Abstract--An accurate odometry is essential for legged-wheel robots operating in unstructured terrains such as bumpy roads and staircases. Existing methods often suffer from pose drift due to their ignorance of terrain geometry. We propose a terrain-awared LiDAR-Inertial odometry (LIO) framework that approximates the terrain using Radial Basis Functions (RBF) whose centers are adaptively selected and weights are recursively updated. The resulting smooth terrain manifold enables "soft constraints" that regularize the odometry optimization and mitigates the z-axis pose drift under abrupt elevation changes during robot's maneuver. To ensure the LIO's real-time performance, we further evaluate the RBF-related terms and calculate the inverse of the sparse kernel matrix with GPU parallelization. Experiments on unstructured terrains demonstrate that our method achieves higher localization accuracy than the state-of-the-art baselines, especially in the scenarios that have continuous height changes or sparse features when abrupt height changes occur. EGGED-WHEEL robots combine the speed advantage of wheeled robots with the terrain adaptability advantage of legged robots. Thus, they are well-suited for traversing complex and uneven environments such as bumpy roads, staircases, etc. However, the uneven surface in these environments will cause impulsive velocity variations during the robot's maneuver.

Neurosymbolic integration (NeSy) blends neural-network learning with symbolic reasoning. The field can be split between methods injecting hand-crafted rules into neural models, and methods inducing symbolic rules from data. We introduce Logic of Hypotheses (LoH), a novel language that unifies these strands, enabling the flexible integration of data-driven rule learning with symbolic priors and expert knowledge. LoH extends propositional logic syntax with a choice operator, which has learnable parameters and selects a subformula from a pool of options. Using fuzzy logic, formulas in LoH can be directly compiled into a differentiable computational graph, so the optimal choices can be learned via backpropagation. This framework subsumes some existing NeSy models, while adding the possibility of arbitrary degrees of knowledge specification. Moreover, the use of Goedel fuzzy logic and the recently developed Goedel trick yields models that can be discretized to hard Boolean-valued functions without any loss in performance. We provide experimental analysis on such models, showing strong results on tabular data and on the Visual Tic-Tac-Toe NeSy task, while producing interpretable decision rules.

Modern anthropomorphic upper limb bioprostheses are typically controlled by electromyographic (EMG) biosignals using a pattern recognition scheme. Unfortunately, there are many factors originating from the human source of objects to be classified and from the human-prosthesis interface that make it difficult to obtain an acceptable classification quality. One of these factors is the high susceptibility of biosignals to contamination, which can considerably reduce the quality of classification of a recognition system. In the paper, the authors propose a new recognition system intended for EMG based control of the hand prosthesis with detection of contaminated biosignals in order to mitigate the adverse effect of contaminations. The system consists of two ensembles: the set of one-class classifiers (OCC) to assess the degree of contamination of individual channels and the ensemble of K-nearest neighbours (KNN) classifier to recognise the patient's intent. For all recognition systems, an original, coherent fuzzy model was developed, which allows the use of a uniform soft (fuzzy) decision scheme throughout the recognition process. The experimental evaluation was conducted using real biosignals from a public repository. The goal was to provide an experimental comparative analysis of the parameters and procedures of the developed method on which the quality of the recognition system depends. The proposed fuzzy recognition system was also compared with similar systems described in the literature.

Credit card fraud is assuming growing proportions as a major threat to the financial position of American household, leading to unpredictable changes in household economic behavior. To solve this problem, in this paper, a new hybrid analysis method is presented by using the Enhanced ANFIS. The model proposes several advances of the conventional ANFIS framework and employs a multi-resolution wavelet decomposition module and a temporal attention mechanism. The model performs discrete wavelet transformations on historical transaction data and macroeconomic indicators to generate localized economic shock signals. The transformed features are then fed into a deep fuzzy rule library which is based on Takagi-Sugeno fuzzy rules with adaptive Gaussian membership functions. The model proposes a temporal attention encoder that adaptively assigns weights to multi-scale economic behavior patterns, increasing the effectiveness of relevance assessment in the fuzzy inference stage and enhancing the capture of long-term temporal dependencies and anomalies caused by fraudulent activities. The proposed method differs from classical ANFIS which has fixed input-output relations since it integrates fuzzy rule activation with the wavelet basis selection and the temporal correlation weights via a modular training procedure. Experimental results show that the RMSE was reduced by 17.8% compared with local neuro-fuzzy models and conventional LSTM models.

Fuzzy implication functions constitute fundamental operators in fuzzy logic systems, extending classical conditionals to manage uncertainty in logical inference. Among the extensive families of these operators, generalizations of the classical material implication have received considerable theoretical attention, particularly $(S,N)$-implications constructed from t-conorms and fuzzy negations, and their further generalizations to $(U,N)$-implications using disjunctive uninorms. Prior work has established characterization theorems for these families under the assumption that the fuzzy negation $N$ is continuous, ensuring uniqueness of representation. In this paper, we disprove this last fact for $(U,N)$-implications and we show that they do not necessarily possess a unique representation, even if the fuzzy negation is continuous. Further, we provide a comprehensive study of uniqueness conditions for both uninorms with continuous and non-continuous underlying functions. Our results offer important theoretical insights into the structural properties of these operators.

Fuzzy implication functions are one of the most important operators used in the fuzzy logic framework. While their flexible definition allows for diverse families with distinct properties, this variety needs a deeper theoretical understanding of their structural relationships. In this work, we focus on the study of construction methods, which employ different techniques to generate new fuzzy implication functions from existing ones. Particularly, we generalize the $F$-chain-based construction, recently introduced by Mesiar et al. to extend a method for constructing aggregation functions to the context of fuzzy implication functions. Our generalization employs collections of fuzzy implication functions rather than single ones, and uses two different increasing functions instead of a unique $F$-chain. We analyze property preservation under this construction and establish sufficient conditions. Furthermore, we demonstrate that our generalized $F$-chain-based construction is a unifying framework for several existing methods. In particular, we show that various construction techniques, such as contraposition, aggregation, and generalized vertical/horizontal threshold methods, can be reformulated within our approach. This reveals structural similarities between seemingly distinct construction strategies and provides a cohesive perspective on fuzzy implication construction methods.

The rapid advancement of large language models (LLMs) has heightened concerns about benchmark data contamination (BDC), where models inadvertently memorize evaluation data during the training process, inflating performance metrics, and undermining genuine generalization assessment. This paper introduces the Data Contamination Risk (DCR) framework, a lightweight, interpretable pipeline designed to detect and quantify BDC risk across four granular levels: semantic, informational, data, and label. By synthesizing contamination scores via a fuzzy inference system, DCR produces a unified DCR Factor that adjusts raw accuracy to reflect contamination-aware performance. Validated on 9 LLMs (0.5B-72B) across sentiment analysis, fake news detection, and arithmetic reasoning tasks, the DCR framework reliably diagnoses contamination severity and with accuracy adjusted using the DCR Factor to within 4% average error across the three benchmarks compared to the uncontaminated baseline. Emphasizing computational efficiency and transparency, DCR provides a practical tool for integrating contamination assessment into routine evaluations, fostering fairer comparisons and enhancing the credibility of LLM benchmarking practices.

Transformers have emerged as a compelling architecture for sequential decision-making by modeling trajectories via self-attention. In reinforcement learning (RL), they enable return-conditioned control without relying on value function approximation. Decision Transformers (DTs) exploit this by casting RL as supervised sequence modeling, but they are restricted to offline data and lack exploration. Online Decision Transformers (ODTs) address this limitation through entropy-regularized training on on-policy rollouts, offering a stable alternative to traditional RL methods like Soft Actor-Critic, which depend on bootstrapped targets and reward shaping. Despite these advantages, ODTs use standard attention, which lacks explicit memory of action-specific outcomes. This leads to inefficiencies in learning long-term action effectiveness. Inspired by cognitive models such as Experience-Weighted Attraction (EWA), we propose Experience-Weighted Attraction with Vector Quantization for Online Decision Transformers (EWA-VQ-ODT), a lightweight module that maintains per-action mental accounts summarizing recent successes and failures. Continuous actions are routed via direct grid lookup to a compact vector-quantized codebook, where each code stores a scalar attraction updated online through decay and reward-based reinforcement. These attractions modulate attention by biasing the columns associated with action tokens, requiring no change to the backbone or training objective. On standard continuous-control benchmarks, EWA-VQ-ODT improves sample efficiency and average return over ODT, particularly in early training. The module is computationally efficient, interpretable via per-code traces, and supported by theoretical guarantees that bound the attraction dynamics and its impact on attention drift.

In this paper, we study a latticized optimization problem with fuzzy relational inequality constraints where the feasible region is formed as the intersection of two inequality fuzzy systems and Sugeno - Weber family of t - norms is considered as fuzzy composition. Sugeno - Weber family of t - norms and t - conorms is one of the most applied one in various fuzzy modelling problems. Thi s family of t - norms and t - conorms was suggested by Weber for modeling intersection and union of fuzzy sets. Also, the t - conorms were suggested as addition rules by Sugeno for so - called - fuzzy measures. The resolution of the feasible region of the problem is firstly investigated when it is defined with max - Sugeno - Weber composition and a necessary and sufficient condition is presented for determining the feasibility. Then, based on some theoretical properties of the problem, an algorithm is presented for sol ving this nonlinear problem. It is proved that the algorithm can find the exact optimal solution and an example is presented to illustrate the proposed algorithm.

Air pollution in cities and the possibilities of reducing this pollution represents one of the most important factors that today's society has to deal with. This paper focuses on a systemic approach to traffic emissions with their relation to meteorological conditions, analyzing the effect of weather on the quantity and dispersion of traffic emissions in a city. Using fuzzy inference systems (FIS) the model for prediction of changes in emissions depending on various conditions is developed. The proposed model is based on traffic, meteorology and emission data measured in Prague, Czech Republic. The main objective of the work is to provide insight into how urban planners and policymakers can plan and manage urban transport more effectively with environmental protection in mind.