In this paper,a robust and consistent COVID-19 emergency decision-making approach is proposed based on q-rung linear diophantine fuzzy set(q-RLDFS),differential evolutionary(DE)optimization principles,and evidential r...In this paper,a robust and consistent COVID-19 emergency decision-making approach is proposed based on q-rung linear diophantine fuzzy set(q-RLDFS),differential evolutionary(DE)optimization principles,and evidential reasoning(ER)methodology.The proposed approach uses q-RLDFS in order to represent the evaluating values of the alternatives corresponding to the attributes.DE optimization is used to obtain the optimal weights of the attributes,and ER methodology is used to compute the aggregated q-rung linear diophantine fuzzy values(q-RLDFVs)of each alternative.Then the score values of alternatives are computed based on the aggregated q-RLDFVs.An alternative with the maximum score value is selected as a better one.The applicability of the proposed approach has been illustrated in COVID-19 emergency decision-making system and sustainable energy planning management.Moreover,we have validated the proposed approach with a numerical example.Finally,a comparative study is provided with the existing models,where the proposed approach is found to be robust to perform better and consistent in uncertain environments.展开更多
The idea of linear Diophantine fuzzy set(LDFS)theory with its control parameters is a strong model for machine learning and optimization under uncertainty.The activity times in the critical path method(CPM)representat...The idea of linear Diophantine fuzzy set(LDFS)theory with its control parameters is a strong model for machine learning and optimization under uncertainty.The activity times in the critical path method(CPM)representation procedures approach are initially static,but in the Project Evaluation and Review Technique(PERT)approach,they are probabilistic.This study proposes a novel way of project review and assessment methodology for a project network in a linear Diophantine fuzzy(LDF)environment.The LDF expected task time,LDF variance,LDF critical path,and LDF total expected time for determining the project network are all computed using LDF numbers as the time of each activity in the project network.The primary premise of the LDF-PERT approach is to address ambiguities in project network activity timesmore simply than other approaches such as conventional PERT,Fuzzy PERT,and so on.The LDF-PERT is an efficient approach to analyzing symmetries in fuzzy control systems to seek an optimal decision.We also present a new approach for locating LDF-CPM in a project network with uncertain and erroneous activity timings.When the available resources and activity times are imprecise and unpredictable,this strategy can help decision-makers make better judgments in a project.A comparison analysis of the proposed technique with the existing techniques has also been discussed.The suggested techniques are demonstrated with two suitable numerical examples.展开更多
This paper addresses the problem of the fuzzy H ∞state feedback control for a class of uncertain nonlinear systems with time delay. The Takagi Sugeno (T S) mo del with time delay and parameter uncertainties is ...This paper addresses the problem of the fuzzy H ∞state feedback control for a class of uncertain nonlinear systems with time delay. The Takagi Sugeno (T S) mo del with time delay and parameter uncertainties is adopted for modeling of nonlinear system. The systematic design procedure for the fuzzy robust controller based on linear matrix inequality (LMI) is given. Some sufficient conditions are derived for the existence of fuzzy H ∞ state feedback controllers such that the closed loop system is asymptotically stable and the effect of the disturbance input on controlled output is reduced to a prescribed level. An example is given to demonstrate the effectiveness of the proposed method.展开更多
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 ...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.展开更多
This paper investigates the robust tracking control problcm for a class of nonlinear networked control systems （NCSs） using the Takagi-Sugeno （T-S） fuzzy model approach. Based on a time-varying delay system transf...This paper investigates the robust tracking control problcm for a class of nonlinear networked control systems （NCSs） using the Takagi-Sugeno （T-S） fuzzy model approach. Based on a time-varying delay system transformed from the NCSs, an augmented Lyapunov function containing more useful information is constructed. A less conservative sufficient condition is established such that the closed-loop systems stability and time-domain integral quadratic constraints （IQCs） are satisfied while both time-varying network- induced delays and packet losses are taken into account. The fuzzy tracking controllers design scheme is derived in terms of linear matrix inequalities （LMIs） and parallel distributed compensation （PDC）. Furthermore, robust stabilization criterion for nonlinear NCSs is given as an extension of the tracking control result. Finally, numerical simulations are provided to illustrate the effectiveness and merits of the proposed method.展开更多
The problem of designing fuzzy static output feedback controller for T-S discrete-time fuzzy bilinear system （DFBS） is presented. Based on parallel distribution compensation method, some sufficient conditions are de...The problem of designing fuzzy static output feedback controller for T-S discrete-time fuzzy bilinear system （DFBS） is presented. Based on parallel distribution compensation method, some sufficient conditions are derived to guarantee the stability of the overall fuzzy system. The stabilization conditions are further formulated into linear matrix inequality （LMI） so that the desired controller can be easily obtained by using the Matlab LMI toolbox. In comparison with the existing results, the drawbacks, such as coordinate transformation, same output matrices, have been elim- inated. Finally, a simulation example shows that the approach is effective.展开更多
A robust adaptive trajectory linearization control （RATLC） algorithm for a class of nonlinear systems with uncertainty and disturbance based on the T-S fuzzy system is presented. The unknown disturbance and uncertai...A robust adaptive trajectory linearization control （RATLC） algorithm for a class of nonlinear systems with uncertainty and disturbance based on the T-S fuzzy system is presented. The unknown disturbance and uncertainty are estimated by the T-S fuzzy system, and a robust adaptive control law is designed by the Lyapunov theory. Irrespective of whether the dimensions of the system and the rules of the fuzzy system are large or small, there is only one parameter adjusting on line. Uniformly ultimately boundedness of all signals of the composite closed-loop system are proved by theory analysis. Finally, a numerical example is studied based on the proposed method. The simulation results demonstrate the effectiveness and robustness of the control scheme.展开更多
The multiple attribute decision making problems are studied, in which the information about attribute weights is partly known and the attribute values take the form of intuitionistic fuzzy numbers. The operational law...The multiple attribute decision making problems are studied, in which the information about attribute weights is partly known and the attribute values take the form of intuitionistic fuzzy numbers. The operational laws of intuitionistic fuzzy numbers are introduced, and the score function and accuracy function are presented to compare the intuitionistic fuzzy numbers. The intuitionistic fuzzy ordered weighted averaging （IFOWA） operator which is an extension of the well-known ordered weighted averaging （OWA） operator is investigated to aggregate the intuitionistic fuzzy information. In order to determine the weights of intuitionistic fuzzy ordered weighted averaging operator, a linear goal programming procedure is proposed for learning the weights from data. Finally, an example is illustrated to verify the effectiveness and practicability of the developed method.展开更多
Intuitionistic Fuzzy Set (IFS) can be used as a general tool for modeling problems of decision making under uncertainty where, the degree of rejection is defined simultaneously with the degree of acceptance of a piece...Intuitionistic Fuzzy Set (IFS) can be used as a general tool for modeling problems of decision making under uncertainty where, the degree of rejection is defined simultaneously with the degree of acceptance of a piece of information in such a way that these degrees are not complement to each other. Accordingly, an attempt is made to solve intuitionistic fuzzy linear programming problems using a technique based on an earlier technique proposed by Zimmermann to solve fuzzy linear programming problem. Our proposed technique does not require the existing ranking of intuitionistic fuzzy numbers. This method is also different from the existing weight assignment method or the Angelov’s method. A comparative study is undertaken and interesting results have been presented.展开更多
An extended robust model predictive control approach for input constrained discrete uncertain nonlinear systems with time-delay based on a class of uncertain T-S fuzzy models that satisfy sector bound condition is pre...An extended robust model predictive control approach for input constrained discrete uncertain nonlinear systems with time-delay based on a class of uncertain T-S fuzzy models that satisfy sector bound condition is presented. In this approach, the minimization problem of the “worst-case” objective function is converted into the linear objective minimization problem in- volving linear matrix inequalities (LMIs) constraints. The state feedback control law is obtained by solving convex optimization of a set of LMIs. Sufficient condition for stability and a new upper bound on robust performance index are given for these kinds of uncertain fuzzy systems with state time-delay. Simulation results of CSTR process show that the proposed robust predictive control approach is effective and feasible.展开更多
Two existing methods for solving a class of fuzzy linear programming (FLP) problems involving symmetric trapezoidal fuzzy numbers without converting them to crisp linear programming problems are the fuzzy primal simpl...Two existing methods for solving a class of fuzzy linear programming (FLP) problems involving symmetric trapezoidal fuzzy numbers without converting them to crisp linear programming problems are the fuzzy primal simplex method proposed by Ganesan and Veeramani [1] and the fuzzy dual simplex method proposed by Ebrahimnejad and Nasseri [2]. The former method is not applicable when a primal basic feasible solution is not easily at hand and the later method needs to an initial dual basic feasible solution. In this paper, we develop a novel approach namely the primal-dual simplex algorithm to overcome mentioned shortcomings. A numerical example is given to illustrate the proposed approach.展开更多
Takagi-Sugeno(T-S) fuzzy model is difficult to be linearized because of membership functions included.So,novel T-S fuzzy state transformation and T-S fuzzy feedback are proposed for the linearization of T-S fuzzy syst...Takagi-Sugeno(T-S) fuzzy model is difficult to be linearized because of membership functions included.So,novel T-S fuzzy state transformation and T-S fuzzy feedback are proposed for the linearization of T-S fuzzy system.The novel T-S fuzzy state transformation is the fuzzy combination of local linear transformation which transforms local linear models in the T-S fuzzy model into the local linear controllable canonical models.The fuzzy combination of local linear controllable canonical model gives controllable canonical T-S fuzzy model and then nonlinear feedback is obtained easily.After the linearization of T-S fuzzy model,a robust H∞ controller with the robustness of sliding model control(SMC) is designed.As a result,controlled T-S fuzzy system shows the performance of H∞ control and the robustness of SMC.展开更多
The existing concepts of picture fuzzy sets(PFS),spherical fuzzy sets(SFSs),T-spherical fuzzy sets(T-SFSs)and neutrosophic sets(NSs)have numerous applications in decision-making problems,but they have various strict l...The existing concepts of picture fuzzy sets(PFS),spherical fuzzy sets(SFSs),T-spherical fuzzy sets(T-SFSs)and neutrosophic sets(NSs)have numerous applications in decision-making problems,but they have various strict limitations for their satisfaction,dissatisfaction,abstain or refusal grades.To relax these strict constraints,we introduce the concept of spherical linearDiophantine fuzzy sets(SLDFSs)with the inclusion of reference or control parameters.A SLDFSwith parameterizations process is very helpful formodeling uncertainties in themulti-criteria decisionmaking(MCDM)process.SLDFSs can classify a physical systemwith the help of reference parameters.We discuss various real-life applications of SLDFSs towards digital image processing,network systems,vote casting,electrical engineering,medication,and selection of optimal choice.We show some drawbacks of operations of picture fuzzy sets and their corresponding aggregation operators.Some new operations on picture fuzzy sets are also introduced.Some fundamental operations on SLDFSs and different types of score functions of spherical linear Diophantine fuzzy numbers(SLDFNs)are proposed.New aggregation operators named spherical linear Diophantine fuzzy weighted geometric aggregation(SLDFWGA)and spherical linear Diophantine fuzzy weighted average aggregation(SLDFWAA)operators are developed for a robust MCDM approach.An application of the proposed methodology with SLDF information is illustrated.The comparison analysis of the final ranking is also given to demonstrate the validity,feasibility,and efficiency of the proposed MCDM approach.展开更多
The problem of fuzzy modeling for state and input time-delays systems with a class of nonlinear uncertainties by fuzzy T-S model is addressed.By using the linear matrix inequality（LMI） method, the problem of fuzzy r...The problem of fuzzy modeling for state and input time-delays systems with a class of nonlinear uncertainties by fuzzy T-S model is addressed.By using the linear matrix inequality（LMI） method, the problem of fuzzy robust H ∞ controller design for the system is studied.Assuming that the nonlinear uncertain functions in the model considered are gain-bounded, a sufficient condition for the robustly asymptotic stability of the closed-loop system is obtained via Lyapunov stability theory.By solving the LMI, a feedback control law which guarantees the robustly asymptotic stability of the closed-loop system is constructed and the effect of the disturbance input on the controlled output is ruduced to a prescribed level.展开更多
In this paper, we propose an interactive method for solving the multilevel linear programming problems based on the intuitionistic fuzzy set theory. Firstly, the membership function and the non-membership function are...In this paper, we propose an interactive method for solving the multilevel linear programming problems based on the intuitionistic fuzzy set theory. Firstly, the membership function and the non-membership function are introduced to describe the uncertainty of the decision makers. Secondly, a satisfactory solution is derived by updating the minimum satisfactory degrees with considerations of the overall satisfactory balance among all levels. In addition, the steps of the proposed method are given in this paper. Finally, numerical examples illustrate the feasibility of this method.展开更多
Under non-random uncertainty, a new idea of finding a possibly optimal solution for linear programming problem is examined in this paper. It is an application of the intuitionistic fuzzy set concept within scope of th...Under non-random uncertainty, a new idea of finding a possibly optimal solution for linear programming problem is examined in this paper. It is an application of the intuitionistic fuzzy set concept within scope of the existing fuzzy optimization. Here, we solve a linear programming problem (LPP) in an intuitionistic fuzzy environment and compare the result with the solution obtained from other existing techniques. In the process, the result of associated fuzzy LPP is also considered for a better understanding.展开更多
This paper is concerned with the robust reliable memory controller design for a class of fuzzy uncertain systems with timevarying delay. The system under consideration is more general than those in other existent work...This paper is concerned with the robust reliable memory controller design for a class of fuzzy uncertain systems with timevarying delay. The system under consideration is more general than those in other existent works. The controller, which is dependent on the magnitudes and derivative of the delay, is proposed in terms of linear matrix inequality （LMI）. The closed-loop system is asymptotically stable for all admissible uncertainties as well as actuator faults. A numerical example is presented for illustration.展开更多
A fuzzy logic compensator is designed for feedback linearizable nonlinear systems with deadzone nonlinearity. The classification property of fuzzy logic systems makes them a natural candidate for the rejection of erro...A fuzzy logic compensator is designed for feedback linearizable nonlinear systems with deadzone nonlinearity. The classification property of fuzzy logic systems makes them a natural candidate for the rejection of errors induced by the deadzone, which has regions in which it behaves differently. A tuning algorithm is given for the fuzzy logic parameters, so that the deadzone compensation scheme becomes adaptive, guaranteeing small tracking errors and bounded parameter estimates. Formal nonlinear stability proofs are given to show that the tracking error is small. The fuzzy logic deadzone compensator is simulated on a one-link robot system to show its efficacy.展开更多
This paper transforms fuzzy number into clear number using the centroid method, thus we can research the traditional linear regression model which is transformed from the fuzzy linear regression model. The model’s in...This paper transforms fuzzy number into clear number using the centroid method, thus we can research the traditional linear regression model which is transformed from the fuzzy linear regression model. The model’s input and output are fuzzy numbers, and the regression coefficients are clear numbers. This paper considers the parameter estimation and impact analysis based on data deletion. Through the study of example and comparison with other models, it can be concluded that the model in this paper is applied easily and better.展开更多
文摘In this paper,a robust and consistent COVID-19 emergency decision-making approach is proposed based on q-rung linear diophantine fuzzy set(q-RLDFS),differential evolutionary(DE)optimization principles,and evidential reasoning(ER)methodology.The proposed approach uses q-RLDFS in order to represent the evaluating values of the alternatives corresponding to the attributes.DE optimization is used to obtain the optimal weights of the attributes,and ER methodology is used to compute the aggregated q-rung linear diophantine fuzzy values(q-RLDFVs)of each alternative.Then the score values of alternatives are computed based on the aggregated q-RLDFVs.An alternative with the maximum score value is selected as a better one.The applicability of the proposed approach has been illustrated in COVID-19 emergency decision-making system and sustainable energy planning management.Moreover,we have validated the proposed approach with a numerical example.Finally,a comparative study is provided with the existing models,where the proposed approach is found to be robust to perform better and consistent in uncertain environments.
基金supported by the Deanship of Scientific Research,Vice Presidency for Graduate Studies and Scientific Research,King Faisal University,Saudi Arabia[Grant No.GRANT3862].
文摘The idea of linear Diophantine fuzzy set(LDFS)theory with its control parameters is a strong model for machine learning and optimization under uncertainty.The activity times in the critical path method(CPM)representation procedures approach are initially static,but in the Project Evaluation and Review Technique(PERT)approach,they are probabilistic.This study proposes a novel way of project review and assessment methodology for a project network in a linear Diophantine fuzzy(LDF)environment.The LDF expected task time,LDF variance,LDF critical path,and LDF total expected time for determining the project network are all computed using LDF numbers as the time of each activity in the project network.The primary premise of the LDF-PERT approach is to address ambiguities in project network activity timesmore simply than other approaches such as conventional PERT,Fuzzy PERT,and so on.The LDF-PERT is an efficient approach to analyzing symmetries in fuzzy control systems to seek an optimal decision.We also present a new approach for locating LDF-CPM in a project network with uncertain and erroneous activity timings.When the available resources and activity times are imprecise and unpredictable,this strategy can help decision-makers make better judgments in a project.A comparison analysis of the proposed technique with the existing techniques has also been discussed.The suggested techniques are demonstrated with two suitable numerical examples.
文摘This paper addresses the problem of the fuzzy H ∞state feedback control for a class of uncertain nonlinear systems with time delay. The Takagi Sugeno (T S) mo del with time delay and parameter uncertainties is adopted for modeling of nonlinear system. The systematic design procedure for the fuzzy robust controller based on linear matrix inequality (LMI) is given. Some sufficient conditions are derived for the existence of fuzzy H ∞ state feedback controllers such that the closed loop system is asymptotically stable and the effect of the disturbance input on controlled output is reduced to a prescribed level. An example is given to demonstrate the effectiveness of the proposed method.
基金The National Natural Science Foundation of China(No.60474049,60835001)Specialized Research Fund for Doctoral Program of Higher Education(No.20090092120027)
文摘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.
基金supported by National Natural Science Foundation of China (No. 60574014, No. 60425310)Doctor Subject Foundation of China (No. 200805330004)+2 种基金Program for New Century Excellent Talents in University (No. NCET-06-0679)Natural Science Foundation of Hunan Province of China (No. 08JJ1010)Science Foundation of Education Department of Hunan Province (No. 08C106)
文摘This paper investigates the robust tracking control problcm for a class of nonlinear networked control systems （NCSs） using the Takagi-Sugeno （T-S） fuzzy model approach. Based on a time-varying delay system transformed from the NCSs, an augmented Lyapunov function containing more useful information is constructed. A less conservative sufficient condition is established such that the closed-loop systems stability and time-domain integral quadratic constraints （IQCs） are satisfied while both time-varying network- induced delays and packet losses are taken into account. The fuzzy tracking controllers design scheme is derived in terms of linear matrix inequalities （LMIs） and parallel distributed compensation （PDC）. Furthermore, robust stabilization criterion for nonlinear NCSs is given as an extension of the tracking control result. Finally, numerical simulations are provided to illustrate the effectiveness and merits of the proposed method.
文摘The problem of designing fuzzy static output feedback controller for T-S discrete-time fuzzy bilinear system （DFBS） is presented. Based on parallel distribution compensation method, some sufficient conditions are derived to guarantee the stability of the overall fuzzy system. The stabilization conditions are further formulated into linear matrix inequality （LMI） so that the desired controller can be easily obtained by using the Matlab LMI toolbox. In comparison with the existing results, the drawbacks, such as coordinate transformation, same output matrices, have been elim- inated. Finally, a simulation example shows that the approach is effective.
基金the National Natural Science Foundation of China (90716028 and 90405011).
文摘A robust adaptive trajectory linearization control （RATLC） algorithm for a class of nonlinear systems with uncertainty and disturbance based on the T-S fuzzy system is presented. The unknown disturbance and uncertainty are estimated by the T-S fuzzy system, and a robust adaptive control law is designed by the Lyapunov theory. Irrespective of whether the dimensions of the system and the rules of the fuzzy system are large or small, there is only one parameter adjusting on line. Uniformly ultimately boundedness of all signals of the composite closed-loop system are proved by theory analysis. Finally, a numerical example is studied based on the proposed method. The simulation results demonstrate the effectiveness and robustness of the control scheme.
基金supported by the National Natural Science Foundation of China (70771025)the Fundamental Research Funds for the Central Universities of Hohai University (2009B04514)Humanities and Social Sciences Foundations of Ministry of Education of China(10YJA630067)
文摘The multiple attribute decision making problems are studied, in which the information about attribute weights is partly known and the attribute values take the form of intuitionistic fuzzy numbers. The operational laws of intuitionistic fuzzy numbers are introduced, and the score function and accuracy function are presented to compare the intuitionistic fuzzy numbers. The intuitionistic fuzzy ordered weighted averaging （IFOWA） operator which is an extension of the well-known ordered weighted averaging （OWA） operator is investigated to aggregate the intuitionistic fuzzy information. In order to determine the weights of intuitionistic fuzzy ordered weighted averaging operator, a linear goal programming procedure is proposed for learning the weights from data. Finally, an example is illustrated to verify the effectiveness and practicability of the developed method.
文摘Intuitionistic Fuzzy Set (IFS) can be used as a general tool for modeling problems of decision making under uncertainty where, the degree of rejection is defined simultaneously with the degree of acceptance of a piece of information in such a way that these degrees are not complement to each other. Accordingly, an attempt is made to solve intuitionistic fuzzy linear programming problems using a technique based on an earlier technique proposed by Zimmermann to solve fuzzy linear programming problem. Our proposed technique does not require the existing ranking of intuitionistic fuzzy numbers. This method is also different from the existing weight assignment method or the Angelov’s method. A comparative study is undertaken and interesting results have been presented.
基金Project (No. 60421002) supported by the National Natural ScienceFoundation of China
文摘An extended robust model predictive control approach for input constrained discrete uncertain nonlinear systems with time-delay based on a class of uncertain T-S fuzzy models that satisfy sector bound condition is presented. In this approach, the minimization problem of the “worst-case” objective function is converted into the linear objective minimization problem in- volving linear matrix inequalities (LMIs) constraints. The state feedback control law is obtained by solving convex optimization of a set of LMIs. Sufficient condition for stability and a new upper bound on robust performance index are given for these kinds of uncertain fuzzy systems with state time-delay. Simulation results of CSTR process show that the proposed robust predictive control approach is effective and feasible.
文摘Two existing methods for solving a class of fuzzy linear programming (FLP) problems involving symmetric trapezoidal fuzzy numbers without converting them to crisp linear programming problems are the fuzzy primal simplex method proposed by Ganesan and Veeramani [1] and the fuzzy dual simplex method proposed by Ebrahimnejad and Nasseri [2]. The former method is not applicable when a primal basic feasible solution is not easily at hand and the later method needs to an initial dual basic feasible solution. In this paper, we develop a novel approach namely the primal-dual simplex algorithm to overcome mentioned shortcomings. A numerical example is given to illustrate the proposed approach.
基金Research financially supported by Changwon National University in 2009
文摘Takagi-Sugeno(T-S) fuzzy model is difficult to be linearized because of membership functions included.So,novel T-S fuzzy state transformation and T-S fuzzy feedback are proposed for the linearization of T-S fuzzy system.The novel T-S fuzzy state transformation is the fuzzy combination of local linear transformation which transforms local linear models in the T-S fuzzy model into the local linear controllable canonical models.The fuzzy combination of local linear controllable canonical model gives controllable canonical T-S fuzzy model and then nonlinear feedback is obtained easily.After the linearization of T-S fuzzy model,a robust H∞ controller with the robustness of sliding model control(SMC) is designed.As a result,controlled T-S fuzzy system shows the performance of H∞ control and the robustness of SMC.
文摘The existing concepts of picture fuzzy sets(PFS),spherical fuzzy sets(SFSs),T-spherical fuzzy sets(T-SFSs)and neutrosophic sets(NSs)have numerous applications in decision-making problems,but they have various strict limitations for their satisfaction,dissatisfaction,abstain or refusal grades.To relax these strict constraints,we introduce the concept of spherical linearDiophantine fuzzy sets(SLDFSs)with the inclusion of reference or control parameters.A SLDFSwith parameterizations process is very helpful formodeling uncertainties in themulti-criteria decisionmaking(MCDM)process.SLDFSs can classify a physical systemwith the help of reference parameters.We discuss various real-life applications of SLDFSs towards digital image processing,network systems,vote casting,electrical engineering,medication,and selection of optimal choice.We show some drawbacks of operations of picture fuzzy sets and their corresponding aggregation operators.Some new operations on picture fuzzy sets are also introduced.Some fundamental operations on SLDFSs and different types of score functions of spherical linear Diophantine fuzzy numbers(SLDFNs)are proposed.New aggregation operators named spherical linear Diophantine fuzzy weighted geometric aggregation(SLDFWGA)and spherical linear Diophantine fuzzy weighted average aggregation(SLDFWAA)operators are developed for a robust MCDM approach.An application of the proposed methodology with SLDF information is illustrated.The comparison analysis of the final ranking is also given to demonstrate the validity,feasibility,and efficiency of the proposed MCDM approach.
基金supported by the Program for Natural Science Foundation of Beijing (4062030)Young Teacher Research Foundation of North China Electric Power University
文摘The problem of fuzzy modeling for state and input time-delays systems with a class of nonlinear uncertainties by fuzzy T-S model is addressed.By using the linear matrix inequality（LMI） method, the problem of fuzzy robust H ∞ controller design for the system is studied.Assuming that the nonlinear uncertain functions in the model considered are gain-bounded, a sufficient condition for the robustly asymptotic stability of the closed-loop system is obtained via Lyapunov stability theory.By solving the LMI, a feedback control law which guarantees the robustly asymptotic stability of the closed-loop system is constructed and the effect of the disturbance input on the controlled output is ruduced to a prescribed level.
基金Supported by the National Natural Science Foundation of China(71471140,71171150,71103135)
文摘In this paper, we propose an interactive method for solving the multilevel linear programming problems based on the intuitionistic fuzzy set theory. Firstly, the membership function and the non-membership function are introduced to describe the uncertainty of the decision makers. Secondly, a satisfactory solution is derived by updating the minimum satisfactory degrees with considerations of the overall satisfactory balance among all levels. In addition, the steps of the proposed method are given in this paper. Finally, numerical examples illustrate the feasibility of this method.
文摘Under non-random uncertainty, a new idea of finding a possibly optimal solution for linear programming problem is examined in this paper. It is an application of the intuitionistic fuzzy set concept within scope of the existing fuzzy optimization. Here, we solve a linear programming problem (LPP) in an intuitionistic fuzzy environment and compare the result with the solution obtained from other existing techniques. In the process, the result of associated fuzzy LPP is also considered for a better understanding.
基金This work was supported by National Natural Science Foundation of PRC (No. 60574084)National 863 Project (No. 2006AA04Z428)the National 973 Program (No. 2002CB312200) of PRC.
文摘This paper is concerned with the robust reliable memory controller design for a class of fuzzy uncertain systems with timevarying delay. The system under consideration is more general than those in other existent works. The controller, which is dependent on the magnitudes and derivative of the delay, is proposed in terms of linear matrix inequality （LMI）. The closed-loop system is asymptotically stable for all admissible uncertainties as well as actuator faults. A numerical example is presented for illustration.
文摘A fuzzy logic compensator is designed for feedback linearizable nonlinear systems with deadzone nonlinearity. The classification property of fuzzy logic systems makes them a natural candidate for the rejection of errors induced by the deadzone, which has regions in which it behaves differently. A tuning algorithm is given for the fuzzy logic parameters, so that the deadzone compensation scheme becomes adaptive, guaranteeing small tracking errors and bounded parameter estimates. Formal nonlinear stability proofs are given to show that the tracking error is small. The fuzzy logic deadzone compensator is simulated on a one-link robot system to show its efficacy.
文摘This paper transforms fuzzy number into clear number using the centroid method, thus we can research the traditional linear regression model which is transformed from the fuzzy linear regression model. The model’s input and output are fuzzy numbers, and the regression coefficients are clear numbers. This paper considers the parameter estimation and impact analysis based on data deletion. Through the study of example and comparison with other models, it can be concluded that the model in this paper is applied easily and better.
