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.

Bio-Inspired Numerical Analysis of COVID-19 with Fuzzy Parameters

Fuzziness or uncertainties arise due to insufficient knowledge,experimental errors,operating conditions and parameters that provide inaccurate information.The concepts of susceptible,infectious and recovered are uncertain due to the different degrees in susceptibility,infectivity and recovery among the individuals of the population.The differences can arise,when the population groups under the consideration having distinct habits,customs and different age groups have different degrees of resistance,etc.More realistic models are needed which consider these different degrees of susceptibility infectivity and recovery of the individuals.In this paper,a Susceptible,Infected and Recovered(SIR)epidemic model with fuzzy parameters is discussed.The infection,recovery and death rates due to the disease are considered as fuzzy numbers.Fuzzy basic reproduction number and fuzzy equilibrium points have been derived for the studied model.Themodel is then solved numerically with three different techniques,forward Euler,Runge-Kutta fourth order method(RK-4)and the nonstandard finite difference(NSFD)methods respectively.The NSFD technique becomes more efficient and reliable among the others and preserves all the essential features of a continuous dynamical system.

A Modified Interactive Stability Algorithm for Solving Multi-Objective NLP Problems with Fuzzy Parameters in Its Objective Functions

This paper presents a modified method to solve multi-objective nonlinear programming problems with fuzzy parameters in its objective functions and these fuzzy parameters are characterized by fuzzy numbers. The modified method is based on normalized trade-off weights. The obtained stability set corresponding to α-Pareto optimal solution, using our method, is investigated. Moreover, an algorithm for obtaining any subset of the parametric space which has the same corresponding α-Pareto optimal solution is presented. Finally, a numerical example to illustrate our method is also given.

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.

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.

Numerical Investigation of Malaria Disease Dynamics in Fuzzy Environment

The application of fuzzy theory is vital in all scientific disciplines.The construction of mathematical models with fuzziness is little studied in the literature.With this in mind and for a better understanding of the disease,an SEIR model of malaria transmission with fuzziness is examined in this study by extending a classicalmodel ofmalaria transmission.The parametersβandδ,being function of the malaria virus load,are considered fuzzy numbers.Three steady states and the reproduction number of the model are analyzed in fuzzy senses.A numerical technique is developed in a fuzzy environment to solve the studied model,which retains essential properties such as positivity and dynamic consistency.Moreover,numerical simulations are carried out to illustrate the analytical results of the developed technique.Unlike most of the classical methods in the literature,the proposed approach converges unconditionally and can be considered a reliable tool for studying malaria disease dynamics.

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.

The Refined Solutions on Multiobjective Programming Problems with Fuzzy Parameters in the Constraints

This paper investigates the multiobjective programming problems with fuzzy parameters in the constraints. First, by the decomposing theorem, we introduce a fuzzy set to characterize the constraints, then give the definition of α-quasi-efficient solution and a-efficient solution, and discuss their properties. Finally, a numerical example is presented to illustrate the differences between the refined solutions and the α-Pareto solution.

Optimal design of structural parameters for shield cutterhead based on fuzzy mathematics and multi-objective genetic algorithm

In order to improve the strength and stiffness of shield cutterhead, the method of fuzzy mathematics theory in combination with the finite element analysis is adopted. An optimal design model of structural parameters for shield cutterhead is formulated,based on the complex engineering technical requirements. In the model, as the objective function of the model is a composite function of the strength and stiffness, the response surface method is applied to formulate the approximate function of objective function in order to reduce the solution scale of optimal problem. A multi-objective genetic algorithm is used to solve the cutterhead structure design problem and the change rule of the stress-strain with various structural parameters as well as their optimal values were researched under specific geological conditions. The results show that compared with original cutterhead structure scheme, the obtained optimal scheme of the cutterhead structure can greatly improve the strength and stiffness of the cutterhead, which can be seen from the reduction of its maximum equivalent stress by 21.2%, that of its maximum deformation by 0.75%, and that of its mass by 1.04%.

Novel ARC-Fuzzy Coordinated Automatic Tracking Control of Four-Wheeled Mobile Robot

Four-wheeled,individual-driven,nonholonomic structured mobile robots are widely used in industries for automated work,inspection and explora-tion purposes.The trajectory tracking control of the four-wheel individual-driven mobile robot is one of the most blooming research topics due to its nonholonomic structure.The wheel velocities are separately adjusted to follow the trajectory in the old-fashioned kinematic control of skid-steered mobile robots.However,there is no consideration for robot dynamics when using a kinematic controller that solely addresses the robot chassis’s motion.As a result,the mobile robot has lim-ited performance,such as chattering during curved movement.In this research work,a three-tiered adaptive robust control with fuzzy parameter estimation,including dynamic modeling,direct torque control and wheel slip control is pro-posed.Fuzzy logic-based parameter estimation is a valuable tool for adjusting adaptive robust controller(ARC)parameters and tracking the trajectories with less tracking error as well as high tracking accuracy.This research considers the O type and 8 type trajectories for performance analysis of the proposed novel control technique.Our suggested approach outperforms the existing control methods such as Fuzzy,proportional–integral–derivative(PID)and adaptive robust controller with discrete projection(ARC–DP).The experimental results show that the scheduled performance index decreases by 2.77%and 4.76%.All the experimen-tal simulations obviously proved that the proposed ARC-Fuzzy performed well in smooth groud surfaces compared to other approaches.

SEQUENTIAL DIAGNOSIS FOR A CENTRIFUGAL PUMP BASED ON FUZZY NEURAL NETWORK

A sequential diagnosis method is proposed based on a fuzzy neural network realized by ＂the partially-linearized neural network （PNN）＂, by which the fault types of rotating machinery can be precisely and effectively distinguished at an early stage on the basis of the possibilities of symptom parameters. The non-dimensional symptom parameters in time domain are defined for reflecting the features of time signals measured for the fault diagnosis of rotating machinery. The synthetic detection index is also proposed to evaluate the sensitivity of non-dimensional symptom parameters for detecting faults. The practical example of condition diagnosis for detecting and distinguishing fault states of a centrifugal pump system, such as cavitation, impeller eccentricity which often occur in a centrifugal pump system, are shown to verify the efficiency of the method proposed in this paper.

THE FUZZY SYNTHETIC JUDGEMENT OF CORRELATING PARAMETER OF FIGHTER DESIGN

An expression of correlating parameter is developed which can be used to synthetically express the close combat maneuverability of fighters by the method of fuzzy mathematics. On the basis of analysis of fighter maneuvering performances, this paper proposes the parameters ωA,ωs, and SEP to measure the maneuvering performances. The linear weighted method, which is one of the basic methods of transforming several objects to a single object in mathematics programming, is used to determine the form of the correlating parameter expression. The focal point of this paper's work is to determine the weight coefficients of maneuvering performances in the expression. In order to solve this problem, the inverse problem of synthetic judgement in fuzzy mathematics is employed. The development of the equation of fuzzy relationship in this paper is based on the judgement data, which are gathered from many experts working in aeronautical field. Therefore, the expression of correlating parameter developed by this paper can be used in the design object at aircraft conceptual design stage and the judgement of synthetical measurement of the maneuverability of fighters.

Computational Investigation of Hand Foot Mouth Disease Dynamics with Fuzziness

The first major outbreak of the severely complicated hand,foot and mouth disease(HFMD),primarily caused by enterovirus 71,was reported in Taiwan in 1998.HFMD surveillance is needed to assess the spread of HFMD.The parameters we use in mathematical models are usually classical mathematical parameters,called crisp parameters,which are taken for granted.But any biological or physical phenomenon is best explained by uncertainty.To represent a realistic situation in any mathematical model,fuzzy parameters can be very useful.Many articles have been published on how to control and prevent HFMD from the perspective of public health and statistical modeling.However,few works use fuzzy theory in building models to simulateHFMDdynamics.In this context,we examined anHFMD model with fuzzy parameters.A Non Standard Finite Difference(NSFD)scheme is developed to solve the model.The developed technique retains essential properties such as positivity and dynamic consistency.Numerical simulations are presented to support the analytical results.The convergence and consistency of the proposed method are also discussed.The proposed method converges unconditionally while the many classical methods in the literature do not possess this property.In this regard,our proposed method can be considered as a reliable tool for studying the dynamics of HFMD.

Computational Analysis for Computer Network Model with Fuzziness

A susceptible,exposed,infectious,quarantined and recovered(SEIQR)model with fuzzy parameters is studied in this work.Fuzziness in the model arises due to the different degrees of susceptibility,exposure,infectivity,quarantine and recovery among the computers under consideration due to the different sizes,models,spare parts,the surrounding environments of these PCs and many other factors like the resistance capacity of the individual PC against the virus,etc.Each individual PC has a different degree of infectivity and resis-tance against infection.In this scenario,the fuzzy model has richer dynamics than its classical counterpart in epidemiology.The reproduction number of the developed model is studied and the equilibrium analysis is performed.Two different techniques are employed to solve the model numerically.Numerical simulations are performed and the obtained results are compared.Positivity and convergence are maintained by the suggested technique which are the main features of the epidemic models.

Boundedness and Positivity Preserving Numerical Analysis of a Fuzzy-Parameterized Delayed Model for Foot and Mouth Disease Dynamics

Foot-and-mouth disease(FMD)is a viral disease that affects cloven-hoofed animals including cattle,pigs,and sheep,hence causing export bans among others,causing high economic losses due to reduced productivity.The global effect of FMD is most felt where livestock rearing forms an important source of income.It is therefore important to understand the modes of transmission of FMD to control its spread and prevent its occurrence.This work intends to address these dynamics by including the efficacy of active migrant animals transporting the disease from one area to another in a fuzzy mathematical modeling framework.Historical models of epidemics are determinable with a set of deterministic parameters and this does not reflect on real-life scenarios as observed in FMD.Fuzzy theory is used in this model as it permits the inclusion of uncertainties in the model;this makes the model more of a reality regarding disease transmission.A time lag,in this case,denotes the incubation period and other time-related factors affecting the spread of FMD and,therefore,is added to the current model for FMD.To that purpose,the analysis of steady states and the basic reproduction number are performed and,in addition,the stability checks are conveyed in the fuzzy environment.For the numerical solution of the model,we derive the Forward Euler Method and the fuzzy delayed non-standard finite difference(FDNSFD)method.Analytical studies of the FDNSFD scheme are performed for convergence,non-negativity,boundedness,and consistency analysis of the numerical projection to guarantee that the numerical model is an accurate discretization of the continuous dynamics of FMD transmission over time.In the following simulation study,we show that the FDNSFD method preserves the characteristics of the constant model and still works if relatively large time steps are employed;this is a bonus over the normal finite difference technique.The study shows how valuable it is to adopt fuzzy theory and time delays when simulating the transmission of the epidemic,especially for such diseases as FMD where uncertainty and migration have a defining role in transmission.This approach gives more sound and flexible grounds for analyzing and controlling the outbreak of FMD in various situations.

A new approach to predicting mining induced surface subsidence

There are many parameters influencing mining induced surface subsidence. These parameters usually interact with one another and some of them have the characteristic of fuzziness. Current approaches to predicting the subsidence cannot take into account of such interactions and fuzziness. In order to overcome this disadvantage, many mining induced surface subsidence cases were accumulated, and an artificial neuro fuzzy inference system(ANFIS) was used to set up 4 ANFIS models to predict the rise angle, dip angle, center angle and the maximum subsidence, respectively. The fitting and generalization prediction capabilities of the models were tested. The test results show that the models have very good fitting and generalization prediction capabilities and the approach can be applied to predict the mining induced surface subsidence.

Study of Multi media Streams Dynamic Rate Control Based on Fuzzy Adaptive PID

A Multimedia streams dynamic rate control algorithm based on Fuzzy adaptive PID （MFPID） has been proposed to implement multimedia streams＇ end sending rate on-line self-regulating and smoothing, and to track system resources in time, so that it can avoid system＇s regulating oscillation and guarantee system＇s stability. And, some work has been done to analyze adaptive session model of multimedia streams, to implement future available bandwidth estimation of IP network, to achieve PID parameters＇ on-line self-tuning by fuzzy controlling. Simulation validated the theoretical results of MFPID.

The Reasoning Mechanism Combining Fuzziness and Randomness

This article introduces the developing process, the main idea and the method of FBEST (Fuzzy set theory Based Expert System Tool) reasoning mechanism.The method reasonably solves the problem of various inputting ways and proposition reasoning which possesses both fuzziness and randomness in ES.