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%.

With the rapid development of the new energy sector, production equipment for battery cells faces increasing challenges in maintaining efficiency and quality. Among these, the laser die cutting and winding machine plays a pivotal role in transforming electrode sheets into finished cells. Its performance directly affects the dimensional precision and internal structural consistency of the cells, which are critical to product quality and production-line efficiency. To tackle the challenges in monitoring and maintaining this critical equipment, we propose a time-series data-driven method based on the Transformer architecture, named multiscale dynamic dilated attention, which effectively predicts sensor offset trajectories and provides early shutdown fault warnings when correction sensors approach their operational limits. Furthermore, this model incorporates adjustable segment sizes and counts, and assigns distinct dilation rates to individual attention heads, this design enables a dynamic tradeoff among receptive field, modeling capacity, and computational cost, allowing fine-grained control over long-range dependence modeling while reducing the canonical self-attention complexity from$O(\mathit {L}^{2})$to approximately$O(\mathit {L})$. Extensive experiments and real-world applications demonstrate that the proposed method achieves state-of-the-art performance in both prediction accuracy and practical deployment, while exhibiting excellent adaptability across diverse operating conditions.

Predictive business process monitoring (PBPM) is particularly valuable in dynamic business environments, and it can help organisations mitigate risks and optimise resource allocation. An interesting task in PBPM is next activity prediction (NAP), which allows the prediction of future activities that will be executed at a certain time based on ongoing business processes. Existing methods typically only utilise the order information of traces when predicting the next activity, without fully leveraging the attribute information present in the logs. Given the usefulness of these for NAP, combining them can help neural networks gain a deeper understanding of the actual business process. In this study, we propose a dual-view deep learning approach to fully extract and fuse the aforementioned two aspects of information. First, we treated traces as sequential texts and extracted the trace order information based on a long short-term memory based self-attention network. Then, we treated traces as unstructured images and captured the implicit attribute fusion information among events using a 12-layer residual network. Finally, two parts of information were fused for NAP. Experiments on 12 real-life event logs prove that the proposed approach is superior to state-of-the-art approaches, exhibiting good performance in accuracy, macro-precision, macro-recall, macro-F1-score, and macro-Gmean.

In existing fault diagnosis methods, fault categories are generally coarse-grained, which may result in failure to precisely identify fault details. Therefore, fine-grained fault diagnosis is explored in this study. In this scenario, the following three challenges arise, first, few-shot learning, second, less distinguishable, third, new fault emerging. To cope with these challenges, a prior knowledge-augmented meta-learning method for fault diagnosis is proposed in this study. The process of prior knowledge augmentation occurs in both the training and test phases. In the training phase, there are two processes: fault mechanism pretraining and true label fine-tuning. The fault mechanism pretraining process is employed to integrated prior knowledge of fault mechanism, where the pseudolabels are constructed by the values of 14 time-domain indicators. Subsequently, in the true label fine-tuning process, the pretrained model is fine-tuned by the training set with class labels. In the test phase, the heatmaps generated by gradient-weighted class activation mapping serve as prior knowledge. By integrating prior knowledge in the training and test phases, the proposed method presents a novel approach to addressing the challenge of fine-grained fault diagnosis in industrial applications. In addition, the deployment of prior knowledge to both the training and testing sets enhances the interpretability of the method. The proposed method is evaluated on rolling bearing and gearbox datasets and exhibits a remarkable capability to identify new fine-grained fault categories from only a few samples.

Convolutional neural networks (CNNs) have been widely used in fault diagnosis due to their superiority in feature extraction. Traditional CNNs are a type of closed-box techniques with little interpretability, and their effectiveness is greatly affected when fault mechanisms and modes are extremely complex. To cope with such issue, this article presents a way to integrate outlier-type prior knowledge into CNNs based on an attention mechanism for fault diagnosis. First, outliers of the image-like data obtained by a sliding window processing from the raw data are formally defined as prior knowledge. Then, the defined outlier-type prior knowledge is integrated into any layer of CNNs by a parameter-free attention mechanism. Compared with existing similar methods, the proposal realizes a novel and flexible definition of prior knowledge and achieves deep fusion of prior knowledge and CNNs with low computational cost. The performance of the proposal was evaluated on the Tennessee Eastman process dataset and the real wind turbine blade icing dataset, which indicates that the proposal could not only realize accurate results but also had good model interpretability in terms of achieving high accuracy. The acquisition of outlier-type prior knowledge was discussed and the results demonstrate the effectiveness of the proposed prior knowledge integration method.

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.

Interval linguistic preference relation is an effective tool for expressing experts’ preference in group decision making under uncertain linguistic environment. A new aggregation operator called continuous chi-square deviation based 2-tuple linguistic ordered weighted quasi-averaging (C-CDLOWQ) operator is proposed to transform the interval linguistic preference relations into precise linguistic preference relations. Some desirable properties and special cases of the C-CDLOWQ operator are analyzed in detail. To take the interactive phenomenon among experts into account, the Shapley weighting vector is presented to integrate the expected linguistic preference relations. The λ-fuzzy measure is employed to simplify the fuzzy measure on expert set. A CS-GDM algorithm is developed to group decision making with interval linguistic preference relations. The application in commercial investment problem is provided to illustrate the effectiveness of CS-GDM algorithm.

Interval-valued hesitant fuzzy sets permit the membership degree of an element to have several possible interval values in [0, 1] rather than real numbers, which can well deal with inherent hesitancy and uncertainty in the human decision-making process. In this paper, we first point out the issue of the existing correlation coefficients of interval-valued hesitant fuzzy sets and then define several new ones, which do not have to consider the lengths of interval-valued hesitant fuzzy elements and the arrangement of their possible interval values. Since the assumption that the elements in a set are independent is usually violated, we further define several Shapley weighted correlation coefficients, which consider their interactions. To deal with the situations where the elements are correlative and the weight formation is incompletely known, models for the optimal fuzzy measures on a feature set and on an attribute set are established, respectively. Finally, a procedure to pattern recognition and multiattribute decision making with incomplete weight information and interactive conditions is developed. Meanwhile, the corresponding examples are provided to show the practicality and feasibility of the proposed procedures.

The aim of this article is to investigate the approach for multi-attribute group decision-making, in which the attribute values take the form of multi-granularity multiplicative linguistic information. Firstly, to process multiple sources of decision information assessed in different multiplicative linguistic label sets, a method for transforming multi-granularity multiplicative linguistic information into multiplicative trapezoidal fuzzy numbers is proposed. Then, a formula for ranking multiplicative trapezoidal fuzzy numbers is given based on geometric mean. Furthermore, the concept of similarity degree between two multiplicative trapezoidal fuzzy numbers is defined. The attribute weights are obtained by solving some optimization models. An effective approach for group decision making with multi-granularity multiplicative linguistic information is developed based on the ordered weighted geometric mean operator and proposed formulae. Finally, a practical example is provided to illustrate the practicality and validity of the proposed method.

The essential role of the particular families of capacities and the capacity identification methods is to help the decision maker to deal with the exponential complexity inherent in the construction process of the capacity. The 2-additive capacities appear to be the most popular among the particular families of capacities since they permit to model interactions between criteria while preserving simplicity. Besides the preference with respect to the decision criteria, most of the capacity identification methods also need to provide the desired overall evaluations of the decision alternatives in the learning set, which is a time-consuming task for the decision maker. In this paper, we propose some models to identify 2-additive capacities only from a kind of refined preference information with respect to the decision criteria called the multicriteria correlation preference information (MCCPI). The MCCPI is a group of 2-D preference information which can be described and obtained by the refined diamond diagram. The common principle of the proposed models is to minimize the different kinds of deviations between the MCCPI and the most desired 2-additive capacity(ies). A multicriteria decision making example is presented to show the feasibility of the proposed methods, and a 2-D scale of the MCCPI is also introduced in the further discussion of the illustrative example.

In this paper, some new operators for aggregating interval-valued intuitionistic fuzzy information are proposed to deal with multiple attribute decision making problems. Firstly, the C-IFOWA operator and C-IFOWG operator are developed to aggregate all the values in the interval-valued intuitionistic fuzzy numbers. Some of their desirable properties are also studied. Secondly, in order to aggregate a set of interval-valued intuitionistic fuzzy numbers, some new aggregation operators are proposed based on the C-IFOWA operator and C-IFOWG operator. Thirdly, two methods for multiple attribute decision making, in which the attribute values are given in the forms of interval-valued intuitionistic fuzzy numbers are presented. Finally, two numerical examples are provided to illustrate the practicality and validity of the proposed methods.

This paper presents a novel method for multiple attribute decision-making based on interval valued intuitionistic fuzzy sets (IVIFSs) theory and TOPSIS method in fuzzy environments. In this paper, the concept of interval-valued intuitionistic fuzzy sets is introduced, and the distance between two interval valued intuitionistic fuzzy sets is defined. Then, according to the ideal of classical TOPSIS method, a closeness coefficient is defined to determine the ranking order of all alternatives by calculating the distances to both the interval valued intuitionistic fuzzy positive-ideal solution and interval valued intuitionistic fuzzy negative-ideal solution. The multi-attribute decision-making process based on IVIFSs is given in fuzzy environments. Finally, an example is shown to highlight the validity and procedure of the proposed method.