Fuzzy relation models play an important role in describing the complex relationships between the antecedent and consequent parts, but suffer from insufficient interpretability and accuracy, and rely on centralized modeling. This paper proposes a granular fuzzy relation model based on horizontal federated learning to enable distributed modeling of fuzzy relation models with privacy protection, while improving both interpretability and accuracy. In the first phase, fuzzy sets are designed with the aid of federated fuzzy clustering. In the second phase, the max-min fuzzy logic operation is employed to develop fuzzy relation models in federated learning. Based on the initial fuzzy relation issued by the global server, each client establishes the local fuzzy relation model using two federated learning strategies, namely gradient-based and average-based approaches, respectively. In the third phase, granular fuzzy relation models are generalized by introducing a granular parameter in specifying the level of information granularity, which is optimized by applying the Differential Evolution algorithm. The overall performance is measured by the product of two conflicting criteria, namely, coverage and specificity. The originality of proposed model lies in the realization of horizontal federated learning for granular fuzzy relation models. In this study, the granular version of fuzzy relation models incorporates richer semantic information, thereby enhancing both the interpretability and accuracy of the model. Meanwhile, each client can complete the training by simply interacting gradients or parameters instead of the original data and location, thus realizing privacy-protecting distributed modeling. Experimental results indicate better performance of the proposed method than that of centralized learning.

In this article, we propose a novel methodology for determining accurate positions of characteristic points encountered in the analysis of bioimpedance signals. The proposed approach fully utilizes two fundamental modeling pursuits based on fuzzy rule-based models and neural networks. We take advantages of the unique capabilities of fuzzy rule-based models to characterize the nonlinear relationship between the acquired bioimpedance signals and their temporal coordinates. The fuzzy modeling approach is used to approximate the process that generates the bioimpedance signals through a collection of rules (if–then statements). In the sequel, the parameters of the models are used as the inputs of neural network models to determine the position of characteristic points. We further augment the numeric neural network to its granular counterpart to accommodate the uncertainty in the available experimental evidence by allocating a certain level of information granularity across the parameter space. The resulting granular outputs (intervals) become reflective of the quality and level of confidence associated with the prediction results. The quality of the prediction results is quantified in terms of the coverage and specificity criteria. The performance index is also enhanced to deal with the situation when the positions provided by experts are also information granules (intervals). The performance of the proposed approach is justified through a collection of experiments carried out on the collected real-world bioimpedance signals. Experimental results show that the proposed approach achieved higher accuracy in determining the position of characteristic points in comparison with other existing methods.

In this study, we elaborate on a realization of fuzzy clustering and the construction of fuzzy rule-based models on the basis of vertically partitioned datasets in a privacy-preserving federated learning approach. The main focus of the overall design process is to construct a family of information granules (clusters) and the corresponding fuzzy rules in the presence of a collection of vertically partitioned datasets without compromising data privacy. These datasets are composed of the same data but are described by different features, and due to security considerations, data cannot be shared. The vertical federated fuzzy clustering can be realized as an iterative optimization process composed of successive cycles: 1) computation (update) of the prototypes and partition matrices performed on the basis of local datasets and 2) an integration of the local sources of knowledge carried out on a central coordinator-server. The update of the partition matrices can be completed using a distance-based or gradient-based approach. The communication of findings between local clients and the coordinator-server is realized through exchanging partition matrices, which are more general than numeric data and can avoid leakage of data privacy. Fuzzy models are optimized in a similar manner through exchanging the gradients of the performance index computed with respect to the parameters between the clients and the global coordinator. The proposed mechanism exhibits significant originality since the realization of fuzzy modeling in a vertical federated learning environment has not been studied. Experimental studies show that the proposed federated clustering and fuzzy model design could effectively reveal the structure of the entire dataset and achieve high performance compared with the results obtained in a centralized manner.

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.

Understanding the rationale behind the predictions produced by machine learning models is a necessary prerequisite for human to build confidence and trust for the intelligent systems. To tackle the problem of interpretability faced by black-box models, a fuzzy local surrogate model is proposed in this study to articulate the rationale for predictions to enhance the interpretability of the results of machine learning models. Fuzzy rule-based model comes with high interpretability since it is composed of a collection of readable rules, and thus is suitable for prediction interpretation. The general scheme of fuzzy local surrogate model is composed of the following phases: i) select data points around the instance of interest, for which we wish to explain the prediction result produced by the predictive model; ii) generate predictions for these newly selected data and weight the selected data based on the distance from the instance of interest; and iii) a fuzzy rule-based model composed a collection of interpretable is constructed to approximate the weighted data and offer meaningful interpretation to the prediction result of the given instance. The proposed fuzzy model for explaining predictions is model-agnostic and could provide high estimation accuracy. The proposed methodology offers a significant original contribution to the interpretation of machine learning models. Experimental studies demonstrate the usefulness of the proposed fuzzy local surrogate model in providing local explanations.

As an effective way for knowledge representation and processing, fuzzy rule-based models have been extensively studied and widely used in practice. In many circumstances, a very limited amount of data or insufficient computational resources make the construction of accurate models a genuine challenge. In this study, a granular augmentation of fuzzy rule-based models is proposed with intent to realize knowledge transfer in system modeling. This research mainly focuses on how to effectively exploit the existing fuzzy model, which has been constructed on extensive previously acquired experimental evidence and could be regarded as source of knowledge, in a new environment where only very limited experimental evidence is available. Rather than constructing a new model from scratch, knowledge conveyed by the existing model could be retained and reused in the target domain. The originality and innovation of this study lies in the adaption of the existing model to the new environment through optimal allocation of information granularity to produce granular fuzzy models, which are more abstract and general than the original numeric constructs. The granular fuzzy models yield results in a granular form whose quality is evaluated using the coverage and specificity criteria.

Automatic path planning problem is essential for efficient mission execution by unmanned aerial vehicles (UAVs), which needs to access the optimal path rapidly in the complicated field. To address this problem, a novel hybrid particle swarm optimization (PSO) algorithm, namely, SDPSO, is proposed in this article. The proposed algorithm improves the update strategy of the global optimal solution in the PSO algorithm by merging the simulated annealing algorithm, which enhances the optimization ability and avoids falling into local convergence; each particle integrates the beneficial information of the optimal solution according to the dimensional learning strategy, which reduces the phenomenon of particles oscillation during the evolution process and increases the convergence speed of the SDPSO algorithm. The simulation results show that compared with PSO, dynamic-group-based cooperative optimization (DGBCO), gray wolf optimizer (GWO), RPSO, and two-swarm learning PSO (TSLPSO), the SDPSO algorithm can quickly plan higher quality paths for UAVs and has better robustness in complex 3-D environments.

With the widespread application of the Industrial Internet of Things (IIoT), industrial control systems (ICSs) greatly improve industrial productivity, efficiency, and product quality. However, IIoT protocols as the bridge of different parts of ICSs are vulnerable to be attacked due to their vulnerabilities. To reduce cyberattack threats, we need to find the vulnerabilities of IIoT protocols by using efficient vulnerability mining methods, such as fuzzing. Fuzzing is often used to mine vulnerabilities for IIoT protocols. However, the traditional fuzzing methods for IIoT protocols have a low passing rate and low code coverage. To solve these problems, we propose a generative adversarial network (GAN), here referred to as coverage-guided GANs (CovGAN), which aims to generate test cases with a high passing rate and code coverage by learning IIoT protocol specifications. Based on the CovGAN, we construct a fuzzing framework (CGFuzzer) for IIoT protocols. Finally, we design a protocol simulator to verify the CovGAN performance. Experimental results show that the proposed methodology outperforms approximately 5%, 7%, and 39% of the passing rate of GANFuzz, SeqFuzzer, and Peach, respectively. In addition, CGFuzzer has a significant improvement in code coverage, which is about 17%, 24%, and 31% higher than GANFuzz, SeqFuzzer, and Peach, respectively.

In this article, we elaborate on a design and realization of fuzzy rule-based model in the horizontal federated learning framework. Traditional machine learning in distributed environment often involves sharing sensitive information with other sites or transferring data to a central server on which a global model is trained. These situations increase the communication overhead and pose serious threats to the privacy of sensitive data. Federated learning opens up the possibility for collaboratively training a global model on a basis of distributed on-site data without sacrificing data privacy. While fuzzy rule-based models have been used in system modeling due to their substantial modeling abilities and good interpretability, the implementation of fuzzy rule-based models in a distributed environment without compromising data privacy still requires careful consideration. This article proposes a two-step federated learning approach to train a global model on a basis of private data located across different sites without their centralization. The first step concerns the determination of the structure of the data through federated collaborative clustering. Subsequently, a shared global model is trained jointly by all the participating clients. An advantage of the proposed method is that it achieves high accuracy without violating data privacy. A series of experimental studies are conducted to gain a detailed insight into the realization steps and demonstrate the effectiveness of the proposed method.

The design of information granules assumes a central position in the discipline of Granular Computing and its applications. The principle of justifiable granularity offers a conceptually and algorithmically attractive way of designing information granule completed on a basis of some experimental evidence (especially present in the form of numeric data). This paper builds upon the existing principle and presents its significant generalization, referred here as an adaptive principle of justifiable information granularity. The method supports a granular data aggregation producing an optimal information granule (with the optimality expressed in terms of the criteria of coverage and specificity commonly used when characterizing quality of information granules). The flexibility of the method stems from an introduction of the adaptive weighting scheme of the data leading to a vector of weights used in the construction of the optimal information granule. A detailed design procedure is provided along with the required optimization vehicle (realized with the aid of the population-based optimization techniques, such as particle swarm optimization and differential evolution). Two direct application areas in which the principle becomes of direct usage include prediction of time series and prediction of spatial data. In both cases, it is advocated that the results formed by the principle are reflective of the precision (quality) of the prediction process.