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.

Evaluation model of the grey fuzzy on eco-environment vulnerability

The basic theory and evaluation index system of eco-environment vulnerability were reviewed. Based on the grey theory and fuzzy mathematics, a new comprehensive evaluation method from qualitative to quantitative, called grey-fuzzy evaluation, was proposed for evaluating eco-environment vulnerability. It was integrated of Association for Healthcare Philanthropy （AHP）, grey correlation analysis, grey statistics and fuzzy judgment. The constitutional principle and method of the new evaluation method were given and its feasibility and effectiveness were proved by the practical example.

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%.

PROGRESS OF GREY SYSTEM MODELS

The progress of grey system models is reviewed, and the general grey numbers, the grey sequence op- erators and several most commonly used grey system models are introduced, such as the absolute degree of grey incidence model, the grey cluster model based on endpoint triangular whitenization functions, the grey cluster model based on center-point triangular whitenization functions, the grey prediction model of the model GM （ 1,1）, and the weighted multi-attribute grey target decision model.

ESTIMATION METHOD FOR AIRCRAFT SIMILARITY BASED ON FUZZY THEORY AND GREY INCIDENCE ANALYSIS

An estimation method for aircraft similarity based on fuzzy theory and grey incidence analysis is presented. This estimation method is made up of the triangular fuzzy transforming model of linguistic variables and the method of grey incidence analysis. Nine feature attributes of aircraft are selected to estimate the similarity between the new aircraft and the existing aircraft. A new aircraft X and other six existing aircrafts are taken as examples. Analyses show that similarity estimation results obtained from the method are in accordance with practice.

RBF neural network regression model based on fuzzy observations

A fuzzy observations-based radial basis function neural network （FORBFNN） is presented for modeling nonlinear systems in which the observations of response are imprecise but can be represented as fuzzy membership functions. In the FORBFNN model, the weight coefficients of nodes in the hidden layer are identified by using the fuzzy expectation-maximization （ EM ） algorithm, whereas the optimal number of these nodes as well as the centers and widths of radial basis functions are automatically constructed by using a data-driven method. Namely, the method starts with an initial node, and then a new node is added in a hidden layer according to some rules. This procedure is not terminated until the model meets the preset requirements. The method considers both the accuracy and complexity of the model. Numerical simulation results show that the modeling method is effective, and the established model has high prediction accuracy.

Study on the Yield Prediction Model of Processing Tomato Based on the Grey System Theory

[Objective] The research aimed to study the yield prediction model of processing tomato based on the grey system theory.[Method] The variation trend of processing tomato yield was studied by using the grey system theory,and GM（1,1）grey model of processing tomato yield prediction was established.The processing tomato yield in Xinjiang during 2001-2009 was as the example to carry out the instance analysis.[Result] The model had the high forecast accuracy and strong generalization ability,and was reliable for the prediction of recent processing tomato yield.[Conclusion] The research provided the reference for the macro-control of tomato industry,the processing and storage of tomato in Xinjiang.

HIERARCHIC GREY QUASI-PREFERRED ANALYSIS MODEL AND ITS APPLICATION

The grey quasi-preferred analysis (GQPA) is one of important methods for realizing system analysis to conquer the limitations of the existing GQPA model, without any considerations to the difference of the different behavioral factor′s importance. It could not be used to analyze the complex system with multi-hierarchy correlation factors, the weighted synthetic method for calculating abstract incidence degrees between the system beha-vioral characteristics and correlative factors in different hierarchies is given out,and the hierarchic grey quasi-preferred analysis (HGQPA) model is established. The effectiveness of the HGQPA model is tested by the scientific-technical system of Jiangsu Province. The depth and the range of the application of GQPA are developed, and the HGQPA model is regarded as a new approach to systemically analyze the complex systems with multi-hierarchy correlation factors.

An Approach to Unsupervised Character Classification Based on Similarity Measure in Fuzzy Model

This paper presents a fuzzy logic approach to efficiently perform unsupervised character classification for improvement in robustness, correctness and speed of a character recognition system. The characters are first split into eight typographical categories. The classification scheme uses pattern matching to classify the characters in each category into a set of fuzzy prototypes based on a nonlinear weighted similarity function. The fuzzy unsupervised character classification, which is natural in the repre...

Construction of Tourist Satisfaction Degree Evaluation Model in Western Tourist Area by Performance Prism and Fuzzy Comprehensive Evaluation Method——with Lijiang in Yunnan Province as the Study Case

Starting from the utilization and protection of local knowledge, with the performance prism as the framework, the evaluation index system of tourist satisfaction degree was established. The weight was determined by using AHP method. Finally, the investigating result was judged with fuzzy comprehensive evaluation method, the evaluation model of tourist satisfaction degree in western tourist area was built, and the case study was carried out. With Lijiang in Yunnan Province as example, according to AHP method, five dimensions weight of the performance prism, various KPI weight and consistency were obtained, fuzzy evaluation on tourist satisfaction degree was conducted. The results showed that the overall was satisfactory, but there were still some problems. Aiming at the utilization and protection of local knowledge, some corresponding countermeasures were put forward which will benefit for further development of tourism in Lijiang of Yunnan Province.

APPLICATION OF FUZZY INFERENCE IN IDENTIFICATION OF HELICOPTER MODEL

Helicopter mathematical model mainly depends on design helicopter control system, flight simulator, and real time control simulation system. But it is difficult to establish a helicopter flight dynamics mathematical model that has features such as rapidness, reliability and precision, because there is no unique and precise expression to some sophisticated phenomenon of helicopter. In this paper a fuzzy helicopter flight model is constructed based on the flight experimental data. The fuzzy model, which is identified by fuzzy inference, has characteristics of computed rapidness and high precision. In order to guarantee the precision of the identified fuzzy model, a new method is adopted to handle the conflict fuzzy rules. Additionally, using fuzzy clustering technology can effectively reduce the number of rules of fuzzy model, namely, the order of the fuzzy model. The simulation results indicate that the method of this paper is effective and feasible.

T-S-fuzzy-model-based quantized control for nonlinear networked control systems

In order to overcome data-quantization, networked-induced delay, network packet dropouts and wrong sequences in the nonlinear networked control system, a novel nonlinear networked control system model is built by the T-S fuzzy method. Two time-varying quantizers are added in the model. The key analysis steps in the method are to construct an improved interval-delay-dependent Lyapunov functional and to introduce the free-weighting matrix. By making use of the parallel distributed compensation technology and the convexity of the matrix function, the improved criteria of the stabilization and stability are obtained. Simulation experiments show that the parameters of the controllers and quantizers satisfying a certain performance can be obtained by solving a set of LMIs. The application of the nonlinear mass-spring system is provided to show that the proposed method is effective.

Multivariable Fuzzy Predictive Control Based on the Modified CPN Model

Through modifying the CPN model, a kind of multivariable fuzzy model is put forward, and the matching fuzzy multistep predictive control algorithm is deduced based on the model. The modified model works in a competitive output manner which results in its local representation property. While studying on line, only a few parameters need to be regulated. So the model has the merits of fast learning and on line self organizing modeling. The control algorithm is simple, adaptive and useful in multivariable and time delay systems. Applying the algorithm in a paper making system, simulation shows its good effect.

TIME SERIES AND GREY MODEL DIAGNOSIS METHOD USED TO CRACK PROBLEMS

In this paper,the vibration signals in the fatigue crack growth process in a chinese steel used in a mining machinery were analyzed by the frequency spectrum, the time series and grey system model,and the critical criterion for crack initiation was proposed.

Prediction model of interval grey number based on DGM(1,1)

In grey system theory,the studies in the field of grey prediction model are focused on real number sequences,rather than grey number ones.Hereby,a prediction model based on interval grey number sequences is proposed.By mining the geometric features of interval grey number sequences on a two-dimensional surface,all the interval grey numbers are converted into real numbers by means of certain algorithm,and then the prediction model is established based on those real number sequences.The entire process avoids the algebraic operations of grey number,and the prediction problem of interval grey number is usefully solved.Ultimately,through an example＇s program simulation,the validity and practicability of this novel model are verified.

Interval grey number sequence prediction by using non-homogenous exponential discrete grey forecasting model

This paper aims to study a new grey prediction approach and its solution for forecasting the main system variable whose accurate value could not be collected while the potential value set could be defined. Based on the traditional nonhomogenous discrete grey forecasting model（NDGM）, the interval grey number and its algebra operations are redefined and combined with the NDGM model to construct a new interval grey number sequence prediction approach. The solving principle of the model is analyzed, the new accuracy evaluation indices, i.e. mean absolute percentage error of mean value sequence（MAPEM） and mean percent of interval sequence simulating value set covered（MPSVSC）, are defined and, the procedure of the interval grey number sequence based the NDGM（IG-NDGM） is given out. Finally, a numerical case is used to test the modelling accuracy of the proposed model. Results show that the proposed approach could solve the interval grey number sequence prediction problem and it is much better than the traditional DGM（1,1） model and GM（1,1） model.