In this paper, we propose a fuzzy linear regression model with LR-type fuzzy input variables and fuzzy output variable, the fuzzy extent of which may be different. Then we give the iterative solution of the proposed m...In this paper, we propose a fuzzy linear regression model with LR-type fuzzy input variables and fuzzy output variable, the fuzzy extent of which may be different. Then we give the iterative solution of the proposed model based on the Weighted Least Squares estimation procedure. Some properties of the estimates are proved. We also define suitable goodness of fit index and its adjusted version useful to evaluate the performances of the proposed model. Based on the Least Median Squares-Weighted Least Squares (LMS-WLS) estimation procedure, we give robust estimation steps for the proposed model. Compared with the well-known fuzzy Least Squares method, the effectiveness of our model on reducing the outliers influence is shown by using two examples.展开更多
In this paper, we shall present the strong laws of large numbers for fuzzy set-valued random variables in the sense of d<sup>∞</sup><sub>H</sub> . The results are based on the result ...In this paper, we shall present the strong laws of large numbers for fuzzy set-valued random variables in the sense of d<sup>∞</sup><sub>H</sub> . The results are based on the result of single-valued random variables obtained by Taylor [1] and set-valued random variables obtained by Li Guan [2].展开更多
Tuned mass dampers (TMD) are well known as one of the most widely adopted devices in vibration control passive strategies. In the past few decades,many methods have been developed to find the optimal parameters of a T...Tuned mass dampers (TMD) are well known as one of the most widely adopted devices in vibration control passive strategies. In the past few decades,many methods have been developed to find the optimal parameters of a TMD installed on a structure and subjected to a random base excitation process,but most of them are usually based on an implicit assumption that all of the structural parameters are deterministic. However,in many real cases this simplification is unacceptable,so robust optimal design criteria becomes aviable alternative to better support engineers in the design process. In Robust Design Optimization (RDO) approaches,indeed the solution must be able to not only minimize the performance but also to limitits variation induced by uncertainty. Most of the currently available RDO methods are based on a probabilistic description of the model uncertainty,even if in many cases they are not able to explicitly include the influence of all the possible sources of uncertainties. Therefore,in this study,a fuzzy version of the robust TMD design optimization problem is proposed. The consistency of the fuzzy approach is studied with respect to the available non-probabilistic formulations reported in the literature and an application to an example of a robust design of a linear TMD subjected to base random vibrations in the presence of fuzzy uncertainties. The results show that the proposed fuzzy-based approach is able to give a set of optimal solutions both in terms of structural efficiency and sensitivity to mechanical and environmental uncertainties.展开更多
A warehouse layout problem where the warehouse has more than one level and both the distance from the cell to the receive/exit bay and demand of item types are fuzzy variables is proposed. The problem is to find a lay...A warehouse layout problem where the warehouse has more than one level and both the distance from the cell to the receive/exit bay and demand of item types are fuzzy variables is proposed. The problem is to find a layout with the minimum transportation cost subject to adjacency and other constraints. A fuzzy expected value model is given and an ant colony system is designed to solve the problem. Computational results indicate the efficiency and effectiveness of the method.展开更多
The key component of finite element analysis of structures with fuzzy parameters, which is associated with handling of some fuzzy information and arithmetic relation of fuzzy variables, was the solving of the governin...The key component of finite element analysis of structures with fuzzy parameters, which is associated with handling of some fuzzy information and arithmetic relation of fuzzy variables, was the solving of the governing equations of fuzzy finite element method. Based on a given interval representation of fuzzy numbers, some arithmetic rules of fuzzy numbers and fuzzy variables were developed in terms of the properties of interval arithmetic. According to the rules and by the theory of interval finite element method, procedures for solving the static governing equations of fuzzy finite element method of structures were presented. By the proposed procedure, the possibility distributions of responses of fuzzy structures can be generated in terms of the membership functions of the input fuzzy numbers. It is shown by a numerical example that the computational burden of the presented procedures is low and easy to implement. The effectiveness and usefulness of the presented procedures are also illustrated.展开更多
The primary goal of this paper is to price European options in the Merton's frame- work with underlying assets following jump-diffusion using fuzzy set theory. Owing to the vague fluctuation of the real financial mar...The primary goal of this paper is to price European options in the Merton's frame- work with underlying assets following jump-diffusion using fuzzy set theory. Owing to the vague fluctuation of the real financial market, the average jump rate and jump sizes cannot be recorded or collected accurately. So the main idea of this paper is to model the rate as a triangular fuzzy number and jump sizes as fuzzy random variables and use the property of fuzzy set to deduce two different jump-diffusion models underlying principle of rational expectations equilibrium price. Unlike many conventional models, the European option price will now turn into a fuzzy number. One of the major advantages of this model is that it allows investors to choose a reasonable European option price under an acceptable belief degree. The empirical results will serve as useful feedback information for improvements on the proposed model.展开更多
In this paper<i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> fuzzy techniques have been used to track the problem of malaria tran...In this paper<i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> fuzzy techniques have been used to track the problem of malaria transmission dynamics. The fuzzy equilibrium of the proposed model was discussed for different amounts of parasites in the body. We proved that when the amounts of parasites are less than the minimum amounts required for disease transmission (<img src="Edit_bced8210-1c24-4e78-bb5b-60ea7d37361c.png" alt="" /></span><span></span><span style="font-family:Verdana;">)</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> we reach the model disease-free equilibrium. Using Choquet integral</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> the fuzzy basic reproduction number through the expected value of fuzzy variable was introduced for the fuzzy Susceptible</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> Exposed</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> Infected</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> Recovered</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> susceptible-Susceptible</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> Exposed and Infected (SEIRS-SEI) malaria model. The fuzzy global stabilities were introduced and discussed. The disease-free equilibrium <img src="Edit_cc2d122d-7c04-4fb7-a96a-3eb919a3785d.png" alt="" /> </span><span style="font-family:Verdana;">is globally asymptotically stable if <img src="Edit_0974e52f-cf63-4bfa-9781-1ebce366a4a3.png" alt="" /></span><span></span><span style="font-family:Verdana;"> or if the basic reproduction number is less than one (<img src="Edit_dbffcb03-cd00-4213-b7e1-ada9a0cf5c98.png" alt="" /></span><span></span><span style="font-family:Verdana;">). When <img src="Edit_5fc38f3d-2561-4189-87c2-197e3ff30b2e.png" alt="" /></span><span></span><span style="font-family:Verdana;"> and <img src="Edit_bfe99d90-7e55-4466-96b2-ce107483f69b.png" alt="" /></span><span></span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> there exists a co-existing endemic equilibrium which is globally asymptotically stable in the interior of feasible set <img src="Edit_543608fd-d8c9-4109-a285-bcf9377f43cc.png" alt="" /></span><span></span><span style="font-family:Verdana;">. Finally</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> the numerical simulation has been done for showing the effectiveness of our analytical results.</span>展开更多
This paper provides an adaptive closed-loop strategy for suppressing the pathological oscillations of the basal ganglia based on a variable universe fuzzy algorithm.The pathological basal ganglia oscillations in the t...This paper provides an adaptive closed-loop strategy for suppressing the pathological oscillations of the basal ganglia based on a variable universe fuzzy algorithm.The pathological basal ganglia oscillations in the theta(4-9 Hz)and beta(12-35 Hz)frequency bands have been demonstrated to be associated with the tremor and rigidity/bradykinesia symptoms in Parkinson’s disease(PD).Although the clinical application of open-loop deep brain stimulation(DBS)is effective,the stimulation waveform with the fixed parameters cannot be self-adjusted as the disease progresses,and thus the stimulation effects go poor.To deal with this difficult problem,a variable universe fuzzy closed-loop strategy is proposed to modulate different PD states.We establish a cortico-basal ganglia-thalamocortical network model to simulate pathological oscillations and test the control effect.The results suggest that the proposed closed-loop control strategy can accommodate the variation of brain states and symptoms,which may become an alternative method to administrate the symptoms in PD.展开更多
Traditionally, the calculation of reliability of fuzzy random structures is based on the well-known formulation of probability of fuzzy events. But sometimes the results of this formulation will not indicating the rea...Traditionally, the calculation of reliability of fuzzy random structures is based on the well-known formulation of probability of fuzzy events. But sometimes the results of this formulation will not indicating the real state of safety of fuzzy-random structures. Based on the possibility theory, a computational procedure for the reliability analysis of fuzzy failure problems and random-fuzzy failure problems of mechanical structures that contain fuzzy variables were presented. A procedure for the analysis of structural reliability of problems of fuzzy failure criterion was also proposed. The failure possibility of fuzzy structures and possibility distribution of the probability of failure of fuzzy-random structures can be given by the proposed methods. It is shown that for the hybrid probabilistic and fuzzy reliability problems, the probability of failure should be suitably taken as a fuzzy variable in order to indicate the real safety of system objectively. Two examples illustrate the validity and rationality of the proposed methods.展开更多
The grey fuzzy variable was defined for the two fold uncertain parameters combining grey and fuzziness factors. On the basis of the credibility and chance measure of grey fuzzy variables, the distribution center inven...The grey fuzzy variable was defined for the two fold uncertain parameters combining grey and fuzziness factors. On the basis of the credibility and chance measure of grey fuzzy variables, the distribution center inventory uncertain programming model was presented. The grey fuzzy simulation technology can generate input-output data for the uncertain functions. The neural network trained from the inputoutput data can approximate the uncertain functions. The designed hybrid intelligent algorithm by embedding the trained neural network into genetic algorithm can optimize the general grey fuzzy programming problems. Finally, one numerical example is provided to illustrate the effectiveness of the model and the hybrid intelligent algorithm.展开更多
A new prioritization method in the analytic hierarchy process (AHP), which improves the group fuzzy preference programming (GFPP) method, is proposed. The fuzzy random theory is applied in the new prioritization m...A new prioritization method in the analytic hierarchy process (AHP), which improves the group fuzzy preference programming (GFPP) method, is proposed. The fuzzy random theory is applied in the new prioritization method. By modifying the principle of decision making implied in the GFPP method, the improved group fuzzy preference programming (IGFPP) method is formulated as a fuzzy linear programming problem to maximize the average degree of the group satisfaction with all possible group priority vectors. The IGFPP method inherits the advantages of the GFPP method, and solves the weighting trouble existed in the GFPP method. Numerical tests indicate that the IGFPP method performs more effectively than the GFPP method in the case of very contradictive comparison judgments from decision makers.展开更多
In order to fully interpret and describe damage mechanics, the origin and development of fuzzy stochastic damage mechanics were introduced based on the analysis of the harmony of damage, probability, and fuzzy members...In order to fully interpret and describe damage mechanics, the origin and development of fuzzy stochastic damage mechanics were introduced based on the analysis of the harmony of damage, probability, and fuzzy membership in the interval of [0,1]. In a complete normed linear space, it was proven that a generalized damage field can be simulated through β probability distribution. Three kinds of fuzzy behaviors of damage variables were formulated and explained through analysis of the generalized uncertainty of damage variables and the establishment of a fuzzy functional expression. Corresponding fuzzy mapping distributions, namely, the half-depressed distribution, swing distribution, and combined swing distribution, which can simulate varying fuzzy evolution in diverse stochastic damage situations, were set up. Furthermore, through demonstration of the generalized probabilistic characteristics of damage variables, the cumulative distribution function and probability density function of fuzzy stochastic damage variables, which show β probability distribution, were modified according to the expansion principle. The three-dimensional fuzzy stochastic damage mechanical behaviors of the Longtan rolled-concrete dam were examined with the self-developed fuzzy stochastic damage finite element program. The statistical correlation and non-normality of random field parameters were considered comprehensively in the fuzzy stochastic damage model described in this paper. The results show that an initial damage field based on the comprehensive statistical evaluation helps to avoid many difficulties in the establishment of experiments and numerical algorithms for damage mechanics analysis.展开更多
The last three decades ha</span><span style="font-family:"">ve</span><span style="font-family:""> witnessed development of optimization under fuzziness and randomn...The last three decades ha</span><span style="font-family:"">ve</span><span style="font-family:""> witnessed development of optimization under fuzziness and randomness also called Fuzzy Stochastic Optimization. The main objective </span><span style="font-family:"">of </span><span style="font-family:"">this new field is the need for basing many human decisions on information which is both fuzzily imprecise and probabilistically uncertain. Consistency indexes providing a union nexus between possibilities and probabilities of uncertain events exist in the literature. Nevertheless, there are no reliable transformations between them. This calls for new paradigms for coping with mathematical models involving both fuzziness and randomness. Fuzzy Stochastic Optimization (FSO) is an attempt to fulfill this need. In this paper, we present a panoramic view of Fuzzy Stochastic Optimization emphasizing the methodological aspects. The merits of existing methods are also briefly discussed along with some related theoretical aspects.展开更多
A high-precision fuzzy controller, based on a state observer, is developed for a class of nonlinear single-input-single-output(SISO) systems with system uncertainties and external disturbances. The state observer is i...A high-precision fuzzy controller, based on a state observer, is developed for a class of nonlinear single-input-single-output(SISO) systems with system uncertainties and external disturbances. The state observer is introduced to resolve the problem of the unavailability of state variables. Assisted by the observer, a variable universe fuzzy system is designed to approximate the ideal control law. Being auxiliary components, a robust control term and a state feedback control term are designed to suppress the influence of the lumped uncertainties and remove the observation error, respectively. Different from the existing results, no additional dynamic order is required for the control design. All the adaptive laws and the control law are built based on the Lyapunov synthesis approach, and the signals involved in the closed-loop system are guaranteed to be uniformly ultimately bounded. Simulation results performed on Duffing forced oscillation demonstrate the advantages of the proposed control scheme.展开更多
Rough set theory has been widely researched for time series prediction problems such as rainfall runoff.Accurate forecasting of rainfall runoff is a long standing but still mostly signicant problem for water resource ...Rough set theory has been widely researched for time series prediction problems such as rainfall runoff.Accurate forecasting of rainfall runoff is a long standing but still mostly signicant problem for water resource planning and management,reservoir and river regulation.Most research is focused on constructing the better model for improving prediction accuracy.In this paper,a rainfall runoff forecast model based on the variable-precision fuzzy neighborhood rough set(VPFNRS)is constructed to predict Watershed runoff value.Fuzzy neighborhood rough set dene the fuzzy decision of a sample by using the concept of fuzzy neighborhood.The fuzzy neighborhood rough set model with variable-precision can reduce the redundant attributes,and the essential equivalent data can improve the predictive capabilities of model.Meanwhile VFPFNRS can handle the numerical data,while it also deals well with the noise data.In the discussed approach,VPFNRS is used to reduce superuous attributes of the original data,the compact data are employed for predicting the rainfall runoff.The proposed method is examined utilizing data in the Luo River Basin located in Guangdong,China.The prediction accuracy is compared with that of support vector machines and long shortterm memory(LSTM).The experiments show that the method put forward achieves a higher predictive performance.展开更多
To address complex work conditions incredibly challenging to the stability of power line inspection robots,we design a walking mechanism and propose a variable universe fuzzy control(VUFC)method based on multi‐work c...To address complex work conditions incredibly challenging to the stability of power line inspection robots,we design a walking mechanism and propose a variable universe fuzzy control(VUFC)method based on multi‐work conditions for flying‐walking power line inspection robots(FPLIRs).The contributions of this paper are as follows:(1)A flexible pressing component is designed to improve the adaptability of the FPLIR to the ground line slope.(2)The influence of multi‐work conditions on the FPLIR's walking stability is quantified using three condition parameters(i.e.,slope,slipping degree and swing angle),and their measurement methods are proposed.(3)The VUFC method based on the condition parameters is proposed to improve the walking stability of the FPLIR.Finally,the effect of the VUFC method on walking stability of the FPLIR is teste.The experimental results show that the maximum climbing angle of the FPLIR reaches 29.1°.Compared with the constant pressing force of 30 N,the average value of slipping degree is 0.93°,increasing by 35%.The maximum and average values of robot's swing angle are reduced by 46%and 54%,respectively.By comparing with fuzzy control,the VUFC can provide a more reasonable pressing force while maintaining the walking stability of the FPLIR.The proposed walking mechanism and the VUFC method significantly improve the stability of the FPLIR,providing a reference for structural designs and stability controls of inspection robots.展开更多
In this paper, a data-driven prognostic model capable to deal with different sources of uncertainty is proposed. The main novelty factor is the application of a mathematical framework, namely a Random Fuzzy Variable (...In this paper, a data-driven prognostic model capable to deal with different sources of uncertainty is proposed. The main novelty factor is the application of a mathematical framework, namely a Random Fuzzy Variable (RFV) approach, for the representation and propagation of the different uncertainty sources affecting </span><span style="font-family:Verdana;">Prognostic Health Management (PHM) applications: measurement, future and model uncertainty. </span><span style="font-family:Verdana;">In this way, it is possible to deal not only with measurement noise and model parameters uncertainty due to the stochastic nature of the degradation process, but also with systematic effects, such as systematic errors in the measurement process, incomplete knowledge of the degradation process, subjective belief about model parameters. Furthermore, the low analytical complexity of the employed prognostic model allows to easily propagate the measurement and parameters uncertainty into the RUL forecast, with no need of extensive Monte Carlo loops, so that low requirements in terms of computation power are needed. The model has been applied to two real application cases, showing high accuracy output, resulting in a potential</span></span><span style="font-family:Verdana;">ly</span><span style="font-family:Verdana;"> effective tool for predictive maintenance in different industrial sectors.展开更多
Due to the uncertainty of the market demand in the supply chain, this paper characterized market demand as a fuzzy variable and proposed single-period and long-term contracts to coordinate the two members (supplier a...Due to the uncertainty of the market demand in the supply chain, this paper characterized market demand as a fuzzy variable and proposed single-period and long-term contracts to coordinate the two members (supplier and buyer) in the supply chain. Comparison of the effectiveness of the two contracts indicates that a long-term contract is more effective than a single-period contract in improving the profit potential of both the total supply chain and each member in the supply chain. This conclusion is useful to the decision-maker in supply chains with fuzzy market demand.展开更多
In economic order quantity models without backordering, both the stock cost of each unit quantity and the order cost of each cycle are characterized as independent fuzzy variables rather than fuzzy numbers as in previ...In economic order quantity models without backordering, both the stock cost of each unit quantity and the order cost of each cycle are characterized as independent fuzzy variables rather than fuzzy numbers as in previous studies. Based on an expected value criterion or a credibility criterion, a fuzzy expected value model and a fuzzy dependent chance programming (DCP) model are constructed. The purpose of the fuzzy expected value model is to find the optimal order quantity such that the fuzzy expected value of the total cost is minimal. The fuzzy DCP model is used to find the optimal order quantity for maximizing the credibility of an event such that the total cost in the planning periods does not exceed a certain budget level. Fuzzy simulations are designed to calculate the expected value of the fuzzy objective function and the credibility of each fuzzy event. A particle swarm optimization (PSO) algorithm based on a fuzzy simulation is designed, by integrating the fuzzy simulation and the PSO algorithm. Finally, a numerical example is given to illustrate the feasibility and validity of the proposed algorithm.展开更多
This paper presents a fuzzy multiple attribute decision-making (FMADM) method in which the attribute weights and decision matrix elements (attribute values) are fuzzy variables. Fuzzy arithmetic and the expected v...This paper presents a fuzzy multiple attribute decision-making (FMADM) method in which the attribute weights and decision matrix elements (attribute values) are fuzzy variables. Fuzzy arithmetic and the expected value operator of fuzzy variables are used to develop the expected value method to solve the FMADM problem. A numerical example is given to demonstrate the feasibility and effectiveness of the method.展开更多
文摘In this paper, we propose a fuzzy linear regression model with LR-type fuzzy input variables and fuzzy output variable, the fuzzy extent of which may be different. Then we give the iterative solution of the proposed model based on the Weighted Least Squares estimation procedure. Some properties of the estimates are proved. We also define suitable goodness of fit index and its adjusted version useful to evaluate the performances of the proposed model. Based on the Least Median Squares-Weighted Least Squares (LMS-WLS) estimation procedure, we give robust estimation steps for the proposed model. Compared with the well-known fuzzy Least Squares method, the effectiveness of our model on reducing the outliers influence is shown by using two examples.
文摘In this paper, we shall present the strong laws of large numbers for fuzzy set-valued random variables in the sense of d<sup>∞</sup><sub>H</sub> . The results are based on the result of single-valued random variables obtained by Taylor [1] and set-valued random variables obtained by Li Guan [2].
文摘Tuned mass dampers (TMD) are well known as one of the most widely adopted devices in vibration control passive strategies. In the past few decades,many methods have been developed to find the optimal parameters of a TMD installed on a structure and subjected to a random base excitation process,but most of them are usually based on an implicit assumption that all of the structural parameters are deterministic. However,in many real cases this simplification is unacceptable,so robust optimal design criteria becomes aviable alternative to better support engineers in the design process. In Robust Design Optimization (RDO) approaches,indeed the solution must be able to not only minimize the performance but also to limitits variation induced by uncertainty. Most of the currently available RDO methods are based on a probabilistic description of the model uncertainty,even if in many cases they are not able to explicitly include the influence of all the possible sources of uncertainties. Therefore,in this study,a fuzzy version of the robust TMD design optimization problem is proposed. The consistency of the fuzzy approach is studied with respect to the available non-probabilistic formulations reported in the literature and an application to an example of a robust design of a linear TMD subjected to base random vibrations in the presence of fuzzy uncertainties. The results show that the proposed fuzzy-based approach is able to give a set of optimal solutions both in terms of structural efficiency and sensitivity to mechanical and environmental uncertainties.
基金the National Natural Science Foundation of China (70471063 ,70171036)
文摘A warehouse layout problem where the warehouse has more than one level and both the distance from the cell to the receive/exit bay and demand of item types are fuzzy variables is proposed. The problem is to find a layout with the minimum transportation cost subject to adjacency and other constraints. A fuzzy expected value model is given and an ant colony system is designed to solve the problem. Computational results indicate the efficiency and effectiveness of the method.
基金Foundation items:the National Natural Science Foundation of China(59575040,59575032)the Areonautics Science Foundation of China(00B53010)
文摘The key component of finite element analysis of structures with fuzzy parameters, which is associated with handling of some fuzzy information and arithmetic relation of fuzzy variables, was the solving of the governing equations of fuzzy finite element method. Based on a given interval representation of fuzzy numbers, some arithmetic rules of fuzzy numbers and fuzzy variables were developed in terms of the properties of interval arithmetic. According to the rules and by the theory of interval finite element method, procedures for solving the static governing equations of fuzzy finite element method of structures were presented. By the proposed procedure, the possibility distributions of responses of fuzzy structures can be generated in terms of the membership functions of the input fuzzy numbers. It is shown by a numerical example that the computational burden of the presented procedures is low and easy to implement. The effectiveness and usefulness of the presented procedures are also illustrated.
基金Supported by the Key Grant Project of Chinese Ministry of Education(309018)National Natural Science Foundation of China(70973104 and 11171304)the Zhejiang Natural Science Foundation of China(Y6110023)
文摘The primary goal of this paper is to price European options in the Merton's frame- work with underlying assets following jump-diffusion using fuzzy set theory. Owing to the vague fluctuation of the real financial market, the average jump rate and jump sizes cannot be recorded or collected accurately. So the main idea of this paper is to model the rate as a triangular fuzzy number and jump sizes as fuzzy random variables and use the property of fuzzy set to deduce two different jump-diffusion models underlying principle of rational expectations equilibrium price. Unlike many conventional models, the European option price will now turn into a fuzzy number. One of the major advantages of this model is that it allows investors to choose a reasonable European option price under an acceptable belief degree. The empirical results will serve as useful feedback information for improvements on the proposed model.
文摘In this paper<i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> fuzzy techniques have been used to track the problem of malaria transmission dynamics. The fuzzy equilibrium of the proposed model was discussed for different amounts of parasites in the body. We proved that when the amounts of parasites are less than the minimum amounts required for disease transmission (<img src="Edit_bced8210-1c24-4e78-bb5b-60ea7d37361c.png" alt="" /></span><span></span><span style="font-family:Verdana;">)</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> we reach the model disease-free equilibrium. Using Choquet integral</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> the fuzzy basic reproduction number through the expected value of fuzzy variable was introduced for the fuzzy Susceptible</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> Exposed</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> Infected</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> Recovered</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> susceptible-Susceptible</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> Exposed and Infected (SEIRS-SEI) malaria model. The fuzzy global stabilities were introduced and discussed. The disease-free equilibrium <img src="Edit_cc2d122d-7c04-4fb7-a96a-3eb919a3785d.png" alt="" /> </span><span style="font-family:Verdana;">is globally asymptotically stable if <img src="Edit_0974e52f-cf63-4bfa-9781-1ebce366a4a3.png" alt="" /></span><span></span><span style="font-family:Verdana;"> or if the basic reproduction number is less than one (<img src="Edit_dbffcb03-cd00-4213-b7e1-ada9a0cf5c98.png" alt="" /></span><span></span><span style="font-family:Verdana;">). When <img src="Edit_5fc38f3d-2561-4189-87c2-197e3ff30b2e.png" alt="" /></span><span></span><span style="font-family:Verdana;"> and <img src="Edit_bfe99d90-7e55-4466-96b2-ce107483f69b.png" alt="" /></span><span></span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> there exists a co-existing endemic equilibrium which is globally asymptotically stable in the interior of feasible set <img src="Edit_543608fd-d8c9-4109-a285-bcf9377f43cc.png" alt="" /></span><span></span><span style="font-family:Verdana;">. Finally</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> the numerical simulation has been done for showing the effectiveness of our analytical results.</span>
基金Project supported by the National Natural Science Foundation of China(Grant Nos.62173241 and 62171312)the Natural Science Foundation of Tianjin,China(Grant Nos.20JCQNJC01160 and 19JCZDJC36500)the financial support provided by Opening Foundation of Key Laboratory of Opto-technology and Intelligent Control(Lanzhou Jiaotong University),Ministry of Education,China(Grant No.KFKT2020-01)
文摘This paper provides an adaptive closed-loop strategy for suppressing the pathological oscillations of the basal ganglia based on a variable universe fuzzy algorithm.The pathological basal ganglia oscillations in the theta(4-9 Hz)and beta(12-35 Hz)frequency bands have been demonstrated to be associated with the tremor and rigidity/bradykinesia symptoms in Parkinson’s disease(PD).Although the clinical application of open-loop deep brain stimulation(DBS)is effective,the stimulation waveform with the fixed parameters cannot be self-adjusted as the disease progresses,and thus the stimulation effects go poor.To deal with this difficult problem,a variable universe fuzzy closed-loop strategy is proposed to modulate different PD states.We establish a cortico-basal ganglia-thalamocortical network model to simulate pathological oscillations and test the control effect.The results suggest that the proposed closed-loop control strategy can accommodate the variation of brain states and symptoms,which may become an alternative method to administrate the symptoms in PD.
文摘Traditionally, the calculation of reliability of fuzzy random structures is based on the well-known formulation of probability of fuzzy events. But sometimes the results of this formulation will not indicating the real state of safety of fuzzy-random structures. Based on the possibility theory, a computational procedure for the reliability analysis of fuzzy failure problems and random-fuzzy failure problems of mechanical structures that contain fuzzy variables were presented. A procedure for the analysis of structural reliability of problems of fuzzy failure criterion was also proposed. The failure possibility of fuzzy structures and possibility distribution of the probability of failure of fuzzy-random structures can be given by the proposed methods. It is shown that for the hybrid probabilistic and fuzzy reliability problems, the probability of failure should be suitably taken as a fuzzy variable in order to indicate the real safety of system objectively. Two examples illustrate the validity and rationality of the proposed methods.
基金Supported bythe Science and Research Foundationof Shanghai Municipal Educational Commssion (05DZ33)
文摘The grey fuzzy variable was defined for the two fold uncertain parameters combining grey and fuzziness factors. On the basis of the credibility and chance measure of grey fuzzy variables, the distribution center inventory uncertain programming model was presented. The grey fuzzy simulation technology can generate input-output data for the uncertain functions. The neural network trained from the inputoutput data can approximate the uncertain functions. The designed hybrid intelligent algorithm by embedding the trained neural network into genetic algorithm can optimize the general grey fuzzy programming problems. Finally, one numerical example is provided to illustrate the effectiveness of the model and the hybrid intelligent algorithm.
基金Sponsored by the National Natural Science Foundation of China (70471063)
文摘A new prioritization method in the analytic hierarchy process (AHP), which improves the group fuzzy preference programming (GFPP) method, is proposed. The fuzzy random theory is applied in the new prioritization method. By modifying the principle of decision making implied in the GFPP method, the improved group fuzzy preference programming (IGFPP) method is formulated as a fuzzy linear programming problem to maximize the average degree of the group satisfaction with all possible group priority vectors. The IGFPP method inherits the advantages of the GFPP method, and solves the weighting trouble existed in the GFPP method. Numerical tests indicate that the IGFPP method performs more effectively than the GFPP method in the case of very contradictive comparison judgments from decision makers.
基金supported by the National Natural Science Foundation of China(Grant No51109118)the China Postdoctoral Science Foundation(Grant No20100470344)+1 种基金the Fundamental Project Fund of Zhejiang Ocean University(Grant No21045032610)the Initiating Project Fund for Doctors of Zhejiang Ocean University(Grant No21045011909)
文摘In order to fully interpret and describe damage mechanics, the origin and development of fuzzy stochastic damage mechanics were introduced based on the analysis of the harmony of damage, probability, and fuzzy membership in the interval of [0,1]. In a complete normed linear space, it was proven that a generalized damage field can be simulated through β probability distribution. Three kinds of fuzzy behaviors of damage variables were formulated and explained through analysis of the generalized uncertainty of damage variables and the establishment of a fuzzy functional expression. Corresponding fuzzy mapping distributions, namely, the half-depressed distribution, swing distribution, and combined swing distribution, which can simulate varying fuzzy evolution in diverse stochastic damage situations, were set up. Furthermore, through demonstration of the generalized probabilistic characteristics of damage variables, the cumulative distribution function and probability density function of fuzzy stochastic damage variables, which show β probability distribution, were modified according to the expansion principle. The three-dimensional fuzzy stochastic damage mechanical behaviors of the Longtan rolled-concrete dam were examined with the self-developed fuzzy stochastic damage finite element program. The statistical correlation and non-normality of random field parameters were considered comprehensively in the fuzzy stochastic damage model described in this paper. The results show that an initial damage field based on the comprehensive statistical evaluation helps to avoid many difficulties in the establishment of experiments and numerical algorithms for damage mechanics analysis.
文摘The last three decades ha</span><span style="font-family:"">ve</span><span style="font-family:""> witnessed development of optimization under fuzziness and randomness also called Fuzzy Stochastic Optimization. The main objective </span><span style="font-family:"">of </span><span style="font-family:"">this new field is the need for basing many human decisions on information which is both fuzzily imprecise and probabilistically uncertain. Consistency indexes providing a union nexus between possibilities and probabilities of uncertain events exist in the literature. Nevertheless, there are no reliable transformations between them. This calls for new paradigms for coping with mathematical models involving both fuzziness and randomness. Fuzzy Stochastic Optimization (FSO) is an attempt to fulfill this need. In this paper, we present a panoramic view of Fuzzy Stochastic Optimization emphasizing the methodological aspects. The merits of existing methods are also briefly discussed along with some related theoretical aspects.
基金supported by National Natural Science Foundation of China(No.61074044)Basic and Cutting-edge Technology of Science and Technology Department of Henan Province(No.092300410178)
文摘A high-precision fuzzy controller, based on a state observer, is developed for a class of nonlinear single-input-single-output(SISO) systems with system uncertainties and external disturbances. The state observer is introduced to resolve the problem of the unavailability of state variables. Assisted by the observer, a variable universe fuzzy system is designed to approximate the ideal control law. Being auxiliary components, a robust control term and a state feedback control term are designed to suppress the influence of the lumped uncertainties and remove the observation error, respectively. Different from the existing results, no additional dynamic order is required for the control design. All the adaptive laws and the control law are built based on the Lyapunov synthesis approach, and the signals involved in the closed-loop system are guaranteed to be uniformly ultimately bounded. Simulation results performed on Duffing forced oscillation demonstrate the advantages of the proposed control scheme.
基金supported by the National Natural Science Foundation of China(61672279)the Open Foundation of State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering,Nanjing Hydraulic Research Institute,China(2016491411)。
文摘Rough set theory has been widely researched for time series prediction problems such as rainfall runoff.Accurate forecasting of rainfall runoff is a long standing but still mostly signicant problem for water resource planning and management,reservoir and river regulation.Most research is focused on constructing the better model for improving prediction accuracy.In this paper,a rainfall runoff forecast model based on the variable-precision fuzzy neighborhood rough set(VPFNRS)is constructed to predict Watershed runoff value.Fuzzy neighborhood rough set dene the fuzzy decision of a sample by using the concept of fuzzy neighborhood.The fuzzy neighborhood rough set model with variable-precision can reduce the redundant attributes,and the essential equivalent data can improve the predictive capabilities of model.Meanwhile VFPFNRS can handle the numerical data,while it also deals well with the noise data.In the discussed approach,VPFNRS is used to reduce superuous attributes of the original data,the compact data are employed for predicting the rainfall runoff.The proposed method is examined utilizing data in the Luo River Basin located in Guangdong,China.The prediction accuracy is compared with that of support vector machines and long shortterm memory(LSTM).The experiments show that the method put forward achieves a higher predictive performance.
基金National Natural Science Foundation of China,Grant/Award Numbers:62063030,62163032Financial Science and Technology Program of the XPCC,Grant/Award Numbers:2021DB003,2022CB002‐07,2022CB011High‐level Talent Project of Shihezi University,Grant/Award Numbers:RCZK2018C31,RCZK2018C32。
文摘To address complex work conditions incredibly challenging to the stability of power line inspection robots,we design a walking mechanism and propose a variable universe fuzzy control(VUFC)method based on multi‐work conditions for flying‐walking power line inspection robots(FPLIRs).The contributions of this paper are as follows:(1)A flexible pressing component is designed to improve the adaptability of the FPLIR to the ground line slope.(2)The influence of multi‐work conditions on the FPLIR's walking stability is quantified using three condition parameters(i.e.,slope,slipping degree and swing angle),and their measurement methods are proposed.(3)The VUFC method based on the condition parameters is proposed to improve the walking stability of the FPLIR.Finally,the effect of the VUFC method on walking stability of the FPLIR is teste.The experimental results show that the maximum climbing angle of the FPLIR reaches 29.1°.Compared with the constant pressing force of 30 N,the average value of slipping degree is 0.93°,increasing by 35%.The maximum and average values of robot's swing angle are reduced by 46%and 54%,respectively.By comparing with fuzzy control,the VUFC can provide a more reasonable pressing force while maintaining the walking stability of the FPLIR.The proposed walking mechanism and the VUFC method significantly improve the stability of the FPLIR,providing a reference for structural designs and stability controls of inspection robots.
文摘In this paper, a data-driven prognostic model capable to deal with different sources of uncertainty is proposed. The main novelty factor is the application of a mathematical framework, namely a Random Fuzzy Variable (RFV) approach, for the representation and propagation of the different uncertainty sources affecting </span><span style="font-family:Verdana;">Prognostic Health Management (PHM) applications: measurement, future and model uncertainty. </span><span style="font-family:Verdana;">In this way, it is possible to deal not only with measurement noise and model parameters uncertainty due to the stochastic nature of the degradation process, but also with systematic effects, such as systematic errors in the measurement process, incomplete knowledge of the degradation process, subjective belief about model parameters. Furthermore, the low analytical complexity of the employed prognostic model allows to easily propagate the measurement and parameters uncertainty into the RUL forecast, with no need of extensive Monte Carlo loops, so that low requirements in terms of computation power are needed. The model has been applied to two real application cases, showing high accuracy output, resulting in a potential</span></span><span style="font-family:Verdana;">ly</span><span style="font-family:Verdana;"> effective tool for predictive maintenance in different industrial sectors.
基金Supported by the National Natural Science Foundation of China(No.70801042)the Scientific Research Launching Foundation for Introduced Talents in Tianjin University of Science and Technology(No.20080430)
文摘Due to the uncertainty of the market demand in the supply chain, this paper characterized market demand as a fuzzy variable and proposed single-period and long-term contracts to coordinate the two members (supplier and buyer) in the supply chain. Comparison of the effectiveness of the two contracts indicates that a long-term contract is more effective than a single-period contract in improving the profit potential of both the total supply chain and each member in the supply chain. This conclusion is useful to the decision-maker in supply chains with fuzzy market demand.
基金the National Natural Science Foundation of China (Nos.70471049 and 70571056)the China PostdoctoralScience Foundation (No. 2004035013)
文摘In economic order quantity models without backordering, both the stock cost of each unit quantity and the order cost of each cycle are characterized as independent fuzzy variables rather than fuzzy numbers as in previous studies. Based on an expected value criterion or a credibility criterion, a fuzzy expected value model and a fuzzy dependent chance programming (DCP) model are constructed. The purpose of the fuzzy expected value model is to find the optimal order quantity such that the fuzzy expected value of the total cost is minimal. The fuzzy DCP model is used to find the optimal order quantity for maximizing the credibility of an event such that the total cost in the planning periods does not exceed a certain budget level. Fuzzy simulations are designed to calculate the expected value of the fuzzy objective function and the credibility of each fuzzy event. A particle swarm optimization (PSO) algorithm based on a fuzzy simulation is designed, by integrating the fuzzy simulation and the PSO algorithm. Finally, a numerical example is given to illustrate the feasibility and validity of the proposed algorithm.
基金Supported by the National Natural Science Foundation of China (N10501009)
文摘This paper presents a fuzzy multiple attribute decision-making (FMADM) method in which the attribute weights and decision matrix elements (attribute values) are fuzzy variables. Fuzzy arithmetic and the expected value operator of fuzzy variables are used to develop the expected value method to solve the FMADM problem. A numerical example is given to demonstrate the feasibility and effectiveness of the method.