Diffusion models have emerged as a leading technique for generating images due to their ability to create high-resolution and realistic images. Despite their strong performance, diffusion models still struggle in managing image collections with significant feature differences. They often fail to capture complex features and produce conflicting results. Research has attempted to address this issue by learning different regions of an image through multiple diffusion paths and then combining them. However, this approach leads to inefficient coordination among multiple paths and high computational costs. To tackle these issues, this paper presents a Diffusion Fuzzy System (DFS), a latent-space multi-path diffusion model guided by fuzzy rules. DFS offers several advantages. First, unlike traditional multi-path diffusion methods, DFS uses multiple diffusion paths, each dedicated to learning a specific class of image features. By assigning each path to a different feature type, DFS overcomes the limitations of multi-path models in capturing heterogeneous image features. Second, DFS employs rule-chain-based reasoning to dynamically steer the diffusion process and enable efficient coordination among multiple paths. Finally, DFS introduces a fuzzy membership-based latent-space compression mechanism to reduce the computational costs of multi-path diffusion effectively. We tested our method on three public datasets: LSUN Bedroom, LSUN Church, and MS COCO. The results show that DFS achieves more stable training and faster convergence than existing single-path and multi-path diffusion models. Additionally, DFS surpasses baseline models in both image quality and alignment between text and images, and also shows improved accuracy when comparing generated images to target references.

Learning the parameters of Partially Observable Markov Decision Processes (POMDPs) from limited data is a significant challenge. We introduce the Fuzzy MAP EM algorithm, a novel approach that incorporates expert knowledge into the parameter estimation process by enriching the Expectation Maximization (EM) framework with fuzzy pseudo-counts derived from an expert-defined fuzzy model. This integration naturally reformulates the problem as a Maximum A Posteriori (MAP) estimation, effectively guiding learning in environments with limited data. In synthetic medical simulations, our method consistently outperforms the standard EM algorithm under both low-data and high-noise conditions. Furthermore, a case study on Myasthenia Gravis illustrates the ability of the Fuzzy MAP EM algorithm to recover a clinically coherent POMDP, demonstrating its potential as a practical tool for data-efficient modeling in healthcare.

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.

--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.

Medical image classification requires not only high predictive performance but also interpretability to ensure clinical trust and adoption. Graph Neural Networks (GNNs) offer a powerful framework for modeling relational structures within datasets; however, standard GNNs often operate as black boxes, limiting transparency and usability, particularly in clinical settings. In this work, we present an interpretable graph-based learning framework named FireGNN that integrates trainable fuzzy rules into GNNs for medical image classification. These rules embed topological descriptors - node degree, clustering coefficient, and label agreement - using learnable thresholds and sharpness parameters to enable intrinsic symbolic reasoning. Additionally, we explore auxiliary self-supervised tasks (e.g., homophily prediction, similarity entropy) as a benchmark to evaluate the contribution of topological learning. Our fuzzy-rule-enhanced model achieves strong performance across five MedMNIST benchmarks and the synthetic dataset MorphoMNIST, while also generating interpretable rule-based explanations. To our knowledge, this is the first integration of trainable fuzzy rules within a GNN. Source Code: https://github.com/basiralab/FireGNN

Continuous Descent Operations (CDO) involve smooth, idle-thrust descents that avoid level-offs, reducing fuel burn, emissions, and noise while improving efficiency and passenger comfort. Despite its operational and environmental benefits, limited research has systematically examined the factors influencing CDO performance. Moreover, many existing methods in related areas, such as trajectory optimization, lack the transparency required in aviation, where explainability is critical for safety and stakeholder trust. This study addresses these gaps by proposing a Fuzzy-Enhanced Explainable AI (FEXAI) framework that integrates fuzzy logic with machine learning and SHapley Additive exPlanations (SHAP) analysis. For this purpose, a comprehensive dataset of 29 features, including 11 operational and 18 weather-related features, was collected from 1,094 flights using Automatic Dependent Surveillance-Broadcast (ADS-B) data. Machine learning models and SHAP were then applied to classify flights' CDO adherence levels and rank features by importance. The three most influential features, as identified by SHAP scores, were then used to construct a fuzzy rule-based classifier, enabling the extraction of interpretable fuzzy rules. All models achieved classification accuracies above 90%, with FEXAI providing meaningful, human-readable rules for operational users. Results indicated that the average descent rate within the arrival route, the number of descent segments, and the average change in directional heading during descent were the strongest predictors of CDO performance. The FEXAI method proposed in this study presents a novel pathway for operational decision support and could be integrated into aviation tools to enable real-time advisories that maintain CDO adherence under varying operational conditions.

The emergence of Symbiotic AI (SAI) introduces new challenges to ethical decision-making as it deepens human-AI collaboration. As symbiosis grows, AI systems pose greater ethical risks, including harm to human rights and trust. Ethical Risk Assessment (ERA) thus becomes crucial for guiding decisions that minimize such risks. However, ERA is hindered by uncertainty, vagueness, and incomplete information, and morality itself is context-dependent and imprecise. This motivates the need for a flexible, transparent, yet robust framework for ERA. Our work supports ethical decision-making by quantitatively assessing and prioritizing multiple ethical risks so that artificial agents can select actions aligned with human values and acceptable risk levels. We introduce ff4ERA, a fuzzy framework that integrates Fuzzy Logic, the Fuzzy Analytic Hierarchy Process (FAHP), and Certainty Factors (CF) to quantify ethical risks via an Ethical Risk Score (ERS) for each risk type. The final ERS combines the FAHP-derived weight, propagated CF, and risk level. The framework offers a robust mathematical approach for collaborative ERA modeling and systematic, step-by-step analysis. A case study confirms that ff4ERA yields context-sensitive, ethically meaningful risk scores reflecting both expert input and sensor-based evidence. Risk scores vary consistently with relevant factors while remaining robust to unrelated inputs. Local sensitivity analysis shows predictable, mostly monotonic behavior across perturbations, and global Sobol analysis highlights the dominant influence of expert-defined weights and certainty factors, validating the model design. Overall, the results demonstrate ff4ERA ability to produce interpretable, traceable, and risk-aware ethical assessments, enabling what-if analyses and guiding designers in calibrating membership functions and expert judgments for reliable ethical decision support.

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.

Rule representations significantly influence the search capabilities and decision boundaries within the search space of Learning Classifier Systems (LCSs), a family of rule-based machine learning systems that evolve interpretable models through evolutionary processes. However, it is very difficult to choose an appropriate rule representation for each problem. Additionally, some problems benefit from using different representations for different subspaces within the input space. Thus, an adaptive mechanism is needed to choose an appropriate rule representation for each rule in LCSs. This article introduces a flexible rule representation using a four-parameter beta distribution and integrates it into a fuzzy-style LCS. The four-parameter beta distribution can form various function shapes, and this flexibility enables our LCS to automatically select appropriate representations for different subspaces. Our rule representation can represent crisp/fuzzy decision boundaries in various boundary shapes, such as rectangles and bells, by controlling four parameters, compared to the standard representations such as trapezoidal ones. Leveraging this flexibility, our LCS is designed to adapt the appropriate rule representation for each subspace. Moreover, our LCS incorporates a generalization bias favoring crisp rules where feasible, enhancing model interpretability without compromising accuracy. Experimental results on real-world classification tasks show that our LCS achieves significantly superior test accuracy and produces more compact rule sets. Our implementation is available at https://github.com/YNU-NakataLab/Beta4-UCS. An extended abstract related to this work is available at https://doi.org/10.36227/techrxiv.174900805.59801248/v1.

Autonomous systems that rely on Machine Learning (ML) utilize online fault tolerance mechanisms, such as runtime monitors, to detect ML prediction errors and maintain safety during operation. However, the lack of human-interpretable explanations for these errors can hinder the creation of strong assurances about the system's safety and reliability. This paper introduces a novel fuzzy-based monitor tailored for ML perception components. It provides human-interpretable explanations about how different operating conditions affect the reliability of perception components and also functions as a runtime safety monitor. We evaluated our proposed monitor using naturalistic driving datasets as part of an automated driving case study. The interpretability of the monitor was evaluated and we identified a set of operating conditions in which the perception component performs reliably. Additionally, we created an assurance case that links unit-level evidence of \textit{correct} ML operation to system-level \textit{safety}. The benchmarking demonstrated that our monitor achieved a better increase in safety (i.e., absence of hazardous situations) while maintaining availability (i.e., ability to perform the mission) compared to state-of-the-art runtime ML monitors in the evaluated dataset.