Construction of a Computational Scheme for the Fuzzy HIV/AIDS Epidemic Model with a Nonlinear Saturated Incidence Rate

This work aimed to construct an epidemic model with fuzzy parameters.Since the classical epidemic model doesnot elaborate on the successful interaction of susceptible and infective people,the constructed fuzzy epidemicmodel discusses the more detailed versions of the interactions between infective and susceptible people.Thenext-generation matrix approach is employed to find the reproduction number of a deterministic model.Thesensitivity analysis and local stability analysis of the systemare also provided.For solving the fuzzy epidemic model,a numerical scheme is constructed which consists of three time levels.The numerical scheme has an advantage overthe existing forward Euler scheme for determining the conditions of getting the positive solution.The establishedscheme also has an advantage over existing non-standard finite difference methods in terms of order of accuracy.The stability of the scheme for the considered fuzzy model is also provided.From the plotted results,it can beobserved that susceptible people decay by rising interaction parameters.

Hybrid Dynamic Variables-Dependent Event-Triggered Fuzzy Model Predictive Control

This article focuses on dynamic event-triggered mechanism(DETM)-based model predictive control(MPC) for T-S fuzzy systems.A hybrid dynamic variables-dependent DETM is carefully devised,which includes a multiplicative dynamic variable and an additive dynamic variable.The addressed DETM-based fuzzy MPC issue is described as a “min-max” optimization problem(OP).To facilitate the co-design of the MPC controller and the weighting matrix of the DETM,an auxiliary OP is proposed based on a new Lyapunov function and a new robust positive invariant(RPI) set that contain the membership functions and the hybrid dynamic variables.A dynamic event-triggered fuzzy MPC algorithm is developed accordingly,whose recursive feasibility is analysed by employing the RPI set.With the designed controller,the involved fuzzy system is ensured to be asymptotically stable.Two examples show that the new DETM and DETM-based MPC algorithm have the advantages of reducing resource consumption while yielding the anticipated performance.

Computation Tree Logic Model Checking of Multi-Agent Systems Based on Fuzzy Epistemic Interpreted Systems

Model checking is an automated formal verification method to verify whether epistemic multi-agent systems adhere to property specifications.Although there is an extensive literature on qualitative properties such as safety and liveness,there is still a lack of quantitative and uncertain property verifications for these systems.In uncertain environments,agents must make judicious decisions based on subjective epistemic.To verify epistemic and measurable properties in multi-agent systems,this paper extends fuzzy computation tree logic by introducing epistemic modalities and proposing a new Fuzzy Computation Tree Logic of Knowledge(FCTLK).We represent fuzzy multi-agent systems as distributed knowledge bases with fuzzy epistemic interpreted systems.In addition,we provide a transformation algorithm from fuzzy epistemic interpreted systems to fuzzy Kripke structures,as well as transformation rules from FCTLK formulas to Fuzzy Computation Tree Logic(FCTL)formulas.Accordingly,we transform the FCTLK model checking problem into the FCTL model checking.This enables the verification of FCTLK formulas by using the fuzzy model checking algorithm of FCTL without additional computational overheads.Finally,we present correctness proofs and complexity analyses of the proposed algorithms.Additionally,we further illustrate the practical application of our approach through an example of a train control system.

Fully Completed Spherical Fuzzy Approach-Based Z Numbers(PHIModel)for Enhanced Group Expert Consensus

This study aims to establish an expert consensus and enhance the efficacy of decision-making processes by integrating Spherical Fuzzy Sets(SFSs)and Z-Numbers(SFZs).A novel group expert consensus technique,the PHImodel,is developed to address the inherent limitations of both SFSs and the traditional Delphi technique,particularly in uncertain,complex scenarios.In such contexts,the accuracy of expert knowledge and the confidence in their judgments are pivotal considerations.This study provides the fundamental operational principles and aggregation operators associated with SFSs and Z-numbers,encompassing weighted geometric and arithmetic operators alongside fully developed operators tailored for SFZs numbers.Subsequently,a case study and comparative analysis are conducted to illustrate the practicality and effectiveness of the proposed operators and methodologies.Integrating the PHI model with SFZs numbers represents a significant advancement in decision-making frameworks reliant on expert input.Further,this combination serves as a comprehensive tool for decision-makers,enabling them to achieve heightened levels of consensus while concurrently assessing the reliability of expert contributions.The case study results demonstrate the PHI model’s utility in resolving complex decision-making scenarios,showcasing its ability to improve consensus-building processes and enhance decision outcomes.Additionally,the comparative analysis highlights the superiority of the integrated approach over traditional methodologies,underscoring its potential to revolutionize decision-making practices in uncertain environments.

Recognition and Anticipation of Diabetic Foot Ulcer in Type Ⅱ Diabetic Patients using Multi-layered Fuzzy Model

Diabetes mellitus is associated with foot ulcers,which frequently pave the way to lower-extremity amputation.Neuropathy,trauma,deformity,high plantar pressures,and peripheral vascular disease are the most common underlying causes.Around 15%of diabetic patients are affected by diabetic foot ulcer in their lifetime.64 million people are affected by diabetics in India and 40000 amputations are done every year.Foot ulcers are evaluated and classified in a systematic and thorough manner to assist in determining the best course of therapy.This paper proposes a novel model which predicts the threat of diabetic foot ulcer using independent agents for various input values and a combination of fuzzy expert systems.The proposed model uses a classification system to distinguish between each fuzzy framework and its parameters.Based on the severity levels necessary prevention,treatment,and medication are recommended.Combining the results of all the fuzzy frameworks derived from its constituent parameters,a risk-specific medication is recommended.The work also has higher accuracy when compared to other related models.

A Double-Interactively Recurrent Fuzzy Cerebellar Model Articulation Controller Model Combined with an Improved Particle Swarm Optimization Method for Fall Detection

In many Eastern and Western countries,falling birth rates have led to the gradual aging of society.Older adults are often left alone at home or live in a long-term care center,which results in them being susceptible to unsafe events(such as falls)that can have disastrous consequences.However,automatically detecting falls fromvideo data is challenging,and automatic fall detection methods usually require large volumes of training data,which can be difficult to acquire.To address this problem,video kinematic data can be used as training data,thereby avoiding the requirement of creating a large fall data set.This study integrated an improved particle swarm optimization method into a double interactively recurrent fuzzy cerebellar model articulation controller model to develop a costeffective and accurate fall detection system.First,it obtained an optical flow(OF)trajectory diagram from image sequences by using the OF method,and it solved problems related to focal length and object offset by employing the discrete Fourier transform(DFT)algorithm.Second,this study developed the D-IRFCMAC model,which combines spatial and temporal(recurrent)information.Third,it designed an IPSO(Improved Particle Swarm Optimization)algorithm that effectively strengthens the exploratory capabilities of the proposed D-IRFCMAC(Double-Interactively Recurrent Fuzzy Cerebellar Model Articulation Controller)model in the global search space.The proposed approach outperforms existing state-of-the-art methods in terms of action recognition accuracy on the UR-Fall,UP-Fall,and PRECIS HAR data sets.The UCF11 dataset had an average accuracy of 93.13%,whereas the UCF101 dataset had an average accuracy of 92.19%.The UR-Fall dataset had an accuracy of 100%,the UP-Fall dataset had an accuracy of 99.25%,and the PRECIS HAR dataset had an accuracy of 99.07%.

基于VWM-GRA的新型Fuzzy-FMEA复杂装备风险评估方法

失效模式和影响分析(Failure Mode and Effect Analysis,FMEA)是一种识别和预防复杂装备潜在故障模式的风险评估方法,然而,现有FMEA方法采用等权重和精确数表征不确定情形下的风险因素评估信息,导致风险优先数(Risk Priority Number,RPN)难以准确评估复杂装备故障模式的风险优先级。针对这一难题,文中提出了一种基于变权方法-灰色关联分析(Variable Weight Method-Grey Relation Analysis,VWM-GRA)的新型Fuzzy-FMEA复杂装备风险评估方法。在风险因素权重分配方面,在模糊熵值法的基础上,考虑风险评估信息对风险因素权重的影响,构建风险因素变权综合模型以动态调整风险因素权重值,据此确定风险因素的客观变权重;在风险优先数排序方面,在模糊语言变量表征风险因素评估信息的基础上,考虑风险因素评估信息不确定性量化对故障模式排序精度的影响,构建故障模式模糊灰色关联分析模型,以获取评估信息数据序列间的相对关联度,据此评估故障模式的风险优先级。最后,通过航空发动机主轴轴承的故障模式风险实例,分析验证文中方法的有效性。案例分析表明:该方法能够有效解决不确定情形下准确评估复杂装备故障模式风险优先级的难题。

A Non-Singleton Type-3 Fuzzy Modeling: Optimized by Square-Root Cubature Kalman Filter

In many problems,to analyze the process/metabolism behavior,a mod-el of the system is identified.The main gap is the weakness of current methods vs.noisy environments.The primary objective of this study is to present a more robust method against uncertainties.This paper proposes a new deep learning scheme for modeling and identification applications.The suggested approach is based on non-singleton type-3 fuzzy logic systems(NT3-FLSs)that can support measurement errors and high-level uncertainties.Besides the rule optimization,the antecedent parameters and the level of secondary memberships are also adjusted by the suggested square root cubature Kalmanfilter(SCKF).In the learn-ing algorithm,the presented NT3-FLSs are deeply learned,and their nonlinear structure is preserved.The designed scheme is applied for modeling carbon cap-ture and sequestration problem using real-world data sets.Through various ana-lyses and comparisons,the better efficiency of the proposed fuzzy modeling scheme is verified.The main advantages of the suggested approach include better resistance against uncertainties,deep learning,and good convergence.

New Trends in Fuzzy Modeling Through Numerical Techniques

Amoebiasis is a parasitic intestinal infection caused by the highly pathogenic amoeba Entamoeba histolytica.It is spread through person-toperson contact or by eating or drinking food or water contaminated with feces.Its transmission rate depends on the number of cysts present in the environment.The traditional models assumed a homogeneous and contradictory transmission with reality.The heterogeneity of its transmission rate is a significant factor when modeling disease dynamics.The heterogeneity of disease transmission can be described mathematically by introducing fuzzy theory.In this context,a fuzzy SEIR Amoebiasis disease model is considered in this study.The equilibrium analysis and reproductive number are studied with fuzziness.Two numerical schemes forward Euler method and a nonstandard finite difference(NSFD)approach,are developed for the learned model,and the results of numerical simulations are presented.The numerical and simulation results reveal that the proposed NSFD method provides an adequate representation of the dynamics of the disease despite the uncertainty and heterogeneity.Moreover,the obtained method generates plausible predictions that regulators can use to support decision-making to design and develop control strategies.

Controlling chaos using Takagi-Sugeno fuzzy model and adaptive adjustment

In this paper, an approach to the control of continuous-time chaotic systems is proposed using the Takagi-Sugeno （TS） fuzzy model and adaptive adjustment. Sufficient conditions are derived to guarantee chaos control from Lyapunov stability theory. The proposed approach offers a systematic design procedure for stabilizing a large class of chaotic systems in the literature about chaos research. The simulation results on Rossler＇s system verify the effectiveness of the proposed methods.

Parallel Distributed Compensation/H∞Control of Lane‑keeping System Based on the Takagi‑Sugeno Fuzzy Model

Current research on lane-keeping systems ignores the effect of the driver and external resistance on the accuracy of tracking the lane centerline.To reduce the lateral deviation of the vehicle,a lane-keeping control method based on the fuzzy Takagi-Sugeno(T-S)model is proposed.The method adopts a driver model based on near and far visual angles,and a driver-road-vehicle closed-loop model based on longitudinal nonlinear velocity variation,obtaining the expected assist torque with a robust H∞controller which is designed based on parallel distributed compensation and linear matrix inequality.Considering the external influences of tire adhesion and aligning torque when the vehicle is steering,a feedforward compensation control is designed.The electric power steering system is adopted as the actuator for lane-keeping,and active steering redressing is realized by a control motor.Simulation results based on Carsim/Simulink and real vehicle test results demonstrate that the method helps to maintain the vehicle in the lane centerline and ensures driving safety.

Quantum Fuzzy Regression Model for Uncertain Environment

In the era of big data,traditional regression models cannot deal with uncertain big data efficiently and accurately.In order to make up for this deficiency,this paper proposes a quantum fuzzy regression model,which uses fuzzy theory to describe the uncertainty in big data sets and uses quantum computing to exponentially improve the efficiency of data set preprocessing and parameter estimation.In this paper,data envelopment analysis(DEA)is used to calculate the degree of importance of each data point.Meanwhile,Harrow,Hassidim and Lloyd(HHL)algorithm and quantum swap circuits are used to improve the efficiency of high-dimensional data matrix calculation.The application of the quantum fuzzy regression model to smallscale financial data proves that its accuracy is greatly improved compared with the quantum regression model.Moreover,due to the introduction of quantum computing,the speed of dealing with high-dimensional data matrix has an exponential improvement compared with the fuzzy regression model.The quantum fuzzy regression model proposed in this paper combines the advantages of fuzzy theory and quantum computing which can efficiently calculate high-dimensional data matrix and complete parameter estimation using quantum computing while retaining the uncertainty in big data.Thus,it is a new model for efficient and accurate big data processing in uncertain environments.

A Nonstandard Computational Investigation of SEIR Model with Fuzzy Transmission, Recovery and Death Rates

In this article,a Susceptible-Exposed-Infectious-Recovered(SEIR)epidemic model is considered.The equilibrium analysis and reproduction number are studied.The conventional models have made assumptions of homogeneity in disease transmission that contradict the actual reality.However,it is crucial to consider the heterogeneity of the transmission rate when modeling disease dynamics.Describing the heterogeneity of disease transmission mathematically can be achieved by incorporating fuzzy theory.A numerical scheme nonstandard,finite difference(NSFD)approach is developed for the studied model and the results of numerical simulations are presented.Simulations of the constructed scheme are presented.The positivity,convergence and consistency of the developed technique are investigated using mathematical induction,Jacobean matrix and Taylor series expansions respectively.The suggested scheme preserves all these essential characteristics of the disease dynamical models.The numerical and simulation results reveal that the proposed NSFD method provides an adequate representation of the dynamics of the disease.Moreover,the obtained method generates plausible predictions that can be used by regulators to support the decision-making process to design and develop control strategies.Effects of the natural immunity on the infected class are studied which reveals that an increase in natural immunity can decrease the infection and vice versa.

Modeling of Computer Virus Propagation with Fuzzy Parameters

Typically,a computer has infectivity as soon as it is infected.It is a reality that no antivirus programming can identify and eliminate all kinds of viruses,suggesting that infections would persevere on the Internet.To understand the dynamics of the virus propagation in a better way,a computer virus spread model with fuzzy parameters is presented in this work.It is assumed that all infected computers do not have the same contribution to the virus transmission process and each computer has a different degree of infectivity,which depends on the quantity of virus.Considering this,the parametersβandγbeing functions of the computer virus load,are considered fuzzy numbers.Using fuzzy theory helps us understand the spread of computer viruses more realistically as these parameters have fixed values in classical models.The essential features of the model,like reproduction number and equilibrium analysis,are discussed in fuzzy senses.Moreover,with fuzziness,two numerical methods,the forward Euler technique,and a nonstandard finite difference(NSFD)scheme,respectively,are developed and analyzed.In the evidence of the numerical simulations,the proposed NSFD method preserves the main features of the dynamic system.It can be considered a reliable tool to predict such types of solutions.

Design of TakagiSugeno fuzzy model based nonlinear sliding model controller

A design method is presented for Takagi-Sugeno （T-S） fuzzy model based nonlinear sliding model controller. First, the closed-loop fuzzy system is divided into a set of dominant local linear systems according to operating sub-regions. In each sub-region the fuzzy system consists of nominal linear system and a group of interacting systems. Then the controller composed two parts is designed. One part is designed to control the nominal system, the other is designed to control the interacting systems with sliding mode theory. The proposed controller can improve the robusmess and gnarantee tracking performance of the fuzzy system. Stability is guaranteed without finding a common positive definite matrix.

Calculation and Evaluation of Ecological Flow of Hydropower Station Based on Fuzzy Evaluation Model

The reasonable determination of ecological flow is of great significance for the efforts to promote the transformation of water ecological environmental protection from pollution management to synergistic management of water resources,water ecology and water environment,and to promote them in an integrated manner.This paper analyzed and calculated the ecological flow process of the Bangsha River diversion power station using the minimum ecological flow method,the annual spreading method,the improved annual spreading method,the NGPRP method,and the month-by-month frequency method,and evaluated the reasonableness of the process and results of the ecological flow calculations by using the fuzzy evaluation model established.The study showed that the minimum ecological flow rate determined by improving the coupling of the spreading method and the NGPRP method was the best,and the suitable ecological flow rate determined by the month-by-month frequency method was the best;the minimum ecological flow rate of the Bangsha River diversion power station was at 0.43-4.21 m 3/s,and the suitable ecological flow rate was at 0.56-4.94 m 3/s,and the trend of its change showed the trend of first increasing and then decreasing,and the trend of change from January to July showed the trend of first increasing and then decreasing.Its trend of change showed an increasing and then decreasing trend,from January to July showed a gradually increasing trend,from August to December showed a gradually decreasing trend.It aimed to provide a theoretical basis for the reasonable determination of the ecological flow of the river hydropower station.

Evaluation of Water Resources Carrying Capacity in Gansu Section of Yellow River Basin Based on Fuzzy Comprehensive Evaluation Model

As a basic natural resource and strategic economic resource,the development and utilization of water resources is an important issue related to the national economy and people's livelihood.How to scientifically evaluate the water resources carrying capacity is the premise to improve the regional water resources carrying capacity and ensure the regional water security.The Gansu section of the Yellow River basin is an important water conservation and recharge area.Whether the water resources in this area can ensure the normal operation of the ecosystem and whether it can carry the sustainable development of social economy is the key to realize the high-quality development of the Yellow River basin.In this study,from the three dimensions of water consumption per capita,water consumption of 10000 yuan GDP and ecological water use rate,by constructing the evaluation index system and index grading standard of water resources carrying capacity,the fuzzy comprehensive evaluation model was used to evaluate the water resources carrying capacity of Gansu section of the Yellow River Basin,in order to provide theoretical decision-making basis for the comprehensive development,utilization and planning management of water resources in Gansu section of the Yellow River basin and even the whole basin,and help the high-quality development of the Yellow River basin.

基于FUZZY-BN-FTA的厂区架空燃气管道泄漏可能性研究

为研究厂区架空燃气管道泄漏的故的可能性,提出模糊数学方法、贝叶斯网络模型以及故障树模型相结合的集成模型。通过GeNIe软件建立架空燃气管道泄漏事故的模糊贝叶斯网络模型;引入Leaky Noisy-or Gate扩展模型对模糊贝叶斯网络中节点的条件概率表进行修正,结合基本事件先验概率预测架空燃气管道泄漏的概率值,并引入3个基本事件重要度确定基本事件的重要性排序,同时进行敏感性分析确定主要影响因素,提出控制措施。研究结果表明:厂区车辆撞击、管道疲劳损耗、管材质量不佳、安装设计不合理、焊接缺陷为导致架空燃气管道泄漏的主要因素。研究结果可为工业企业安全管理人员有针对性地制定控制措施,减少事故发生率提供参考。

Takagi–Sugeno Fuzzy Modeling and Control for Effective Robotic Manipulator Motion

Robotic manipulators are widely used in applications that require fast and precise motion.Such devices,however,are prompt to nonlinear control issues due to the flexibility in joints and the friction in the motors within the dynamics of their rigid part.To address these issues,the Linear Matrix Inequalities(LMIs)and Parallel Distributed Compensation(PDC)approaches are implemented in the Takagy–Sugeno Fuzzy Model(T-SFM).We propose the following methodology;initially,the state space equations of the nonlinear manipulator model are derived.Next,a Takagy–Sugeno Fuzzy Model(T-SFM)technique is used for linearizing the state space equations of the nonlinear manipulator.The T-SFM controller is developed using the Parallel Distributed Compensation(PDC)method.The prime concept of the designed controller is to compensate for all the fuzzy rules.Furthermore,the Linear Matrix Inequalities(LMIs)are applied to generate adequate cases to ensure stability and control.Convex programming methods are applied to solve the developed LMIs problems.Simulations developed for the proposed model show that the proposed controller stabilized the system with zero tracking error in less than 1.5 s.

Impulsive control for a Takagi-Sugeno fuzzy model with time-delay and its application to chaotic systems

A control approach where the fuzzy logic methodology is combined with impulsive control is developed for controlling some time-delay chaotic systems in this paper. We first introduce impulses into each subsystem with delay of the Takagi-Sugeno （TS） fuzzy IF-THEN rules and then present a unified TS impulsive fuzzy model with delay for chaos control. Based on the new model, a simple and unified set of conditions for controlling chaotic systems is derived by the Lyapunov Razumikhin method, and a design procedure for estimating bounds on control matrices is also given. Several numerical examples are presented to illustrate the effectiveness of this method.