Jianhua Yang

The economic dispatch problem (EDP) poses a significant challenge in energy management for modern power systems, particularly as these systems undergo expansion. This growth escalates the demand for communication resources and increases the risk of communication failures. To address this challenge, we propose a distributed algorithm with network‐independent step sizes and an event‐triggered mechanism, which reduces communication requirements and enhances adaptability. Unlike traditional methods, our algorithm uses network‐independent step sizes derived from each agent's local cost functions, thus eliminating the need for detailed network topology knowledge. The theoretical derivation identifies a range of step size values that depend solely on the objective function's strong convexity and the gradient's Lipschitz continuity. Furthermore, the proposed algorithm is shown to achieve a linear convergence rate, assuming the event triggering threshold criteria are met for linear convergence. Numerical experiments further validate the effectiveness and advantages of our proposed distributed algorithm by demonstrating its ability to maintain good convergence characteristics while reducing communication frequency.

In this study, we introduce a distributed algorithm that is specifically designed to address optimization problems featuring a decomposable objective function and equality constraints. To minimize the amount of communication required, we incorporate an event-triggered mechanism that enables information exchange only when variable values exceed predefined thresholds. Importantly, our proposed algorithm possesses a distinctive characteristic where the determination of step size is solely based on the properties of the objective function, regardless of the structure of the communication network. Even in situations where changes occur in the network structure, our algorithm remains valid without necessitating any updates to its step size. Assuming strong convexity and smoothness in local objective functions, along with appropriate event-triggered thresholds, our algorithm achieves a convergence rate that is linear. Several numerical experiments provide evidence supporting the effectiveness and superiority of our proposed approach.

In this article, a hypersphere information granule-based fuzzy classifier integrated with Fuzzy Cognitive Maps (FCM), named FCM-IGFC, is proposed for the classification of imbalanced data. The proposed FCM-IGFC is structured by sequentially linking a Takagi-Sugeno-Kang (TSK) fuzzy system (FCM-TSK) – which is embedded with FCMs – and a rule-based fuzzy system (IGFS) based on hypersphere information granules. The FCM-TSK leverages the inference capabilities of the FCM to allow for the movement of data within the original space, while the IG-FS creates a mapping between samples and majority and minority classes using information granules. In this study, we introduced an innovative bottom-up granulation method and an overlap elimination technique for constructing hypersphere information granules. These methods facilitate the creation of information granules that accurately represent the structure of classes, even when dealing with im- balanced data. Moreover, the stacked structure of the FCM-IGFC offers data transfer capabilities. This helps reduce the complexity of distributions such as small, disjointed clusters and irregular class boundaries, with the support of the FCM, thereby making it easier to use information granules to describe the class structure. A series of experiments conducted on 12 publicly available datasets demonstrated that the performance of FCM-IGFC significantly surpasses that of existing granule-based fuzzy classifiers. Additionally, it is competitive with top-tier classifiers that incorporate sampling methods.

Knowledge graphs are regarded as structured knowledge bases that embody various facts coming from the real world. Their completeness is still far from satisfactory. Relational learning models in link prediction can automatically find the missing relationships between entities to increase the integrality of the knowledge bases, which form two categories purely embedding-based and hybrid embedding-based. Several models including HolE and RotatE belong to purely embedding-based with inefficient performers and few element interactions. Based on the above, this paper advances a novel Knowledge Graph Embedding relational model that leverages a circular correlation operation in the complex domain and dubs as CircularE, which increases interactions between entities and relations to a great extent by this compressed operator without expanding the dimension of space. It gives expression of the interactions between element semantics to achieve good performance in relational learning. Besides, a self-adaption adversarial negative sampling scheme is proposed on account of the KGs structure and the probability semantic of the triples. This negative sampler efficiently optimizes the knowledge representation capability of CircularE and far more than enhances the outputs of several relational original models in embedding-based. Experiments indicate that the competitive properties of CircularE on the four large-scale benchmarks of knowledge base completion tasks are superior to the state-of-the-art methods.

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.

A novel design method for time series modeling and prediction with fuzzy cognitive maps (FCM) is proposed in this paper. The developed model exploits the least square method to learn the weight matrix of FCM derived from the given historical data of time series. A fuzzy c-means clustering algorithm is used to construct the concepts of the FCM. Compared with the traditional FCM, the least square fuzzy cognitive map (LSFCM) is a direct solution procedure without iterative calculations. LSFCM model is a straightforward, robust and rapid learning method, owing to its reliable and efficient. In addition, the structure of the LSFCM can be further optimized with refinements the position of the concepts for the higher prediction precision, in which the evolutionary optimization algorithm is used to find the optimal concepts. Withal, we discussed in detail the number of concepts and the parameters of activation function on the impact of FCM models. The publicly available time series data sets with different statistical characteristics coming from different areas are applied to evaluate the proposed modeling approach. The obtained results clearly show the effectiveness of the approach.

The problem of classification for imbalanced datasets is frequently encountered in practical applications. The data to be classified in this problem are skewed, i.e., the samples of one class (the minority class) are much less than those of other classes (the majority class). When dealing with imbalanced datasets, most classifiers encounter a common limitation, that is, they often obtain better classification performances on the majority classes than those on the minority class. To alleviate the limitation, in this study, a fuzzy rule-based modeling approach using information granules is proposed. Information granules, as some entities derived and abstracted from data, can be used to describe and capture the characteristics (distribution and structure) of data from both majority and minority classes. Since the geometric characteristics of information granules depend on the distance measures used in the granulation process, the main idea of this study is to construct information granules on each class of imbalanced data using Minkowski distance measures and then to establish the classification models by using “If-Then” rules. The experimental results involving synthetic and publicly available datasets reflect that the proposed Minkowski distance-based method can produce information granules with a series of geometric shapes and construct granular models with satisfying classification performance for imbalanced datasets.

Information granules are fundamental, abstract and easy-to-operate constructs supporting the human-centered handling way in granular computing (GrC). One of the basic properties of information granules comes with its hierarchy. Information granularity is the quantification expression of hierarchy of an information granule. Forming information granules with multi-granularity to hierarchically describe the nature of data is an important task in GrC. In this study, a cone-shaped fuzzy set-based granular description method with multi-granularity is proposed for multidimensional data. Its fundamental idea is to realize the synergy of quantification of information granularity and a hierarchical description of data by means of α-cuts of cone-shaped fuzzy sets. The proposed method first partition the entire dataset into a series of data chunks. Then, some mutually non-overlapping cone-shaped fuzzy sets are constructed by optimally determining their cores and support radii in terms of the coverage of α-cuts of these fuzzy sets to the data located in individual chunks and the corresponding specificity. Finally, by implementing α-cuts processing for these constructed cone-shaped fuzzy sets, a collection of families of hyper-spherical information granules used to hierarchically describe the structural characteristics of the dataset are completely emerged. Besides, the quality of the resulting families of hyper-spherical information granules is evaluated along the granular perspective and the application perspective, respectively. A series of experimental studies concerning several synthetic and publicly available datasets are covered. The experimental results demonstrates the superiority of the proposed granular description method of data with multi-granularity.