Fuzzy Structure Research Articles

Enabling Industry 5.0-Driven Circular Economy Transformation: A Strategic Roadmap

Because Industry 4.0 is not a better solution to the problems of the circular economy development process, the European Union proposed Industry 5.0 as a supplement to Industry 4.0. However, presently, no relevant research exists on the promotion of a circular economy under Industry 5.0, and the limited understanding of this process is the fundamental obstacle for enterprises to pursue digitalization and sustainable operations. This study addresses this knowledge gap by developing a roadmap explaining the use of the drivers of Industry 5.0 to support and promote the transformation to a circular economy. This study first screens the literature and determines 11 drivers of Industry 5.0. Secondly, on this basis, a fuzzy explanatory structure model of these drivers promoting a circular economy is constructed. Finally, a strategic roadmap is constructed for Industry 5.0 to promote a circular economy. The results reveal that the 11 key factors driving the circular economy are complementary, among which the quantitative criteria and indicators are the most critical and are present at the bottom of the strategic map. Value chain integration and the transformation into a sustainable business model are the most complex drivers. The strategic roadmap can explain the effects of the various drivers on the transformation to a circular economy and the order required to promote this transformation. The resulting management mindset is expected to assist manufacturers, industrialists, academia, and governments in providing services, thus forming a strategic guideline driven by Industry 5.0 factors to promote the circular economy.

Adaptive Robust Control of Nonlinear Constrained Stirred‐Tank Reactors via Self‐Organizing Fuzzy Neural Network

ABSTRACTThis paper presents an adaptive robust constraint controller for a continuous stirred tank reactor (CSTR) system based on a self‐organizing fuzzy neural network (SOFNN). Due to the high complexity of the chemical reactions, the CSTR system contains many strong nonlinearities and uncertainties. This is the first time to introduce the SOFNN into the adaptive controller design of the CSTR system, which improves the adaptability to dynamic system changes through the adjustment of the fuzzy network structure. Meanwhile, the time‐varying integral barrier Lyapunov functions (TVIBLFs) are employed to ensure the dimensionless reactant concentration and mixture temperature within a reasonable scope, which can improve the stability and safety of the CSTR system. Based on Lyapunov stability analysis, all the signals in a closed‐loop system are ultimately bounded. Simulation results substantiate the efficacy of the proposed control scheme.

Geometric properties of ternary fuzzy relations

Ternary fuzzy relations, and fuzzy betweenness relations in particular, are witnessing increasing attention in recent years. A key reason is that axiomatic properties of ternary fuzzy relations seem to be ideally suited to capture geometric characteristics of the abstract notion of betweenness. In this paper, we introduce several new properties of ternary fuzzy relations, including the Peano property, the Pasch property and the sand-glass property, that can be qualified as geometric properties. We investigate their interrelationships as well as their connections with various types of fuzzy betweenness relations. Additionally, in the context of our study of the Pasch property and the sand-glass property, we introduce the convexity property of ternary fuzzy relations by taking inspiration from the solid theoretical basis of the theory of fuzzy convex structures.

Reinforcement Learning for Fuzzy Structured Adaptive Optimal Control of Discrete-Time Nonlinear Complex Networks

Reinforcement Learning for Fuzzy Structured Adaptive Optimal Control of Discrete-Time Nonlinear Complex Networks

On Lie Homomorphisms of Complex IntuitionisticFuzzy Lie Algebras

In this paper, we investigate the properties of complex intuitionistic fuzzy Lie subalgebras and ideals under Lie algebra homomorphisms, focusing on both images and inverse images. We provide detailed proofs for several new results concerning the preservation of complex intuitionistic fuzzy structures through homomorphisms, and we introduce additional homomorphism-related properties for these structures. This work extends known results to the context of complex intuitionistic fuzzy Lie algebras, contributing new insights into their behavior under algebraic mappings.

Geometry-Aware Enhanced Mutual-Supervised Point Elimination with Overlapping Mask Contrastive Learning for Partitial Point Cloud Registration

Point cloud registration is one of the fundamental tasks in computer vision, but faces challenges under low overlap conditions. Recent approaches use transformers and overlapping masks to improve perception, but mask learning only considers Euclidean distances between features, ignores mismatches caused by fuzzy geometric structures, and is often computationally inefficient. To address these issues, we introduce a novel matching framework. Firstly, we fuse adaptive graph convolution with PPF features to obtain rich feature perception. Subsequently, we construct a PGT framework that uses GeoTransformer and combines it with location information encoding to enhance the geometry perception between source and target clouds. In addition, we improve the visibility of overlapping regions through information exchange and the AIS module, aiming at subsequent keypoint extraction, preserving points with distinct geometrical structures while suppressing the influence of non-overlapping regions to improve computational efficiency. Finally, the mask is refined through contrast learning to preserve geometric and distance similarity, which helps to compute the transformation parameters more accurately. We have conducted comprehensive experiments on synthetic and real-world scene datasets, demonstrating superior registration performance compared to recent deep learning methods. Our approach shows remarkable improvements of 68.21% in RRMSE and 76.31% in tRMSE on synthetic data, while also excelling in real-world scenarios with enhancements of 76.46% in RRMSE and 45.16% in tRMSE.

Adaptive hierarchical interval type-2 fuzzy control for trajectory tracking of an underactuated AUV with uncertain dynamics

In this study, an adaptive hierarchical interval type-2 fuzzy control (AHIT2FC) scheme is presented for three-dimensional (3D) trajectory tracking control of an underactuated autonomous underwater vehicle (AUV), which has only three independent control inputs and is subject to partially parametric uncertainty and unknown external disturbances. To decrease reliance on hydrodynamic parameters, an interval type-2 fuzzy logic system (IT2FLS) is utilized, which exhibits superior capabilities in handling high levels of uncertainties prevalent in the underwater environment as compared to a type-1 fuzzy logic system. However, the traditional fuzzy system structure encounters the “curse of dimensionality” issue, which results in high computational complexity and imposes a significant burden on the limited computing resources underwater. The proposed AHIT2FC framework, based on a hierarchical structure, can substantially enhance computational speed while ensuring excellent control performance. Subsequently, Lyapunov’s theory is adopted to guarantee that all the tracking errors in the closed-loop system are semiglobally uniformly bounded (SGUB). Finally, comparative simulation results demonstrate the effectiveness and superiority of the proposed AHIT2FC scheme.

A simple method and case study of task planning for collaborative design based on FDSM

In multiperson collaborative mechanical product design, unreasonable task allocation can result in excessive coupling between tasks, complex design communication, and rework, particularly in small enterprises and teams that rely primarily on experience. Hence, this study proposes a simple and efficient task-planning method based on a fuzzy design structure matrix (FDSM), which involves single-level task decomposition, three-level number assignment of the coupling relationship, decoupling of the structural tree algorithm, and validation of the optimization results based on the G-value. Design tasks are promptly allocated into a single level based on the functional structure module of the product. The task-correlation degree is quantified based on three levels of numerical values through personal experience to construct an FDSM, the latter of which is decoupled by the correlation degree of the structural tree algorithm to obtain the optimized sequence and allocation of the collaborative design task. Finally, the effectiveness of the planning is verified by calculating the tightness of the corresponding matrix before and after the planning. A task-planning case of a riveting-machine design for capacitor cover plates is established to validate this method.

New types of domination to characterize the preservation of T-subgroups under aggregation

This study builds upon results concerning the preservation of fuzzy structures by aggregation operators. We analyze when an aggregation operator preserves the structure of T-subgroup in the last cases remaining unresolved in the characterization of such operators. In order to characterize these operators for different groups, relaxed forms of domination are introduced and their properties and interconnections are studied. We also include a thorough review of the features that an aggregation operator must fulfill to preserve T-subgroups of an arbitrary group.

Construction of a highly ordered SiC nanofiber@C fiber heterojunction hybrid with a fuzzy grass-like structure for enhanced microwave absorbing performance

Carbon fibers (Cf) materials with excellent dielectric loss are increasingly attracting attention in the field of microwave absorption. However, the inherent high conductivity of carbon materials usually causes impedance mismatch, which seriously limits their widespread applications in the field of electromagnetic wave (EMW) absorption. To solve this problem, a highly ordered SiC nanofiber@C fiber (SiCnf@Cf) heterojunction hybrid with a fuzzy grass-like structure was fabricated through a simple chemical vapor deposition (CVD) method. Providing a heterogeneous interface on the surface of carbon fibers not only improves their impedance matching capability but also enhances their interfacial loss capability. As a result, a minimum reflection loss (RLmin) for SiCnf@Cf heterojunction hybrid is −44.04 dB at 13.6 GHz with a thickness of 1.2 mm, and a maximum effective absorption bandwidth (EABmax) is 3.44 GHz with a thin thickness of 1.1 mm. Furthermore, it also exhibits outstanding thermal insulation performance, which make it a potential candidate for heat-insulating applications. And due to its lightweight and soft characteristics, it perfectly meets the needs of wearable flexible absorbing materials. Therefore, this study not only provides a straightforward for preparing EMW-absorbing materials with exceptional performance, but also offers a solution for improving the thermal stability of the carbon-based material.

The identification and analysis of pivotal factors influencing the corrosion of natural gas pipelines using fuzzy cognitive map

Corrosion presents the gas industry with the formidable challenge of sustaining natural gas energy resources. Given the intricate nature of corrosion, it is imperative to devise a comprehensive model and formulate cognitive sets to effectively manage the risks associated with corrosion in the gas industry. Therefore, the present research was conducted with the objective of identifying and presenting a fuzzy cognitive map delineating the critical factors of corrosion. The statistical population of the research comprises corrosion experts. The statistical sample for this study encompasses 30 experts possessing requisite knowledge and experience, with a minimum of 10 years of expertise in engineering disciplines such as materials science and metallurgy. The findings revealed that the cathodic protection factor exerts the most significant influence on corrosion. The fuzzy cognitive mapping structure of the study comprises 19 edges. The factors “CO2″, ”H2S“, and ”Pipeline Age“ exhibit the highest susceptibility with input degrees of 0.895 and 0.6, respectively. Additionally, ”Cathodic Protection“ ranks highest in terms of influence with a degree of 0.895, whereas ”Working Temperature“ has the least impact with an output degree of − 0.895. The reliability of expert opinions using the Z-number theory has been assessed, yielding fuzzy numbers (0.47, 0.7, 0.93), indicating a reliable and highly certain relationship. The identified factors furnish essential insights to bolster evidence-based policy formulation, facilitating effective monitoring and evaluation of policies within the gas industry.

Two-mode weakly linear systems of fuzzy relation equations: Structures of solutions, computation methods, and applications

The problem of aggregating large fuzzy relational structures is of major importance. One of the main issues is seeking a simpler fuzzy relational structure, while keeping the structure properties of the original fuzzy relational structure as much as possible. This paper covers the mathematical foundations of the described problem, and deals with the solvability issues of two-mode weakly linear systems over complete residuated lattices. Within these systems, our objective is to identify a pair of unknown fuzzy relations that are present on both sides of the equation or inequality. We provide a characterization of the set of all pairs of fuzzy relations that are solutions to two-mode weakly linear systems to a desired degree, and develop an algorithm to compute the greatest such pair. We also present an algorithm to determine a pair that solves a two-mode weakly linear system to a given extent, such that each component is a fuzzy preorder (resp. fuzzy equivalence). Ultimately, we demonstrate the application aspects of aggregating fuzzy relational structures.

A Multi-Criteria Framework for Assessing the Sustainable E-Waste Management Methods with Complex Fuzzy Environment

Due to the substantial economic and environmental repercussions of improper E-waste management and treatment, the issue has gained indispensable attention. In recent years, the research has been done about the selection of proper E-waste management methods like site selection, disposal method selection, etc. with fuzzy environments. But in real situations, the major reasons for improper e-waste management are lack of awareness and improper disposal with sustainability. In finding a sustainable awareness-creating program and disposal method for E-waste, the uncertainty and its sustainability of the information make challenges to decision makers, so the problem becomes a two-dimensional problem with uncertainty. This paper uses complex fuzzy terms to illustrate this two-dimensional uncertain information, in which amplitude term represents the uncertainty about alternative and phase term represents the uncertainty about the sustainability of an alternative. First, we present a new framework MULTIMOORA under complex fuzzy structure. Then, in order to solve two-dimensional uncertain information about E-waste, the proposed complex fuzzy-MULTIMOORA method is applied, in which E-waste awareness-creating program and treatment technology selection are done. The sensitivity and comparative analysis are further delivered to validate the effectiveness of the proposed technique.

Effects of boundary conditions on the core-halo mass scaling relation of fuzzy dark matter structures

Effects of boundary conditions on the core-halo mass scaling relation of fuzzy dark matter structures

Holiday Peak Load Forecasting Using Grammatical Evolution-Based Fuzzy Regression Approach

Peak load forecasting plays an important role in electric utilities. However, the daily peak load forecasting problem, especially for holidays, is fuzzy and highly nonlinear. In order to address the nonlinearity and fuzziness of the holiday load behaviors, a grammatical evolution-based fuzzy regression approach is proposed in this paper. The proposed hybrid approach is based on the theorem that fuzzy polynomial regression can model all fuzzy functions. It employs the rules of the grammatical evolution to generate fuzzy nonlinear structures in polynomial form. Then, a two-stage fuzzy regression approach is used to determine the coefficients and calculate the fitness of the fuzzy functions. An artificial bee colony algorithm is used as the evolution system to update the elements of the grammatical evolution system. The process is repeated until a fuzzy model that best fits the load data is found. After that, the developed fuzzy nonlinear model is applied to forecast holiday peak load. Considering that different holidays possess different load patterns, a separate forecaster model is built for each holiday. Test results on real load data show that an averaged absolute percent error less than 2% can be achieved, which significantly outperforms existing methods involved in the comparison.

Fuzzy slicing structure property with some results

Fuzzy slicing structure property with some results

Renewable energy resource management using an integrated robust decision making model under entropy and similarity measures of fuzzy hypersoft set

The demand for renewable energy has significantly increased over the last decade with increased attention to the preservation of the environment and sustainable, optimal resource management. As traditional sources of energy production are depleting at an alarming rate and causing long-lasting environmental damage, it is essential to explore green and cost-effective methodologies for meeting energy demand. With each country having different geographical, political, social, and natural factors, the problem arises of which renewable energy should be utilized for optimal resource management. This multi-criteria decision making (MCDM) challenge is tackled by applying a dynamic fuzzy hypersoft set-based Method for the evaluation of currently deployed Renewable Energy systems and providing a decision support system for the installation of new ones based on the factors mentioned above for Turkey. As the installation of new renewable energy projects and the evaluation of old ones is significantly influenced by human judgment, it leaves great room for uncertainty primarily because of the psychological factors of the expert. The novel concept of Fuzzy Hypersoft Sets (FHSs) and their Entropy (EN) and TOPSIS-based operations are first discussed with reference to the problem at hand. The presented structure is superior to the ones in the literature by allowing access to data parameters as sub-parametric values while utilizing the versatility of Fuzzy structures to deal with uncertainty. The technique has great potential to serve as a potential decision support system in any setting. For now, hypothetical expert ratings are used to illustrate the working of the dynamic structure along with a sensitivity analysis to investigate the primary criterion weights in sorting. The evaluation of currently deployed renewable energy systems using our methodology revealed an average improvement in system performance compared to traditional methods. Furthermore, the decision support system for the installation of new projects based on geographical, political, social, and natural factors exhibited a potential increase in overall system efficiency. These numeric outcomes highlight the effectiveness and practical applicability of our approach in optimizing resource management and fostering sustainable energy practices.

Interval-valued (p,q,r)-spherical fuzzy sets and their applications in MCGDM and MCDM based on TOPSIS method and aggregation operators

The (p,q,r)-Spherical fuzzy set is a useful generalization of other fuzzy structures such as fuzzy, intuitionistic fuzzy, Pythagorean fuzzy, picture fuzzy, q-rung orthopair fuzzy, spherical fuzzy, and T-spherical fuzzy sets. In this paper, we define concept of interval-valued (p,q,r)-spherical fuzzy set (IVpqr-SFS) and Set-theoretical and arithmetic operations of them. Two aggregation operators named interval-valued (p,q,r)-spherical fuzzy weighted arithmetic (IVpqr-SFWAA) and interval-valued (p,q,r)-spherical fuzzy weighted geometric (IVpqr-SFWGA) aggregation operators are introduced for IVpqr-SF numbers (IVpqr-SFN) and their properties were examined. The proposed operators are explained with examples. Furthermore, the score and accuracy functions of an IVpqr-SFN are introduced. We also define distance measures between two same types IVpqr-SFSs based on Hamming, Euclidean, and Hausdorff distance measures. Moreover, a multi-criteria group decision-making (MCGDM) method is developed based on the TOPSIS method by using the proposed distance measures and score function, and a numerical example is given to show the process of the proposed MCGDM method. In addition, a multi-criteria decision-making (MCDM) method is developed using the proposed IVpqr-SFWAA, IVpqr-SFWGA operators, and an illustrative example is given to show the process of the proposed MCDM method. Finally, a comparative analysis is presented between the proposed methods and the existing methods.

Safe Robust Adaptive Motion Control for Underactuated Marine Robots.

This article presents an innovative approach to the design of a safe adaptive backstepping control system. Tailored specifically for underactuated marine robots, the system utilizes simple sensors for enhanced practicality and efficiency. Given their operation in diverse oceanic environments fraught with various sources of uncertainties, ensuring the system's safe and robust behavior holds paramount importance in the control literature. To address this concern, this paper introduces a control strategy designed to ensure robustness at both the kinematic and dynamic levels. By emphasizing the compensation for the system uncertainties, the design integrates a straightforward fuzzy system structure. To further ensure the system's safety, a funnel surface is defined, followed by the design of a suitable nonlinear sliding surface as a function of the funnel and tracking error. Using Lyapunov theory, the study formally establishes the Semi-globally Practically Finite-time Stability of the closed-loop system, validated through simulations conducted on underactuated marine robots.

Collaborative gas source localization strategy with networked nano-drones in unknown cluttered environments

This paper introduces a novel approach for improving gas source localization in dynamic urban environments, employing a swarm of nano-Crazyflie drones through a hybrid strategy that integrates Adaptive Robotic Particle Swarm Optimization (ARPSO) with Bidirectional Brain Emotional Learning (BBEL). The proposed method refines the ARPSO algorithm into two phases: an initial exploration phase and a subsequent seeking phase. The exploration phase activates when no gas is detected, seamlessly transitioning to the seeking phase upon gas detection. This facilitates efficient information exchange and desired velocity generation within the particle swarm. During the seeking phase, particles conduct measurements, share the global best position, intelligently navigate obstacles, and avoid collisions while directly identifying the global concentration field maximum. Unlike conventional methods, the ARPSO algorithm autonomously adapts its parameters online, mitigating algorithmic failures and local optima challenges. It also considers the limited communication of robots in complex environments, a factor often overlooked in recent methods. To enhance plume tracking robustness, facilitate the controller gain tuning process, and ensure system resilience against environmental disturbances and uncertainties, the BBEL method incorporates a sophisticated fuzzy neural network structure with reinforcement learning-based adaptation mechanisms. The stability of the closed-loop control system is rigorously proven using Lyapunov theory. Numerical simulations in complex urban scenarios validate the algorithm’s effectiveness, showcasing a significant 20% improvement in turnaround time and a flawless 100% success rate with no collisions, in addition to enhanced capabilities in handling uncertainties and disturbances compared to benchmarks like ARPSO-BBEL with unlimited communication range and no delayed communications (ARPSO-BBELU), Sniffy Bug (SB)-BBELU, and ARPSO-PIDU.