Fuzzy Integral Research Articles

Leveraging Industry 4.0 for Sustainable Manufacturing: A Quantitative Analysis Using FI-RST

The Fourth Industrial Revolution, also known as Industry 4.0, which is the intensified digitalization and automation in industry, embraces cyber–physical systems, the Internet of Things (IoT), and artificial intelligence, among others. This study utilizes Fuzzy Integration–Rough Set Theory (FI-RST) analysis to quantify the impacts of the imperative Industry 4.0 technologies for manufacturing firms located in Fujian Province, China, namely, Manufacturing Execution Systems (MES), the Industrial Internet of Things (IIoT), and Additive Manufacturing (AM), on the sustainable development performance of firms. The findings of the study indicate that these technologies greatly improve the effectiveness of the utilization of resources, reduce the costs of operations, and reduce the impact on the environment. In addition, they have a favorable influence on social considerations, such as preserving the well-being of employees and the outcome of training programs. This research work has convincingly provided an underlying strategic adoption of these technologies for sustainability production by raising important insights that could be valuable for industry managers and policymakers, especially those seeking sustainability at the global level.

Retraction Note: Enhancing quality of service in wireless systems using iterative weighted least squares with fuzzy logic integration algorithm

Retraction Note: Enhancing quality of service in wireless systems using iterative weighted least squares with fuzzy logic integration algorithm

Generalization of the Fuzzy Fejér–Hadamard Inequalities for Non-Convex Functions over a Rectangle Plane

Integral inequalities with generalized convexity play a vital role in both theoretical and applied mathematics. The theory of integral inequalities is one of the branches of mathematics that is now developing at the quickest rate due to its wide range of applications. We define a new Hermite–Hadamard inequality for the novel class of coordinated ƛ-pre-invex fuzzy number-valued mappings (C-ƛ-pre-invex 𝘍 𝘕 𝘝 𝘔s) and examine the idea of C-ƛ-pre-invex 𝘍 𝘕 𝘝 𝘔s in this paper. Furthermore, using C-ƛ-pre-invex 𝘍 𝘕 𝘝 𝘔s, we construct several new integral inequalities for fuzzy double Riemann integrals. Several well-known results, as well as recently discovered results, are included in these findings as special circumstances. We think that the findings in this work are new and will help to stimulate more research in this area in the future. Additionally, unique choices lead to new outcomes.

Research on Heave Compensation System Based on Switched Reluctance Motor

Aiming at the requirements of the marine work platform for real-time control, time-varying speed and the time-varying torque control of the motor-driven active heave compensation device, this paper introduces a composite control strategy based on the switched reluctance motor (SRM)-driven active heave compensation device. As for the compensation error caused by the time lag in the real-time system, the model prediction trajectory algorithm is used to predict the compensation displacement obtained using the dynamic model. The next time, the control parameters are then provided for the SRM control system in advance to reduce the compensation error. The SRM control strategy selects a double closed-loop compound control strategy of Back Propagation (BP) fuzzy neural network Proportion Integration Differentiation (PID) control. Its outer speed loop uses a fuzzy controller to quickly track a wide range of speed changes. The torque inner loop uses BP neural network adaptive PID control. This helps to reduce torque ripple and to ensure that the electromagnetic torque output of the SRM remains stable. Finally, the system feasibility is verified by setting different wave parameters. The simulation results show that the simulation conditions can reach 97.5% and 96.4% under the 3 and 4 wave levels, respectively. The simulation effect is satisfying, which verifies the feasibility of the proposed scheme.

Application of the Sugeno integral in Fuzzy Rule-Based Classification

Fuzzy Rule-Based Classification System (FRBCS) is a well-known technique to deal with classification problems. Recent studies have considered the usage of the Choquet integral and its generalizations (e.g.: CT-integral, CF-Integral and CC-integral) to enhance the performance of such systems. Such fuzzy integrals were applied to the Fuzzy Reasoning Method (FRM) to aggregate the fired fuzzy rules when classifying new data. However, the Sugeno integral, another well-known aggregation operator, obtained good results in other applications, such as brain–computer interfaces. These facts led to the present study, in which we consider the Sugeno integral in classification problems. That is, the Sugeno integral is applied in the FRM of a widely used FRBCS, and its performance is analyzed over 33 different datasets from the literature, also considering different fuzzy measures. To show the efficiency of this new approach, the results obtained are also compared with previous studies that involved the application of different aggregation functions. Finally, we perform a statistical analysis of the application.

On permutations dependent operators

In this paper, we introduce permutations dependent operators. The motivation for studying such a concept arises from standard fuzzy integrals, where permutations play a crucial role. In contrast to standard fuzzy integrals, our construction allows any permutation of the basic set in a formula to be considered, rather than limiting it to permutations that reorder the components of the input vector monotonically. We herein present an approach to integration with respect to sets of permutation pairs, i.e., databases in which each vector has a preselected permutation. This new operator generalizes several concepts known in the literature. We investigate the properties of this new concept and highlight its practical utility in image processing.

Research on Satellite Navigation Control of Six‐Crawler Machinery Based on Fuzzy PID Algorithm

ABSTRACTThe six‐crawler driving mechanism plays a crucial role in the operation of large machines such as bucket‐wheel excavators, dumping machines, and mobile crushing stations, as it serves functions like bearing, movement and steering. The driving characteristics of this mechanism directly influence the safety and efficiency of these machinery systems. To enhance the design methodology for multi‐crawler machinery, improve path controllability, and achieve adaptive driving, a satellite navigation control system for six‐crawler machinery was developed based on the principles of real‐time kinematic (RTK) satellite positioning. This system utilizes the distance deviation and heading angle deviation between the actual path and the predetermined path of the six‐crawler machinery as inputs to a fuzzy proportion integration differentiation (fuzzy PID) controller. This controller regulates the deviation angle of the steering crawler and the driving speeds of each track, thereby ensuring precise path tracking control. To evaluate the path tracking control performance under both straight and curved driving conditions, a virtual prototype model of the six‐crawler mechanical system was established, and co‐simulation analysis was conducted. In addition, an experimental platform for path tracking control of six‐crawler machinery was established to validate the efficacy of the satellite navigation system. The actual tracking data obtained from various driving conditions and initial deviations demonstrated that the RTK satellite navigation path tracking control system exhibited excellent control performance.

Vulnerability analysis of socio-ecological systems on small islands from the perspective of fisheries and tourism: A case study of Zhoushan Gouqi Island

Small island social-ecological systems are increasingly vulnerable to the combined impacts of human activities and environmental changes, making focused vulnerability analyses critical for sustainable governance. In this study, Gouqi Island, a remote island, was selected as the research site to establish a comprehensive vulnerability assessment framework based on the Vulnerability-Sensitivity-Danger (VSD) model. To account for potential interdependencies among indicators, a fuzzy integration method was employed to quantitatively assess vulnerability trends from 2016 to 2022. The analysis revealed that vulnerability reached its lowest point in 2018, peaked at 0.876 in 2020, and remained above 2016 levels through 2022, despite a slight decline. Additionally, machine learning techniques were used to identify key factors influencing vulnerability, highlighting indicators such as D24 (proportion of fisheries and tourism output), D41 (number of tourists), and D52 (aquaculture production) as particularly significant, though distinct from traditional sensitivity indicators. These findings inform the identification of critical factors affecting the island's sustainable development and lead to the proposal of adaptive governance strategies. The insights from this study provide valuable guidance for promoting sustainable development in similar remote islands.

Some convergence theorems of fuzzy concave integral on fuzzy σ-algebra

Some convergence theorems of fuzzy concave integral on fuzzy σ-algebra

A New Approach for Deepfake Detection with the Choquet Fuzzy Integral

A New Approach for Deepfake Detection with the Choquet Fuzzy Integral

Idempotent measures: Monads, convexities and a fuzzy integral

We explore the isomorphism between the idempotent measure monad, which relies on the maximum and addition operations, and the idempotent measure monad, which is built upon the maximum and multiplication operations. One of the implications of this result is the development of a fuzzy integral that utilizes the maximum and addition operations. Additionally, we delve into the study of convexities associated with these monads.

Comparison between Genetic Algorithms of Proportional–Integral–Derivative and Linear Quadratic Regulator Controllers, and Fuzzy Logic Controllers for Cruise Control System

One of the most significant and widely used features currently in autonomous vehicles is the cruise control system that not only deals with constant vehicle velocities but also aims to optimize the safety and comfortability of drivers and passengers. The accuracy and precision of system responses are responsible for cruise control system efficiency via control techniques and algorithms. This study presents the dynamic cruise control system model, then investigates a genetic algorithm of the proportional–integral–derivative (PID) controller with the linear quadratic regulator (LQR) based on four fitness functions, the mean squared error (MSE), the integral squared error (ISE), the integral time squared error (ITSE) and the integral time absolute error (ITAE). Then, the response of the two controllers, PID and LQR, with the genetic algorithm was compared to the response performance of the fuzzy and fuzzy integral (Fuzzy-I) controllers. The MATLAB 2024a program simulation was employed to represent the system time response of each proposed controller. The output simulation of these controllers shows that the type of system stability response was related to the type of controller implemented. The results show that the Fuzzy-I controller outperforms the other proposed controllers according to the least Jmin function, which represents the minimum summation of the overshoot, settling time, and steady-state error of the cruise control system. This study demonstrates the effectiveness of driving accuracy, safety, and comfortability during acceleration and deceleration due to the smoothness and stability of the Fuzzy-I controller with a settling time of 5.232 s and when converging the steady-state error to zero.

Numerical solution of fuzzy stochastic Volterra integral equations with constant delay

This paper considers the nonlinear fuzzy stochastic Volterra integral equations with constant delay, which are general and include many fuzzy stochastic integral and differential equations discussed in literature. Since Doob's martingale inequality is no longer applicable to such equations, a new maximum inequality is obtained. Combining with the Picard approximation method, the existence and uniqueness of solutions to nonlinear fuzzy stochastic Volterra integral equations with constant delay are given. Moreover we prove that the solution behaves stably in the case of small changes of initial values, kernels and nonlinearities. We further develop a Euler-Maruyama (EM) scheme and prove the strong convergence of the scheme. It is shown that the strong convergence order of the EM method is 0.5 under Lipschitz condition. Moreover, the strong superconvergence order is 1 if further, the kernel h(t,s) of the stochastic term satisfies h(t,t)=0. Numerical examples demonstrated that the numerical results are consistent with the theoretical research conclusions. Furthermore, the application model of the fuzzy stochastic Volterra integral equation with constant delay in population dynamics is considered, and the exact solution of the numerical example is given in explicit form.

Evaluation of Qualifications of Emergency Assembly Areas in Istanbul using the Spherical Fuzzy MAIRCA Process

Disasters are inevitable facts of life. It is difficult to deal with disasters and emergencies because of the uncertainties they contain. Managing disasters and emergencies requires integrity with before and after processes. No matter how well-informed people may be when faced with a disaster, they may not act consciously due to the shock of the event, fear and anxiety. Therefore, the recovery phase after a disaster is very important. In the presented paper, meeting areas after a disaster for Istanbul, which is one of the closest witnesses of the earthquake reality, were examined. The motivation of the paper is to evaluate the assembly areas in Istanbul on the basis of all districts under expert opinions and to compare and rank the suitability of the currently existing emergency assembly areas for the expected major Istanbul earthquake. This ranking was made by the help of the fuzzy logic integration of the Multi Attributive Ideal Real Comparative Analysis (MAIRCA) method, which is one of the Multi-Criteria Decision-Making Techniques (MCDM). It is thought that this ranking will be useful in revealing the current situation of the districts and raising awareness. As far as is known, according to the results obtained from the paper in which the spherical fuzzy logic integrated MAIRCA technique was used for the first time, Kadıköy district was determined as the district with the best conditions assembly areas.

Retraction Note: Optimization using the firefly algorithm of ensemble neural networks with type-2 fuzzy integration for COVID-19 time series prediction

Retraction Note: Optimization using the firefly algorithm of ensemble neural networks with type-2 fuzzy integration for COVID-19 time series prediction

Morphological classification of neurons based on Sugeno fuzzy integration and multi-classifier fusion

In order to extract more important morphological features of neuron images and achieve accurate classification of the neuron type, a method is proposed that uses Sugeno fuzzy integral integration of three optimized deep learning models, namely AlexNet, VGG11_bn, and ResNet-50. Firstly, using the pre-trained model of AlexNet and the output layer is fine-tuned to improve the model’s performance. Secondly, in the VGG11_bn network, Global Average Pooling (GAP) is adopted to replace the traditional fully connected layer to reduce the number of parameters. Additionally, the generalization ability of the model is improved by transfer learning. Thirdly, the SE(squeeze and excitation) module is added to the ResNet-50 variant ResNeXt-50 to adjust the channel weight and capture the key information of the input data. The GELU activation function is used to better fit the data distribution. Finally, Sugeno fuzzy integral is used to fuse the output of each model to get the final classification result. The experimental results showed that on the Img_raw, Img_resample and Img_XYalign dataset, the accuracy of 4-category classification reached 98.04%, 91.75% and 93.13%, respectively, and the accuracy of 12-category classification reached 97.82%, 85.68% and 87.60%, respectively. The proposed method has good classification performance in the morphological classification of neurons.

Unified Paradigm of Start-Up Strategy for Pumped Storage Hydropower Stations: Variable Universe Fuzzy PID Controller and Integrated Operation Optimization

Unified Paradigm of Start-Up Strategy for Pumped Storage Hydropower Stations: Variable Universe Fuzzy PID Controller and Integrated Operation Optimization

Ultra-high-precision pneumatic force servo system based on a novel improved particle swarm optimization algorithm integrating Gaussian mutation and fuzzy theory

In this study, an ultra-high-precision pneumatic force servo system (UPFSS) is proposed. On the one hand, a novel air-floating pneumatic cylinder (AFPC) with an air-floating piston capable of independent air supply and exhaust is developed for this system, and its special flow channel design allows the air-floating piston to be suspended in the cylinder without being constrained by the pressure in the chambers. The friction force of the AFPC is less than 0.0049 N. On the other hand, a leakage chamber is constructed to simulate the clearance between the air-floating piston and the cylinder wall, and a fuzzy proportional integral (FPI)-based pressure control system (PCS) is designed for the simulated leakage chamber. Furthermore, a novel particle swarm optimization algorithm integrating Gaussian mutation and fuzzy theory (IGF-PSO) is presented. After testing, the IGF-PSO algorithm is found to have outstanding optimization performance. Then, the parameters of the FPI controller are optimized through the IGFPSO algorithm. Experimental comparisons reveal that the steady-state error achieved by the parameter-optimized pressure controller in response to the leakage condition is about 38 % smaller than that achieved by the pressure controller with parameters obtained using the trial-and-error method. Finally, the UPFSS is tested by using the optimized PCS to supply compressed air to the chamber of the AFPC. The results show that the UPFSS achieves a steady-state error of no more than 0.0279 N in the continuous step response within the range of 240 N.

A systematic reliability-centred maintenance framework with fuzzy computational integration – a case study of manufacturing process machinery

PurposeThis study presents a systematic framework for maintenance strategy development of manufacturing process machinery. The framework is developed based on the reliability-centred maintenance (RCM) approach to minimise the high downtime of a production line, thus increasing its reliability and availability. A case study of a production line from the ghee and soap manufacturing industry in Taiz, Yemen, is presented for framework validation purposes. The framework provides a systematic process to identify the critical system(s) and guide further investigation for functional significant items (FSIs) based on quantitative and qualitative analyses before recommending appropriate maintenance strategies and specific tasks.Design/methodology/approachThe proposed framework integrates conventional RCM procedure with the fuzzy computational process to improve FSIs criticality estimation, which is the main part of failure mode effect criticality analysis (FMECA) applications. The framework consists of four main implementation stages: identification of the critical system(s), technical analysis, Fuzzy-FMECA application for FSIs criticality estimation and maintenance strategy selection. Each stage has its objective(s) and related scientific techniques that are applied to systematically guide the framework implementation.FindingsThe proposed framework validation is summarised as follows. The first stage results demonstrate that the seaming system (top and bottom systems) caused 50% of the total production line downtime, indicating it is a critical system that requires further analysis. The outcomes of the second stage provide significant technical information on the subject (seaming system), helping team members to identify and understand the structure and functional complexities of the seaming system. This stage also provides a better understanding of how the seaming system functions and how it can fail. In stage 3, the application of FMECA with the fuzzy computation integration process presents a systematic way to analyse the failure mode, effect and cause of items (components of the seaming system). This stage also includes items’ criticality estimation and ranking assessment. Finally, stage four guides team members in recommending the appropriate countermeasures (maintenance strategies and task selection) based on their priority level.Originality/valueThis paper proposes an original maintenance strategies development framework based on the RCM approach for production system equipment. Specifically, it considers a fuzzy computational process based on the Gaussian function in the third stage of the proposed framework. Adopting the fuzzy computational process improves the risk priority number (RPN) estimation, resulting in better criticality ranking determination. Another significant contribution is introducing an extended item criticality ranking assessment process to provide maximum levels of criticality item ranking. Finally, the proposed RCM framework also provides detailed guidance on maintenance strategy selection based on criticality levels, unique functionality and failure characteristics of each FSI.

Forecast combination using grey relational analysis and Choquet fuzzy integral for container throughput forecasting

Utilizing the accurate and reliable demand forecasting model for the port logistics industry decision makers, can prevent misguided decisions ensuing from inaccurate forecasting. Current forecasting models of container throughput forecasting focus on the development of single or related hybrid models. However, these studies focus on improving the forecast accuracy, while neglecting the risk of failure. Combination forecasting can improve the forecast accuracy and reduce the risks from model selection failure. The previous research on port container throughput (PCT) combination forecasting focused on using a small number of linear models to generate the combined values, and neglected the nonlinear combined models reflecting the interaction between variables. Given the significance of combination forecasting for the PCT prediction, this study establishes a nonlinear combined model using the grey relational analysis (GRA) and Choquet fuzzy integral. The empirical results indicate that the proposed combined model outperforms both the other considered linear and nonlinear models. The findings assist the port decision-makers in both the public and private sectors for understanding the future PCT, and devising timely response plans aligned with actual circumstances and trends, besides formulating the appropriate development plans and decisions to modify the current situation or sustain competitive advantages.