The integration of different learning paradigms has long been a focus of machine learning research, aimed at overcoming the inherent limitations of individual methods. Fuzzy rule-based models excel in interpretability and have seen widespread application across diverse fields. However, they face challenges such as complex design specifications and scalability issues with large datasets. The fusion of different techniques and strategies, particularly Gradient Boosting, with Fuzzy Rule-Based Models offers a robust solution to these challenges. This paper proposes an Integrated Fusion Framework that merges the strengths of both paradigms to enhance model performance and interpretability. At each iteration, a Fuzzy Rule-Based Model is constructed and controlled by a dynamic factor to optimize its contribution to the overall ensemble. This control factor serves multiple purposes: it prevents model dominance, encourages diversity, acts as a regularization parameter, and provides a mechanism for dynamic tuning based on model performance, thus mitigating the risk of overfitting. Additionally, the framework incorporates a sample-based correction mechanism that allows for adaptive adjustments based on feedback from a validation set. Experimental results substantiate the efficacy of the presented gradient boosting framework for fuzzy rule-based models, demonstrating performance enhancement, especially in terms of mitigating overfitting and complexity typically associated with many rules. By leveraging an optimal factor to govern the contribution of each model, the framework improves performance, maintains interpretability, and simplifies the maintenance and update of the models.

Classical machine learning classifiers tend to be overconfident can be unreliable outside of the laboratory benchmarks. Properly assessing the reliability of the output of the model per sample is instrumental for real-life scenarios where these systems are deployed. Because of this, different techniques have been employed to properly quantify the quality of prediction for a given model. These are most commonly Bayesian statistics and, more recently, conformal learning. Given a calibration set, conformal learning can produce outputs that are guaranteed to cover the target class with a desired significance level, and are more reliable than the standard confidence intervals used by Bayesian methods. In this work, we propose to use conformal learning with fuzzy rule-based systems in classification and show some metrics of their performance. Then, we discuss how the use of type 2 fuzzy sets can improve the quality of the output of the system compared to both fuzzy and crisp rules. Finally, we also discuss how the fine-tuning of the system can be adapted to improve the quality of the conformal prediction.

--Rule-based systems are a very popular form of explainable AI, particularly in the fuzzy community, where fuzzy rules are widely used for control and classification problems. However, fuzzy rule-based classifiers struggle to reach bigger traction outside of fuzzy venues, because users sometimes do not know about fuzzy and because fuzzy partitions are not so easy to interpret in some situations. In this work, we propose a methodology to reduce fuzzy rule-based classifiers to crisp rule-based classifiers. We study different possible crisp descriptions and implement an algorithm to obtain them. Also, we analyze the complexity of the resulting crisp classifiers. We believe that our results can help both fuzzy and non-fuzzy practitioners understand better the way in which fuzzy rule bases partition the feature space and how easily one system can be translated to another and vice versa. Our complexity metric can also help to choose between different fuzzy classifiers based on what the equivalent crisp partitions look like.

In group decision-making (GDM) scenarios, uncertainty, dynamic social structures, and vague information present major challenges for traditional opinion dynamics models. To address these issues, this study proposes a novel social network group decision-making (SNGDM) framework that integrates three-way decision (3WD) theory, dynamic network reconstruction, and linguistic opinion representation. First, the 3WD mechanism is introduced to explicitly model hesitation and ambiguity in agent judgments, thereby preventing irrational decisions. Second, a connection adjustment rule based on opinion similarity is developed, enabling agents to adaptively update their communication links and better reflect the evolving nature of social relationships. Third, linguistic terms are used to describe agent opinions, allowing the model to handle subjective, vague, or incomplete information more effectively. Finally, an integrated multi-agent decision-making framework is constructed, which simultaneously considers individual uncertainty, opinion evolution, and network dynamics. The proposed model is applied to a multi-UAV cooperative decision-making scenario, where simulation results and consensus analysis demonstrate its effectiveness. Experimental comparisons further verify the advantages of the algorithm in enhancing system stability and representing realistic decision-making behaviors.

In this study, we present an Evolving Fuzzy System within the context of Federated Learning, which adapts dynamically with the addition of new clusters and therefore does not require the number of clusters to be selected apriori. Unlike traditional methods, Federated Learning allows models to be trained locally on clients' devices, sharing only the model parameters with a central server instead of the data. Our method, implemented using PyTorch, was tested on clustering and classification tasks. The results show that our approach outperforms established classification methods on several well-known UCI datasets. While computationally intensive due to overlap condition calculations, the proposed method demonstrates significant advantages in decentralized data processing.

In this paper, we propose a new measure for detecting overlap in multivariate Gaussian clusters. The aim of online learning from data streams is to create clustering, classification, or regression models that can adapt over time based on the conceptual drift of streaming data. In the case of clustering, this can result in a large number of clusters that may overlap and should be merged. Commonly used distribution dissimilarity measures are not adequate for determining overlapping clusters in the context of online learning from streaming data due to their inability to account for all shapes of clusters and their high computational demands. Our proposed dissimilarity measure is specifically designed to detect overlap rather than dissimilarity and can be computed faster compared to existing measures. Our method is several times faster than compared methods and is capable of detecting overlapping clusters while avoiding the merging of orthogonal clusters.

Fuzzy systems are a way to allow machines, systems and frameworks to deal with uncertainty, which is not possible in binary systems that most computers use. These systems have already been deployed for certain use cases, and fuzzy systems could be further improved as proposed in this paper. Such technologies to draw inspiration from include machine learning and federated learning. Machine learning is one of the recent breakthroughs of technology and could be applied to fuzzy systems to further improve the results it produces. Federated learning is also one of the recent technologies that have huge potential, which allows machine learning training to improve by reducing privacy risk, reducing burden on networking infrastructure, and reducing latency of the latest model. Aspects from federated learning could be used to improve federated learning, such as applying the idea of updating the fuzzy rules that make up a key part of fuzzy systems, to further improve it over time. This paper discusses how these improvements would be implemented in fuzzy systems, and how it would improve fuzzy systems. It also discusses certain limitations on the potential improvements. It concludes that these proposed ideas and improvements require further investigation to see how far the improvements are, but the potential is there to improve fuzzy systems.

We present a reinforcement learning method for training neuro-fuzzy controllers using Proximal Policy Optimization (PPO). Unlike prior approaches that used Deep Q-Networks (DQN) with Adaptive Neuro-Fuzzy Inference Systems (ANFIS), our PPO-based framework leverages a stable on-policy actor-critic setup. Evaluated on the CartPole-v1 environment across multiple seeds, PPO-trained fuzzy agents consistently achieved the maximum return of 500 with zero variance after 20, 000 updates, outperforming ANFIS-DQN baselines in both stability and convergence speed. This highlights PPO's potential for training explainable neuro-fuzzy agents in reinforcement learning tasks.

A reliable evaluation of surgical difficulty can improve the success of the treatment for rectal cancer and the current evaluation method is based on clinical data. However, more data about rectal cancer can be collected with the development of technology. Meanwhile, with the development of artificial intelligence, its application in rectal cancer treatment is becoming possible. In this paper, a multi-view rectal cancer dataset is first constructed to give a more comprehensive view of patients, including the high-resolution MRI image view, pressed-fat MRI image view, and clinical data view. Then, an interpretable incomplete multi-view surgical evaluation model is proposed, considering that it is hard to obtain extensive and complete patient data in real application scenarios. Specifically, a dual representation incomplete multi-view learning model is first proposed to extract the common information between views and specific information in each view. In this model, the missing view imputation is integrated into representation learning, and second-order similarity constraint is also introduced to improve the cooperative learning between these two parts. Then, based on the imputed multi-view data and the learned dual representation, a multi-view surgical evaluation model with the TSK fuzzy system is proposed. In the proposed model, a cooperative learning mechanism is constructed to explore the consistent information between views, and Shannon entropy is also introduced to adapt the view weight. On the MVRC dataset, we compared it with several advanced algorithms and DRIMV_TSK obtained the best results.

--Evolving fuzzy systems build and adapt fuzzy models--such as predictors and controllers--by incrementally updating their rule-base structure from data streams. On the occasion of the 60-year anniversary of fuzzy set theory, commemorated during the Fuzz-IEEE 2025 event, this brief paper revisits the historical development and core contributions of classical fuzzy and adaptive modeling and control frameworks. It then highlights the emergence and significance of evolving intelligent systems in fuzzy modeling and control, emphasizing their advantages in handling nonstationary environments. Key challenges and future directions are discussed, including safety, interpretability, and principled structural evolution. Research in fuzzy modeling, control, and applications has grown rapidly since Zadeh's seminal work in 1965 [1], evolving into a vast and multifaceted field.