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Keywords = fuzzy double integral

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27 pages, 2158 KB  
Article
Threshold Effects of PM2.5 on Pension Contributions: A Fuzzy Regression Discontinuity Design and Machine Learning Approach
by Bingxia Wang, Zailan Siri and Mohd Azmi Haron
Sustainability 2025, 17(19), 8620; https://doi.org/10.3390/su17198620 - 25 Sep 2025
Viewed by 264
Abstract
Air pollution risk significantly impacts social and economic systems. Given the critical role of the pension system in socioeconomic stability, it is crucial to explore the impact of air pollution on pension contributions. Utilizing panel data from eight Chinese provinces between 2014 and [...] Read more.
Air pollution risk significantly impacts social and economic systems. Given the critical role of the pension system in socioeconomic stability, it is crucial to explore the impact of air pollution on pension contributions. Utilizing panel data from eight Chinese provinces between 2014 and 2024, this study quantifies the impact of Particulate Matter (PM2.5) on pension contributions and explores its nonlinear and lagged effects through a fuzzy regression discontinuity design (FRDD) coupled with double machine learning (DML) techniques. Through the application of the FRDD, we found that pension contributions are significantly reduced when the PM2.5 concentration exceeds the standard annual threshold of 35 µg/m3, and the effects differ between the Urban Employees Basic Pension Insurance (UEBPI) and the Urban and Rural Residents’ Pension Scheme (URRPS). Further, the DML approach validated these findings and suggested that a complex hysteresis response mechanism exists in relation to air pollution. Additionally, it indicated that when PM2.5 concentrations do not exceed the threshold, this similarly has a negative effect on pension contributions. These findings emphasize the need for policymakers and pension fund managers to integrate environmental considerations into pension sustainability strategies to increase resilience to ongoing environmental risks. Full article
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17 pages, 2866 KB  
Article
Fuzzy Rule-Based Optimal Direct Yaw Moment Allocation for Stability Control of Four-Wheel Steering Mining Trucks
by Feiyu Wang, Jiadian Liu, Jiaqi Li and Xinxin Zhao
Appl. Sci. 2025, 15(18), 10155; https://doi.org/10.3390/app151810155 - 17 Sep 2025
Viewed by 380
Abstract
To address the poor trajectory tracking of mining trucks in narrow, high-curvature paths, this study explores the impact of four-wheel steering (4WS) and direct yaw moment control (DYC) on vehicle stability. A validated two-degree-of-freedom 4WS vehicle model was developed. A fuzzy logic controller [...] Read more.
To address the poor trajectory tracking of mining trucks in narrow, high-curvature paths, this study explores the impact of four-wheel steering (4WS) and direct yaw moment control (DYC) on vehicle stability. A validated two-degree-of-freedom 4WS vehicle model was developed. A fuzzy logic controller with dual inputs (yaw rate and yaw angular acceleration) and a single output (compensatory yaw moment) was designed, alongside an optimal torque distribution controller based on tire friction circle theory to allocate the resultant yaw moment. A co-simulation platform integrating TruckSim and MATLAB/Simulink was established, and experiments were conducted under steady-state and double-lane-change conditions. Comparative analysis with traditional front-wheel steering and alternative control methods reveals that the 4WS mining truck with fuzzy-controlled optimal torque distribution achieves a reduced turning radius, enhancing maneuverability and stability. Hardware-in-the-loop (HIL) testing further validates the controller’s effectiveness in real-time applications. Full article
(This article belongs to the Section Transportation and Future Mobility)
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27 pages, 3479 KB  
Article
A Hybrid IVFF-AHP and Deep Reinforcement Learning Framework for an ATM Location and Routing Problem
by Bahar Yalcin Kavus, Kübra Yazici Sahin, Alev Taskin and Tolga Kudret Karaca
Appl. Sci. 2025, 15(12), 6747; https://doi.org/10.3390/app15126747 - 16 Jun 2025
Viewed by 1051
Abstract
The impact of alternative distribution channels, such as bank Automated Teller Machines (ATMs), on the financial industry is growing due to technological advancements. Investing in ideal locations is critical for new ATM companies. Due to the many factors to be evaluated, this study [...] Read more.
The impact of alternative distribution channels, such as bank Automated Teller Machines (ATMs), on the financial industry is growing due to technological advancements. Investing in ideal locations is critical for new ATM companies. Due to the many factors to be evaluated, this study addresses the problem of determining the best location for ATMs to be deployed in Istanbul districts by utilizing the multi-criteria decision-making framework. Furthermore, the advantages of fuzzy logic are used to convert expert opinions into mathematical expressions and incorporate them into decision-making processes. For the first time in the literature, a model has been proposed for ATM location selection, integrating clustering and the interval-valued Fermatean fuzzy analytic hierarchy process (IVFF-AHP). With the proposed methodology, the districts of Istanbul are first clustered to find the risky ones. Then, the most suitable alternative location in this district is determined using IVFF-AHP. After deciding the ATM locations with IVFF-AHP, in the last step, a Double Deep Q-Network Reinforcement Learning model is used to optimize the Cash in Transit (CIT) vehicle route. The study results reveal that the proposed approach provides stable, efficient, and adaptive routing for real-world CIT operations. Full article
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21 pages, 4512 KB  
Article
Design and Experiment of an Automatic Leveling System for Tractor-Mounted Implements
by Haibin Yao, Engen Zhang, Yufei Liu, Juan Du and Xiang Yin
Sensors 2025, 25(12), 3707; https://doi.org/10.3390/s25123707 - 13 Jun 2025
Viewed by 839
Abstract
The body roll of the tractor propagates through its rigid hitch system to the mounted implement, causing asymmetrical soil penetration depths between the implement’s lateral working elements, which affects the operational effectiveness of the implement. To address this issue, this study developed an [...] Read more.
The body roll of the tractor propagates through its rigid hitch system to the mounted implement, causing asymmetrical soil penetration depths between the implement’s lateral working elements, which affects the operational effectiveness of the implement. To address this issue, this study developed an automatic leveling system based on a dual closed-loop fuzzy Proportional-Integral-Derivative (PID) algorithm for tractor-mounted implements. The system employed an attitude angle sensor to detect implement posture in real time and utilized two double-acting hydraulic cylinders to provide a compensating torque for the implement that is opposite to the direction of the body’s roll. The relationship model between the implement’s roll angle and the actuator’s response time was established. The controller performed implement leveling by regulating the spool position and holding time of the solenoid directional valve. Simulink simulations showed that under the control of the dual closed-loop fuzzy PID algorithm, the implement’s roll angle adjusted from 10° to 0° in 1.72 s, which was 56.89% shorter than the time required by the fuzzy PID algorithm, with almost no overshoot. This demonstrates that the dual closed-loop fuzzy PID algorithm outperforms the traditional fuzzy PID algorithm. Static tests showed the system adjusted the implement roll angle from ±10° to 0° within 1.3 s. Field experiments demonstrated that the automatic leveling system achieved a maximum absolute error (MaxAE) of 0.91°, a mean absolute error (MAE) of 0.19°, and a root mean square error (RMSE) of 0.28°, with errors within 0.5° for 92.52% of the time. Results from terrain mutation tests indicate that under a sudden 5° vehicle roll angle change, the system confines implement deviation to ±1.5°. The system exhibits high control precision, stability, and robustness, fulfilling the demands of tractor-mounted implement leveling. Full article
(This article belongs to the Section Sensors and Robotics)
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18 pages, 3087 KB  
Article
Asymmetric Double-Sideband Composite Signal and Dual-Carrier Cooperative Tracking-Based High-Precision Communication–Navigation Convergence Positioning Method
by Zhongliang Deng, Zhenke Ding, Xiangchuan Gao and Peijia Liu
Sensors 2025, 25(11), 3405; https://doi.org/10.3390/s25113405 - 28 May 2025
Viewed by 515
Abstract
To enhance positioning capability and reliability within existing Communication Navigation Fusion Systems (CNFSs), this paper proposes an Asymmetric Double-Sideband Composite Localization Signal (ADCLS) and a dual-carrier aggregation dual-code loop tracking mechanism with fuzzy control. By organically integrating an embedded signal into the original [...] Read more.
To enhance positioning capability and reliability within existing Communication Navigation Fusion Systems (CNFSs), this paper proposes an Asymmetric Double-Sideband Composite Localization Signal (ADCLS) and a dual-carrier aggregation dual-code loop tracking mechanism with fuzzy control. By organically integrating an embedded signal into the original positioning signal, the code loop is optimized via fuzzy control, while the ADCLS signal is processed as an asymmetric double-sideband signal for joint signal extraction. Experimental validation employs the 5G New Radio (NR) Time-Delay Line (TDL) channel model to simulate multipath propagation effects. The results show that this method improves the tracking accuracy of the code loop and the main carrier loop, thereby enhancing the ranging accuracy. Full article
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17 pages, 281 KB  
Article
Fuzzy Double Yang Transform and Its Application to Fuzzy Parabolic Volterra Integro-Differential Equation
by Atanaska Georgieva, Slav I. Cholakov, Maria Vasileva and Yordanka Gudalova
Symmetry 2025, 17(4), 606; https://doi.org/10.3390/sym17040606 - 16 Apr 2025
Viewed by 571
Abstract
This article introduces a new fuzzy double integral transformation called fuzzy double Yang transformation. We review some of the main properties of the transformation and find the conditions for its existence. We prove the theorems for partial derivatives and fuzzy unitary convolution. All [...] Read more.
This article introduces a new fuzzy double integral transformation called fuzzy double Yang transformation. We review some of the main properties of the transformation and find the conditions for its existence. We prove the theorems for partial derivatives and fuzzy unitary convolution. All of the new results are applied to find an analytical solution to the fuzzy parabolic Volterra integro-differential equation (FPVIDE) with a suitably selected memory kernel. In addition, a numerical example is provided to illustrate how the proposed method might be helpful for solving FPVIDE utilizing symmetric triangular fuzzy numbers. Compared with other symmetric transforms, we conclude that our new approach is simpler and needs less calculations. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Fuzzy Control)
19 pages, 11314 KB  
Article
Design of Dynamic Deep Sowing System for Peanut Planter with Double-Loop Feedback Fuzzy PID Control
by Moxian Li, Xueliang Chang, Yaqing Gu, Ping Wang and Shuqi Shang
Agriculture 2025, 15(8), 808; https://doi.org/10.3390/agriculture15080808 - 8 Apr 2025
Cited by 1 | Viewed by 777
Abstract
To enhance peanut sowing depth consistency, an active depth adjustment planter was designed. This study employs inclination and pressure sensors for ridge surface detection, coupled with a hydraulic cylinder and profiling mechanism to dynamically adjust furrow depth according to ground variations. A mathematical [...] Read more.
To enhance peanut sowing depth consistency, an active depth adjustment planter was designed. This study employs inclination and pressure sensors for ridge surface detection, coupled with a hydraulic cylinder and profiling mechanism to dynamically adjust furrow depth according to ground variations. A mathematical model integrating detection, adjustment, and execution processes was established. The control system adopts an improved DLF-Fuzzy PID (double-loop feedback fuzzy PID) control strategy, with co-simulation in MATLAB/AMESIM for performance comparison. The results demonstrate the improved algorithm’s superiority in sowing depth accuracy. Field experiments evaluated three operational parameters (vehicle speed, pressure, and sowing depth) with the qualification rate as the metric. At 50 mm sowing depth and 3 km/h speed, the system achieved a 94.6% dynamic qualification rate and 2.38% maximum depth variation coefficient. Compared with existing methods, this approach enhances sowing depth control effectiveness by 6.05% and reduces variation by 2.85%. Full article
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18 pages, 282 KB  
Article
A New Double Fuzzy Integral Transform for Solving an Advection–Diffusion Equation
by Atanaska Georgieva, Slav I. Cholakov and Mira Spasova
Axioms 2025, 14(4), 240; https://doi.org/10.3390/axioms14040240 - 21 Mar 2025
Viewed by 334
Abstract
This article presents a new approach to solving fuzzy advection–diffusion equations using double fuzzy transforms, called the double fuzzy Yang–General transform. This unique double fuzzy transformation is a combination of single fuzzy Yang and General transforms. Some of the basic properties of this [...] Read more.
This article presents a new approach to solving fuzzy advection–diffusion equations using double fuzzy transforms, called the double fuzzy Yang–General transform. This unique double fuzzy transformation is a combination of single fuzzy Yang and General transforms. Some of the basic properties of this new transform include existence and linearity and how they relate to partial derivatives. A solution framework for the linear fuzzy advection–diffusion equation is developed to show the application of the double fuzzy Yang–General transform. To illustrate the proposed method for solving these equations, we have included a solution to a numerical problem. Full article
(This article belongs to the Special Issue Advances in Fuzzy Logic with Applications)
23 pages, 1437 KB  
Article
The Establishment and Evaluation Model of the Thematic Deep-Learning Teaching Module
by Kai-Chao Yao, Li-Chiou Hsu, Jiunn-Shiou Fang, Yi-Jung Chen and Zhou-Kai Guo
Appl. Sci. 2025, 15(5), 2335; https://doi.org/10.3390/app15052335 - 21 Feb 2025
Cited by 1 | Viewed by 927
Abstract
In recent years, the application of artificial intelligence (AI) in industry has matured, requiring deeper learning and integration of existing technologies. This study started with technical education to improve the professional quality of human resources. The double-triangular fuzzy number and gray area testing [...] Read more.
In recent years, the application of artificial intelligence (AI) in industry has matured, requiring deeper learning and integration of existing technologies. This study started with technical education to improve the professional quality of human resources. The double-triangular fuzzy number and gray area testing methods in the fuzzy Delphi method (FDM) were used to evaluate expert consensus, plan technical capability indicators, and ensure the integrity and appropriateness of teaching materials. Based on these indicators, special subject teaching course units were designed and integrated into existing courses for experimental teaching and evaluation. The teaching module arrangement in this research used a virtual instrument control system with LabVIEW v2021 as the GUI and the myRIO controller. The proposed system integrates an artificial neural network (ANN) AI model built with Python v3.7 for data analysis and prediction, forming an embedded teaching module for a deep learning-oriented intelligent robotic environmental monitoring system. This study evaluated students’ acceptance of deep learning robotics teaching modules and their impact on improving their technical skills. The psychomotor scale established by the scholars was adopted and revised, including this study’s technical ability indicators. The test-retest reliability of the psychomotor scale was high. The results revealed that the post-test scores of the psychomotor scale were significantly better than those of the pre-test, indicating that students’ overall technical abilities improved. Students’ affective attitudes toward the four dimensions of teaching material and equipment, cognitive development, skills performance, and self-exploration were positive. Feedback revealed that students who participated in the teaching experiment responded positively on all levels of the affective scale, indicating increased motivation and willingness to continue learning. This study successfully constructed a teaching module and evaluation model for deep learning robotic environmental sensing and control. The teaching module and evaluation model established through this research contribute to the cultivation and effectiveness evaluation of relevant technical talents. Full article
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16 pages, 5201 KB  
Article
Robotic Fast Patch Clamp in Brain Slices Based on Stepwise Micropipette Navigation and Gigaseal Formation Control
by Jinyu Qiu, Qili Zhao, Ruimin Li, Yuzhu Liu, Biting Ma and Xin Zhao
Sensors 2025, 25(4), 1128; https://doi.org/10.3390/s25041128 - 13 Feb 2025
Viewed by 1214
Abstract
The patch clamp technique has become the gold standard for neuron electrophysiology research in brain science. Brain slices have been widely utilized as the targets of the patch clamp technique due to their higher optical transparency compared to a live brain and their [...] Read more.
The patch clamp technique has become the gold standard for neuron electrophysiology research in brain science. Brain slices have been widely utilized as the targets of the patch clamp technique due to their higher optical transparency compared to a live brain and their intercellular connectivity in comparison to cultured single neurons. However, the narrow working space, small scope, and depth of the field of view make the positioning of the operation’s micropipette to the target neuron a time-consuming task reliant on a high level of experience, significantly slowing down operation of the patch clamp technique in brain slices. Further, the current poor controllability in gigaseal formation, which is the key to electrophysiology signal recording, significantly lowers the patch clamp success rate. In this paper, a stepwise navigation of the micropipette is conducted to accelerate the positioning process of the micropipette tip to the target neuron in the brain slice. Then, a fuzzy proportional–integral–derivative controller is designed to control the gigaseal formation process along a designed resistance curve. The experimental results demonstrate an almost doubled patch clamp technique speed, with a 25% improvement in the success rate compared to the conventional manual method. The above advantages may promote the application of our method in brain science research based on brain slice platforms. Full article
(This article belongs to the Special Issue Advanced Sensors and AI Integration for Human–Robot Teaming)
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29 pages, 883 KB  
Article
Energy-Efficient and Secure Double RIS-Aided Wireless Sensor Networks: A QoS-Aware Fuzzy Deep Reinforcement Learning Approach
by Sarvenaz Sadat Khatami, Mehrdad Shoeibi, Reza Salehi and Masoud Kaveh
J. Sens. Actuator Netw. 2025, 14(1), 18; https://doi.org/10.3390/jsan14010018 - 10 Feb 2025
Cited by 18 | Viewed by 2591
Abstract
Wireless sensor networks (WSNs) are a cornerstone of modern Internet of Things (IoT) infrastructure, enabling seamless data collection and communication for many IoT applications. However, the deployment of WSNs in remote or inaccessible locations poses significant challenges in terms of energy efficiency and [...] Read more.
Wireless sensor networks (WSNs) are a cornerstone of modern Internet of Things (IoT) infrastructure, enabling seamless data collection and communication for many IoT applications. However, the deployment of WSNs in remote or inaccessible locations poses significant challenges in terms of energy efficiency and secure communication. Sensor nodes, with their limited battery capacities, require innovative strategies to minimize energy consumption while maintaining robust network performance. Additionally, ensuring secure data transmission is critical for safeguarding the integrity and confidentiality of IoT systems. Despite various advancements, existing methods often fail to strike an optimal balance between energy efficiency and quality of service (QoS), either depleting limited energy resources or compromising network performance. This paper introduces a novel framework that integrates double reconfigurable intelligent surfaces (RISs) into WSNs to enhance energy efficiency while ensuring secure communication. To jointly optimize both RIS phase shift matrices, we employ a fuzzy deep reinforcement learning (FDRL) framework that integrates reinforcement learning (RL) with fuzzy logic and long short-term memory (LSTM)-based architecture. The RL component learns optimal actions by iteratively interacting with the environment and updating Q-values based on a reward function that prioritizes both energy efficiency and secure communication. The LSTM captures temporal dependencies in the system state, allowing the model to make more informed predictions about future network conditions, while the fuzzy logic layer manages uncertainties by using optimized membership functions and rule-based inference. To explore the search space efficiently and identify optimal parameter configurations, we use the advantage of the multi-objective artificial bee colony (MOABC) algorithm as an optimization strategy to fine-tune the hyperparameters of the FDRL framework while simultaneously optimizing the membership functions of the fuzzy logic system to improve decision-making accuracy under uncertain conditions. The MOABC algorithm enhances convergence speed and ensures the adaptability of the proposed framework in dynamically changing environments. This framework dynamically adjusts the RIS phase shift matrices, ensuring robust adaptability under varying environmental conditions and maximizing energy efficiency and secure data throughput. Simulation results validate the effectiveness of the proposed FDRL-based double RIS framework under different system configurations, demonstrating significant improvements in energy efficiency and secrecy rate compared to existing methods. Specifically, quantitative analysis demonstrates that the FDRL framework improves energy efficiency by 35.4%, the secrecy rate by 29.7%, and RSMA by 27.5%, compared to the second-best approach. Additionally, the model achieves an R² score improvement of 12.3%, confirming its superior predictive accuracy. Full article
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25 pages, 1585 KB  
Article
Fuzzy Control of Multivariable Nonlinear Systems Using T–S Fuzzy Model and Principal Component Analysis Technique
by Basil Mohammed Al-Hadithi and Javier Gómez
Processes 2025, 13(1), 217; https://doi.org/10.3390/pr13010217 - 14 Jan 2025
Cited by 4 | Viewed by 1316
Abstract
In this work, a new nonlinear control method is proposed, which integrates the Takagi–Sugeno (T–S) fuzzy model with the Principal Component Analysis (PCA) technique. The approach uses PCA to reduce the system’s dimensionality, minimizing the number of fuzzy rules required in the T–S [...] Read more.
In this work, a new nonlinear control method is proposed, which integrates the Takagi–Sugeno (T–S) fuzzy model with the Principal Component Analysis (PCA) technique. The approach uses PCA to reduce the system’s dimensionality, minimizing the number of fuzzy rules required in the T–S fuzzy model. This reduction not only simplifies the system variables but also decreases the computational complexity, resulting in a more efficient control with smooth transient responses and zero steady-state error. To validate the performance of this PCA-based approach for both system identification and control, an interconnected double-tank system was employed. The results demonstrate the method’s capacity to maintain control accuracy while reducing computational load, making it a promising solution for applications in industrial and engineering systems that require robust, efficient control mechanisms. Full article
(This article belongs to the Special Issue Fuzzy Control System: Design and Applications)
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30 pages, 1605 KB  
Article
Risk Analysis of Digital Twin Project Operation Based on Improved FMEA Method
by Longyu Li, Jianxin You and Tao Xu
Systems 2025, 13(1), 48; https://doi.org/10.3390/systems13010048 - 13 Jan 2025
Viewed by 2451
Abstract
With the advent of digitization, digital twin technology is gradually becoming one of the core technologies of the Industry 4.0 era, highlighting the increasing importance of digital twin project management. Despite its potential, DT projects face significant risks during implementation, stemming from technical, [...] Read more.
With the advent of digitization, digital twin technology is gradually becoming one of the core technologies of the Industry 4.0 era, highlighting the increasing importance of digital twin project management. Despite its potential, DT projects face significant risks during implementation, stemming from technical, managerial, and operational complexities. To address these challenges, this study proposes an improved failure mode and effect analysis (FMEA) framework by integrating double hierarchy hesitant fuzzy linguistic term sets (DHHFLTSs) and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). This framework converts qualitative assessments into quantitative metrics and calculates weights using a hybrid approach, enabling more precise risk prioritisation. Application of the model to an automotive manufacturing company’s DT project identified key risks, particularly in the iteration and upgrade phase, emphasising the importance of cross-departmental collaboration and robust digital infrastructure. The proposed model provides a systematic framework for enterprises to assess and mitigate risks, ensuring the successful deployment of DT projects. Full article
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22 pages, 4190 KB  
Article
A Consensus Reaching Process for Product Design Decision-Making by Integrating Intuitionistic Fuzzy Sets and Trust Network
by Yanpu Yang, Kai Zhang and Zijing Lei
Systems 2024, 12(11), 494; https://doi.org/10.3390/systems12110494 - 15 Nov 2024
Cited by 2 | Viewed by 1727
Abstract
In the process of product design decision-making (PDDM), decision-makers (DMs) conventionally engage in discussions to evaluate design alternatives. Achieving a consistent result is essential for selecting optimal product design schemes, as it helps eliminate preference conflicts. However, uncertainties and ambiguities, along with the [...] Read more.
In the process of product design decision-making (PDDM), decision-makers (DMs) conventionally engage in discussions to evaluate design alternatives. Achieving a consistent result is essential for selecting optimal product design schemes, as it helps eliminate preference conflicts. However, uncertainties and ambiguities, along with the interrelationships among DMs, make it challenging to attain an acceptable consensus level in PDDM. To address this issue, intuitionistic fuzzy sets (IFSs) are introduced to capture DMs’ preferences regarding product design schemes, and a trust network is integrated to analyze DMs’ interrelationships. A double hierarchy linguistic term set (LTS) is employed to assess DMs’ relationships, and an incomplete trust network is supplemented by leveraging the transitivity principle, thereby determining DMs’ weights. By establishing a consensus measurement model, DMs contributing less to consensus are identified, and consensus optimization is achieved through the modification of DMs’ preferences or the calibration of their trust relationships. A consensus reaching process (CRP) for PDDM is proposed, and the technique for order preference by similarity to ideal solution (TOPSIS) is utilized to rank product design schemes after consensus is reached. A case study involving the decision-making process for a specific household disinfection machine design illustrates the efficacy of our method in achieving consensus by integrating vague PDDM data. Full article
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15 pages, 969 KB  
Article
Double Decomposition and Fuzzy Cognitive Graph-Based Prediction of Non-Stationary Time Series
by Junfeng Chen, Azhu Guan and Shi Cheng
Sensors 2024, 24(22), 7272; https://doi.org/10.3390/s24227272 - 14 Nov 2024
Cited by 1 | Viewed by 1147
Abstract
Deep learning models, such as recurrent neural network (RNN) models, are suitable for modeling and forecasting non-stationary time series but are not interpretable. A prediction model with interpretability and high accuracy can improve decision makers’ trust in the model and provide a basis [...] Read more.
Deep learning models, such as recurrent neural network (RNN) models, are suitable for modeling and forecasting non-stationary time series but are not interpretable. A prediction model with interpretability and high accuracy can improve decision makers’ trust in the model and provide a basis for decision making. This paper proposes a double decomposition strategy based on wavelet decomposition (WD) and empirical mode decomposition (EMD). We construct a prediction model of high-order fuzzy cognitive maps (HFCM), called the WE-HFCM model, which considers interpretability and strong reasoning ability. Specifically, we use the WD and EDM algorithms to decompose the time sequence signal and realize the depth extraction of the signal’s high-frequency, low-frequency, time-domain, and frequency domain features. Then, the ridge regression algorithm is used to learn the HFCM weight vector to achieve modeling prediction. Finally, we apply the proposed WE-HFCM model to stationary and non-stationary datasets in simulation experiments. We compare the predicted results with the autoregressive integrated moving average (ARIMA) and long short-term memory (LSTM) models.For stationary time series, the prediction accuracy of the WE-HFCM model is about 45% higher than that of the ARIMA, about 35% higher than that of the SARIMA model, and about 16% higher than that of the LSTM model. For non-stationary time series, the prediction accuracy of the WE-HFCM model is 69% higher than that of the ARIMA and SARIMA models. Full article
(This article belongs to the Special Issue Emerging Machine Learning Techniques in Industrial Internet of Things)
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