To better handle real-world uncertainty, concepts such as fuzzy sets, neutrosophic sets, rough sets, and soft sets have been introduced. For example, neutrosophic sets, which simultaneously represent truth, indeterminacy, and falsehood, have proven to be valuable tools for modeling uncertainty in complex systems. These set concepts are increasingly studied in graphized forms, and generalized graph concepts now encompass well-known structures such as hypergraphs and superhypergraphs. Furthermore, hyperconcepts and superhyperconcepts are being actively researched in areas beyond graph theory. Combinatorics, uncertain sets (including fuzzy sets, neutrosophic sets, rough sets, soft sets, and plithogenic sets), uncertain graphs, and hyper and superhyper concepts are active areas of research with significant mathematical and practical implications. Recognizing their importance, this paper explores new graph and set concepts, as well as hyper and superhyper concepts, as detailed in the "Results" section of "The Structure of the Paper." Additionally, this work aims to consolidate recent findings, providing a survey-like resource to inform and engage readers. For instance, we extend several graph concepts by introducing Neutrosophic Oversets, Neutrosophic Undersets, Neutrosophic Offsets, and the Nonstandard Real Set. This paper defines a variety of concepts with the goal of inspiring new ideas and serving as a valuable resource for researchers in their academic pursuits.

Link prediction is crucial for understanding complex networks but traditional Graph Neural Networks (GNNs) often rely on random negative sampling, leading to suboptimal performance. This paper introduces Fuzzy Graph Attention Networks (FGAT), a novel approach integrating fuzzy rough sets for dynamic negative sampling and enhanced node feature aggregation. Fuzzy Negative Sampling (FNS) systematically selects high-quality negative edges based on fuzzy similarities, improving training efficiency. FGAT layer incorporates fuzzy rough set principles, enabling robust and discriminative node representations. Experiments on two research collaboration networks demonstrate FGAT's superior link prediction accuracy, outperforming state-of-the-art baselines by leveraging the power of fuzzy rough sets for effective negative sampling and node feature learning.

Generative Models (GMs), particularly Large Language Models (LLMs), have garnered significant attention in machine learning and artificial intelligence for their ability to generate new data by learning the statistical properties of training data and creating data that resemble the original. This capability offers a wide range of applications across various domains. However, the complex structures and numerous model parameters of GMs make the input-output processes opaque, complicating the understanding and control of outputs. Moreover, the purely data-driven learning mechanism limits GM's ability to acquire broader knowledge. There remains substantial potential for enhancing the robustness and generalization capabilities of GMs. In this work, we introduce the fuzzy system, a classical modeling method that combines data and knowledge-driven mechanisms, to generative tasks. We propose a novel Generative Fuzzy System framework, named GenFS, which integrates the deep learning capabilities of GM with the interpretability and dual-driven mechanisms of fuzzy systems. Specifically, we propose an end-to-end GenFS-based model for sequence generation, called FuzzyS2S. A series of experimental studies were conducted on 12 datasets, covering three distinct categories of generative tasks: machine translation, code generation, and summary generation. The results demonstrate that FuzzyS2S outperforms the Transformer in terms of accuracy and fluency. Furthermore, it exhibits better performance on some datasets compared to state-of-the-art models T5 and CodeT5.

Natural language allows robot programming to be accessible to everyone. However, the inherent fuzziness in natural language poses challenges for inflexible, traditional robot systems. We focus on instructions with fuzzy time requirements (e.g., "start in a few minutes"). Building on previous robotics research, we introduce fuzzy skills. These define an execution by the robot with so-called satisfaction functions representing vague execution time requirements. Such functions express a user's satisfaction over potential starting times for skill execution. When the robot handles multiple fuzzy skills, the satisfaction function provides a temporal tolerance window for execution, thus, enabling optimal scheduling based on satisfaction. We generalized such functions based on individual user expectations with a user study. The participants rated their satisfaction with an instruction's execution at various times. Our investigations reveal that trapezoidal functions best approximate the users' satisfaction. Additionally, the results suggest that users are more lenient if the execution is specified further into the future.

Unwanted vibrations stemming from the energy-optimized design of Delta robots pose a challenge in their operation, especially with respect to precise reference tracking. To improve tracking accuracy, this paper proposes an adaptive mismatch-compensated iterative learning controller based on input shaping techniques. We establish a dynamic model considering the electromechanical rigid-flexible coupling of the Delta robot, which integrates the permanent magnet synchronous motor. Using this model, we design an optimization-based input shaper, considering the natural frequency of the robot, which varies with the configuration. We proposed an iterative learning controller for the delta robot to improve tracking accuracy. Our iterative learning controller incorporates model mismatch where the mismatch approximated by a fuzzy logic structure. The convergence property of the proposed controller is proved using a Barrier Composite Energy Function, providing a guarantee that the tracking errors along the iteration axis converge to zero. Moreover, adaptive parameter update laws are designed to ensure convergence. Finally, we perform a series of high-fidelity simulations of the Delta robot using Simscape to demonstrate the effectiveness of the proposed control strategy.

This paper presents a monitoring framework that infers the level of autonomous vehicle (AV) collision risk based on its object detector's performance using only monocular camera images. Essentially, the framework takes two sets of predictions produced by different algorithms and associates their inconsistencies with the collision risk via fuzzy inference. The first set of predictions is obtained through retrieving safety-critical 2.5D objects from a depth map, and the second set comes from the AV's 3D object detector. We experimentally validate that, based on Intersection-over-Union (IoU) and a depth discrepancy measure, the inconsistencies between the two sets of predictions strongly correlate to the safety-related error of the 3D object detector against ground truths. This correlation allows us to construct a fuzzy inference system and map the inconsistency measures to an existing collision risk indicator. In particular, we apply various knowledge- and data-driven techniques and find using particle swarm optimization that learns general fuzzy rules gives the best mapping result. Lastly, we validate our monitor's capability to produce relevant risk estimates with the large-scale nuScenes dataset and show it can safeguard an AV in closed-loop simulations.

Data compression techniques that are focused on information preservation have become essential in the modern era of big data. In this work, an encoderdecoder architecture has been designed where adversaria! The goal of this proposal is to obtain an intermediate representation of the astronomical stellar spectra, in which the contribution to the flux of a star due to the most influential physical properties (its surface temperature and gravity) disappears and the variance reflects only the effect of the chemical composition over the spectrum. We apply a scheme of deep learning with the aim of unraveling in the latent space the desired parameters of the rest of the information contained in the data. This work propases a version of adversaria! training that makes use of one discriminator per parameter to be disentangled, thus avoiding the exponential combination that occurs in the use of a single discriminator, as a result of the discretization of the values to be untangled. To test the effectiveness of the method, synthetic astronomical data are used from the APOGEE and Gaia surveys. In conjunction with the work presented, an ad-hoc framework (GANDALF) is provided, which allows the replication, visualization, and extension of the method to domains of any nature. Keywords: Generative Adversaria! Neural Networks, Disentangled Representation, Astronomical Spectra, Gaia mission, APOGEE Preprint submitted to Applied Soft Computing November 8, 2024 l. Introduction Finding representations of the data that can ease the extraction of useful inforrnation and irnprove algorithrn performance in classification or pararnetrization problerns has becorne a field in itself in the rnachine learning cornrnunity, and is known as representation learning. The process of unraveling these underlying factors in a cornprehensive representation is called disentangled representation. There is abundant literature on the problern of how to decode or separate representations of a signal into projections that include only inforrnation relevant to a specific problern. In Wang et al. [1] the current state of the literature is exhaustively reviewed discussing different rnethodologies, rnetrics, rnodels, and applications.

Dose prediction is an area of ongoing research that facilitates radiotherapy planning. Most commercial models utilise imaging data and intense computing resources. This study aimed to predict the dose-volume of rectum and bladder from volumes of target, at-risk structure organs and their overlap regions using machine learning. Dose-volume information of 94 patients with prostate cancer planned for 6000cGy in 20 fractions was exported from the treatment planning system as text files and mined to create a training dataset. Several statistical modelling, machine learning methods, and a new fuzzy rule-based prediction (FRBP) model were explored and validated on an independent dataset of 39 patients. The median absolute error was 2.0%-3.7% for bladder and 1.7-2.4% for rectum in the 4000-6420cGy range. For 5300cGy, 5600cGy and 6000cGy, the median difference was less than 2.5% for rectum and 3.8% for bladder. The FRBP model produced errors of 1.2%, 1.3%, 0.9% and 1.6%, 1.2%, 0.1% for the rectum and bladder respectively at these dose levels. These findings indicate feasibility of obtaining accurate predictions of the clinically important dose-volume parameters for rectum and bladder using just the volumes of these structures.

An improved bilinear fuzzy genetic algorithm (BFGA) is introduced in this chapter for the design optimization of steel structures with semi-rigid connections. Semi-rigid connections provide a compromise between the stiffness of fully rigid connections and the flexibility of fully pinned connections. However, designing such structures is challenging due to the non-linear behavior of semi-rigid connections. The BFGA is a robust optimization method that combines the strengths of fuzzy logic and genetic algorithm to handle the complexity and uncertainties of structural design problems. The BFGA, compared to standard GA, demonstrated to generate highquality solutions in a reasonable time. The application of the BFGA is demonstrated through the optimization of steel structures with semi-rigid connections, considering the weight, and performance criteria. The results show that the proposed BFGA is capable of finding optimal designs that satisfy all the design requirements and constraints. The proposed approach provides a promising solution for the optimization of complex structures with non-linear behavior.

Autonomous surface vessels (ASVs) are becoming increasingly significant in enhancing the safety and sustainability of maritime operations. To ensure the reliability of modern control algorithms utilized in these vessels, digital twins (DTs) provide a robust framework for conducting safe and effective simulations within a virtual environment. Digital twins are generally classified on a scale from 0 to 5, with each level representing a progression in complexity and functionality: Level 0 (Standalone) employs offline modeling techniques; Level 1 (Descriptive) integrates sensors and online modeling to enhance situational awareness; Level 2 (Diagnostic) focuses on condition monitoring and cybersecurity; Level 3 (Predictive) incorporates predictive analytics; Level 4 (Prescriptive) embeds decision-support systems; and Level 5 (Autonomous) enables advanced functionalities such as collision avoidance and path following. These digital representations not only provide insights into the vessel's current state and operational efficiency but also predict future scenarios and assess life endurance. By continuously updating with real-time sensor data, the digital twin effectively corrects modeling errors and enhances decision-making processes. Since DTs are key enablers for complex autonomous systems, this paper introduces a comprehensive methodology for establishing a digital twin framework specifically tailored for ASVs. Through a detailed literature survey, we explore existing state-of-the-art enablers across the defined levels, offering valuable recommendations for future research and development in this rapidly evolving field.