Complex Query Answering (CQA) over incomplete Knowledge Graphs (KGs), typically formalized as reasoning with Existential First-Order predicate logic with one free variable (EFO\textsubscript{1}), faces a fundamental tradeoff between logic fidelity and computational efficiency. This work establishes a Grounding-Skolemization dichotomy to systematically analyze this challenge and motivate a paradigm shift in CQA. While Grounding-based methods inherently suffer from combinatorial explosion, most Skolemization-based methods neglect to explicitly model Skolem functions and compromise logical consistency. To address these limitations, we propose the Logic-constrained Vector Symbolic Architecture (LVSA), a neuro-symbolic framework that unifies a differentiable Skolemization module and a neural negator, as well as a logical constraint-driven optimization protocol to harmonize geometric and logical requirements. Theoretically, LVSA guarantees universality for all EFO\textsubscript{1} queries with low computational complexity. Empirically, it outperforms state-of-the-art Skolemization-based methods and reduces inference costs by orders of magnitude compared to Grounding-based baselines.

The sim-to-real gap, where agents trained in a simulator face significant performance degradation during testing, is a fundamental challenge in reinforcement learning. Extansive works adopt the framework of distributionally robust RL, to learn a policy that acts robustly under worst case environment shift. Within this framework, our objective is to devise algorithms that are sample efficient with interactive data collection and large state spaces. By assuming d-rectangularity of environment dynamic shift, we identify a fundamental hardness result for learning in online Markov game, and address it by adopting minimum value assumption. Then, a novel least square value iteration type algorithm, DR-CCE-LSI, with exploration bonus devised specifically for multiple agents, is proposed to find an \episilon-approximate robust Coarse Correlated Equilibrium(CCE). To obtain sample efficient learning, we find that: when the feature mapping function satisfies certain properties, our algorithm, DR-CCE-LSI, is able to achieve ε-approximate CCE with a regret bound of O{dHmin{H,1/min{σ_i}}\sqrt{K}}, where K is the number of interacting episodes, H is the horizon length, d is the feature dimension, and \simga_i represents the uncertainty level of player i. Our work introduces the first sample-efficient algorithm for this setting, matches the best result so far in single agent setting, and achieves minimax optimalsample complexity in terms of the feature dimension d. Meanwhile, we also conduct simulation study to validate the efficacy of our algorithm in learning a robust equilibrium.

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.

Multivariate time series data come as a collection of time series describing different aspects of a certain temporal phenomenon. Anomaly detection in this type of data constitutes a challenging problem yet with numerous applications in science and engineering because anomaly scores come from the simultaneous consideration of the temporal and variable relationships. In this paper, we propose a clustering-based approach to detect anomalies concerning the amplitude and the shape of multivariate time series. First, we use a sliding window to generate a set of multivariate subsequences and thereafter apply an extended fuzzy clustering to reveal a structure present within the generated multivariate subsequences. Finally, a reconstruction criterion is employed to reconstruct the multivariate subsequences with the optimal cluster centers and the partition matrix. We construct a confidence index to quantify a level of anomaly detected in the series and apply Particle Swarm Optimization as an optimization vehicle for the problem of anomaly detection. Experimental studies completed on several synthetic and six real-world datasets suggest that the proposed methods can detect the anomalies in multivariate time series. With the help of available clusters revealed by the extended fuzzy clustering, the proposed framework can detect anomalies in the multivariate time series and is suitable for identifying anomalous amplitude and shape patterns in various application domains such as health care, weather data analysis, finance, and disease outbreak detection.

In the era of smart manufacturing, predictive maintenance (PdM) plays a pivotal role in improving equipment reliability and reducing operating costs. In this paper, we propose a novel Markov Decision Process (MDP) framework that integrates advanced soft computing techniques - Fourier Neural Operator (FNO), Denoising Autoencoder (DAE), Graph Neural Network (GNN), and Proximal Policy Optimisation (PPO) - to address the multidimensional challenges of predictive maintenance in complex manufacturing systems. Specifically, the proposed framework innovatively combines the powerful frequency-domain representation capability of FNOs to capture high-dimensional temporal patterns; DAEs to achieve robust, noise-resistant latent state embedding from complex non-Gaussian sensor data; and GNNs to accurately represent inter-device dependencies for coordinated system-wide maintenance decisions. Furthermore, by exploiting PPO, the framework ensures stable and efficient optimisation of long-term maintenance strategies to effectively handle uncertainty and non-stationary dynamics. Experimental validation demonstrates that the approach significantly outperforms multiple deep learning baseline models with up to 13% cost reduction, as well as strong convergence and inter-module synergy. The framework has considerable industrial potential to effectively reduce downtime and operating expenses through data-driven strategies.

Label learning is a fundamental task in machine learning that aims to construct intelligent models using labeled data, encompassing traditional single-label and multi-label classification models. Traditional methods typically rely on logical labels, such as binary indicators (e.g., "yes/no") that specify whether an instance belongs to a given category. However, in practical applications, label annotations often involve significant uncertainty due to factors such as data noise, inherent ambiguity in the observed entities, and the subjectivity of human annotators. Therefore, representing labels using simplistic binary logic can obscure valuable information and limit the expressiveness of label learning models. To overcome this limitation, this paper introduces the concept of fuzzy labels, grounded in fuzzy set theory, to better capture and represent label uncertainty. We further propose an efficient fuzzy labeling method that mines and generates fuzzy labels from the original data, thereby enriching the label space with more informative and nuanced representations. Based on this foundation, we present fuzzy-label-enhanced algorithms for both single-label and multi-label learning, using the classical K-Nearest Neighbors (KNN) and multi-label KNN algorithms as illustrative examples. Experimental results indicate that fuzzy labels can more effectively characterize the real-world labeling information and significantly enhance the performance of label learning 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.

Underwater multi-robot cooperative coverage remains challenging due to partial observability, limited communication, environmental uncertainty, and the lack of access to global localization. To address these issues, this paper presents a semantics-guided fuzzy control framework that couples Large Language Models (LLMs) with interpretable control and lightweight coordination. Raw multimodal observations are compressed by the LLM into compact, human-interpretable semantic tokens that summarize obstacles, unexplored regions, and Objects Of Interest (OOIs) under uncertain perception. A fuzzy inference system with pre-defined membership functions then maps these tokens into smooth and stable steering and gait commands, enabling reliable navigation without relying on global positioning. Then, we further coordinate multiple robots by introducing semantic communication that shares intent and local context in linguistic form, enabling agreement on who explores where while avoiding redundant revisits. Extensive simulations in unknown reef-like environments show that, under limited sensing and communication, the proposed framework achieves robust OOI-oriented navigation and cooperative coverage with improved efficiency and adaptability, narrowing the gap between semantic cognition and distributed underwater control in GPS-denied, map-free conditions.

--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.

Breast cancer remains one of the leading causes of mortality among women worldwide, with early diagnosis being critical for effective treatment and improved survival rates. However, timely detection continues to be a challenge due to the complex nature of the disease and variability in patient risk factors . This study presents a fuzzy soft set theory - based expert system designed to assess the risk of breast cancer in patients using measurable clinical and physiological parameters. The proposed system integrates Body Mass Index (BMI), Insulin Level (IL), Lep tin Level (LL), Adiponectin Level (AL), and age as input variables to estimate breast cancer risk through a set of fuzzy inference rules and soft set computations. These parameters can be obtained from routine blood analyses, enabling a non - invasive and ac cessible method for preliminary assessment. The dataset used for model development and validation was obtained from the UCI Machine Learning Repository. The proposed expert system aims to support healthcare professionals in identifying high - risk patients a nd determining the necessity of further diagnostic procedures such as biopsies.