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.

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.

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.

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.

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.

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.

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.

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.

AN IDENTIFICATION ALGORITHM OF FUZZY MODELS

An identification approach of dynamic system is put forward in this paperwhich can provide the fuzzy models with fairly high accuracy.This method consists ofpremise structure identification,premise parameters identification,consequent structureand parameters identification.It has been applied to some industrial processes modeling.The simulation study shows its effectiveness.

Parallel Machine Scheduling Models with Fuzzy Parameters and Precedence Constraints: A Credibility Approach

A method for modeling the parallel machine scheduling problems with fuzzy parameters and precedence constraints based on credibility measure is provided. For the given n jobs to be processed on m machines, it is assumed that the processing times and the due dates are nonnegative fuzzy numbers and all the weights are positive, crisp numbers. Based on credibility measure, three parallel machine scheduling problems and a goal-programming model are formulated. Feasible schedules are evaluated not only by their objective values but also by the credibility degree of satisfaction with their precedence constraints. The genetic algorithm is utilized to find the best solutions in a short period of time. An illustrative numerical example is also given. Simulation results show that the proposed models are effective, which can deal with the parallel machine scheduling problems with fuzzy parameters and precedence constraints based on credibility measure.

Exploring Taiwan’s China Landscape Painting Aesthetic Preferences Through Evaluation Grid Method and the Continuous Fuzzy Kano Model

The primary objective of this study is to apply the Evaluation Grid Method(EGM)and the continuous fuzzy Kano quality model to explore the cognitive preferences of Taiwan China residents regarding the beauty of Taiwan’s China landscape paintings.The aim is to contribute to the development of social and cultural art and promote the widespread appeal of art products.Through a literature review,consultations with aesthetic experts,and the application of Miryoku Engineering’s EGM,this paper consolidates the factors that contribute to the attractiveness of painting art products among Taiwan China residents,taking into account various aesthetic qualities.Simultaneously,the paper introduces the use of the triangular fuzzy golden ratio scale semantics,specifically the equal-ratio aesthetic scale semantics,as a replacement for the traditional subjective consciousness model.Departing from the traditional discrete Kano model that employs the mode as the standard for evaluating quality,this study applies triangular fuzzy numbers to the continuous Kano quality model to analyze the diverse preferences and evaluation standards of the public.The hope is that this research methodology will not only deepen Taiwan China residents’understanding and aesthetic literacy of painting art but also serve as a reference for the popularization of art products.

Supervised Fuzzy Mixture of Local Feature Models

This paper addresses an important issue in model combination, that is, model locality. Since usually a global linear model is unable to reflect nonlinearity and to characterize local features, especially in a complex sys-tem, we propose a mixture of local feature models to overcome these weaknesses. The basic idea is to split the entire input space into operating domains, and a recently developed feature-based model combination method is applied to build local models for each region. To realize this idea, three steps are required, which include clustering, local modeling and model combination, governed by a single objective function. An adaptive fuzzy parametric clustering algorithm is proposed to divide the whole input space into operating regimes, local feature models are created in each individual region by applying a recently developed fea-ture-based model combination method, and finally they are combined into a single mixture model. Corre-spondingly, a three-stage procedure is designed to optimize the complete objective function, which is actu-ally a hybrid Genetic Algorithm (GA). Our simulation results show that the adaptive fuzzy mixture of local feature models turns out to be superior to global models.

Fuzzy Set Based Models and Methods of Decision Making and Power Engineering Problems

The results of research into the use of fuzzy set based models and methods of multicriteria decision making for solving power engineering problems are presented. Two general classes of models related to multiobjective (X,M> models) and multiattribute (X,R> models) problems are considered. The analysisX,M> of models is based on the use of the Bellman-Zadeh approach to decision making in a fuzzy environment. Its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems. Several techniques based on fuzzy preference modeling are considered for the analysis of?X,R> models. A review of the authors’ results associated with the application of these models and methods for solving diverse types of problems of power system and subsystems planning and operation is presented. The recent results on the use ofX,M> andX,R> models and methods of their analysis for the allocation of reactive power sources in distribution systems and for the prioritization in maintenance planning in distribution systems, respectively, are considered.

A Blind Spot in the Reframing of a Universe of Possibles: Towards a Suitable Model for Decision-Making Theory and A.I.

Bayesian inference model is an optimal processing of incomplete information that, more than other models, better captures the way in which any decision-maker learns and updates his degree of rational beliefs about possible states of nature, in order to make a better judgment while taking new evidence into account. Such a scientific model proposed for the general theory of decision-making, like all others in general, whether in statistics, economics, operations research, A.I., data science or applied mathematics, regardless of whether they are time-dependent, have in common a theoretical basis that is axiomatized by relying on related concepts of a universe of possibles, especially the so-called universe (or the world), the state of nature (or the state of the world), when formulated explicitly. The issue of where to stand as an observer or a decision-maker to reframe such a universe of possibles together with a partition structure of knowledge (i.e. semantic formalisms), including a copy of itself as it was initially while generalizing it, is not addressed. Memory being the substratum, whether human or artificial, wherein everything stands, to date, even the theoretical possibility of such an operation of self-inclusion is prohibited by pure mathematics. We make this blind spot come to light through a counter-example (namely Archimedes’ Eureka experiment) and explore novel theoretical foundations, fitting better with a quantum form than with fuzzy modeling, to deal with more than a reference universe of possibles. This could open up a new path of investigation for the general theory of decision-making, as well as for Artificial Intelligence, often considered as the science of the imitation of human abilities, while being also the science of knowledge representation and the science of concept formation and reasoning.

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。

Constrained predictive control based on T-S fuzzy model for nonlinear systems

A constrained generalized predictive control （GPC） algorithm based on the T-S fuzzy model is presented for the nonlinear system. First, a Takagi-Sugeno （T-S） fuzzy model based on the fuzzy cluster algorithm and the orthogonalleast square method is constructed to approach the nonlinear system. Since its consequence is linear, it can divide the nonlinear system into a number of linear or nearly linear subsystems. For this T-S fuzzy model, a GPC algorithm with input constraints is presented. This strategy takes into account all the constraints of the control signal and its increment, and does not require the calculation of the Diophantine equations. So it needs only a small computer memory and the computational speed is high. The simulation results show a good performance for the nonlinear systems.

A unified approach to fuzzy modelling and robust synchronization of different hyperchaotic systems

In this paper, a Takagi Sugeno （T-S） fuzzy model-based method is proposed to deal with the problem of synchronization of two identical or different hyperchaotic systems. The T S fuzzy models with a small number of fuzzy IF-THEN rules are employed to represent many typical hyperchaotic systems exactly. The benefit of employing the T-S fuzzy models lies in mathematical simplicity of analysis. Based on the T-S fuzzy hyperchaotic models, two fuzzy controllers arc designed via parallel distributed compensation （PDC） and exact linearization （EL） techniques to synchronize two identical hyperchaotic systems with uncertain parameters and two different hyperchaotic systems, respectively. The sufficient conditions for the robust synchronization of two identical hyperchaotic systems with uncertain parameters and the asymptotic synchronization of two different hyperchaotic systems are derived by applying the Lyapunov stability theory. This method is a universal one of synchronizing two identical or different hyperchaotic systems. Numerical examples are given to demonstrate the validity of the proposed fuzzy model and hyperchaotic synchronization scheme.