consistency is defined as its performance index. Based on the proposed model and algorithm, a consensus evolution realizing a continuous improvement of consensus is subsequently developed. Finally, the framework of the proposed approach is presented. The applicability of the proposed approach was analyzed through a case study concerning the concept selection of a turbofan engine's component. Discussions on parameter settings and time-consuming of the approach show its great effectiveness and time efficiency. Comparison with other similar approaches demonstrates that the proposed approach is able to achieve larger consistency and consensus improvement with a smaller preference adjustment amount.

Speckle noise is an inherent nature of synthetic aperture radar (SAR) images, which degrades the quality of the images and makes the interpretation of SAR images difficult. In this letter, we propose a despeckling method by simultaneously exploring low-rank prior and multi-scale prior of SAR images. Especially, we propose a low-rank minimization model by considering a data fidelity term derived from the Fisher-Tippett distribution and a weighted nuclear norm regularization term. Furthermore, we explore the multi-scale prior by selecting similar patches from different scales of the SAR image. The resulting optimization problem is solved by the alternating direction method of multipliers (ADMM). Experiments conducted on both simulated and real SAR images demonstrate that the proposed method can provide promising despeckling results in terms of speckle reduction and texture and edge details preservation.

In this paper, we propose a new synthetic aperture radar (SAR) image despeckling method based on the nonlocal low-rank minimization model. First, some similar image patches are selected for each pixel to construct the patch group matrix (PGM). Then, a new low-rank minimization model, called Fisher-Tippett distribution (FT)-weighted nuclear norm minimization (WNNM), is proposed to recover the underlying low-rank component from the PGM. Specifically, the FT-WNNM is developed by reformulating the despeckling problem as the maximizing a posterior probability problem. The new model consists of a data fidelity term and a regularization term (also called prior term). The data fidelity term is derived from the statistical distribution of SAR images in the logarithm domain, which is known as the Fisher-Tippett distribution, and the regularization term is the recent weighted nuclear norm. Then, the alternating direction method of multipliers (ADMM) is introduced to solve the corresponding optimization problem. Under ADMM framework, the resulting subproblems can be solved efficiently and the convergence can be guaranteed. Extensive experiments on both simulated and real SAR images demonstrate that the proposed method can achieve comparable or even better despeckling performance than some state-of-the-art despeckling algorithms.

For synthetic aperture radar (SAR) image land cover classification, traditional feature-based methods are not always effective because of the heavy multiplicative noise. To solve this problem, we herein propose a new classification method for SAR images considering adaptive spatial contextual information. In contrast to preceding studies, the spatial contextual information of the SAR images is exploited via composite kernels (CKs). Additionally, an image superpixel strategy is employed to design an adaptive neighborhood, which enables the extraction of more accurate spatial information than a fixed-size neighborhood. Specifically, a modified superpixel map is first generated to produce the neighborhood. With this neighborhood, a context kernel is then defined by means of the Gaussian radial basis function. The resulting context kernel is combined with the conventional feature kernel via the designed CKs scheme. The relative proportion of these two kernels is controlled by a weight parameter. The label of each pixel is predicted by feeding the final CKs into a support vector machine classifier. Experiments on two real SAR images demonstrate that the proposed method can greatly improve the classification performance, both visually and quantitatively, in comparison to other traditional feature-based methods.