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
Purpose–The purpose of this paper is to study a nascent theory and an emerging concept of solving a fully fuzzy linear system(FFLS)with no non negative restrictions on the triangular fuzzy numbers chosen as parameter...Purpose–The purpose of this paper is to study a nascent theory and an emerging concept of solving a fully fuzzy linear system(FFLS)with no non negative restrictions on the triangular fuzzy numbers chosen as parameters.Two new simplified computational methods are proposed to solve a FFLS without any sign restrictions.The first method eliminates the non-negativity constraint from the coefficient matrix while the second method eliminates the constraint of non-negativity on the solution vector.The methods are introduced with an objective to broaden the domain of fuzzy linear systems to encompass a wide range of problems occurring in reality.Design/methodology/approach–The design of numerical methods is motivated by decomposing the fuzzy based linear system into its equivalent crisp linear form which can be further solved by variety of classical methods to solve a crisp linear system.Further the paper investigates Schur complement technique to solve the crisp equivalent of the FFLS.Findings–The results that are obtained reveal interesting properties of a FFLS.By using the proposed methods,the authors are able to check the consistency of the fuzzy linear system as well as obtain the nature of obtained solutions,i.e.trivial,unique or infinite.Further it is also seen that an n£n FFLS may yield finitely many solutions which may not be entirely feasible(strong).Also the methods successfully remove the non-negativity restriction on the coefficient matrix and the solution vector,respectively.Research limitations/implications–Evolving methods with better computational complexity and that which remove the non-negativity restriction jointly on all the parameters are left as an open problem.Originality/value–The proposed methods are new and conceptually simple to understand and apply in several scientific areas where fuzziness persists.The methods successfully remove several constraints that have been employed exhaustively by researchers and thus eventually tend to widen the breadth of applicability and usability of fuzzy linear models in real life situations.Heretofore,the usability of FFLS is largely dormant.展开更多
A Mobile Ad-hoc NETwork(MANET)contains numerous mobile nodes,and it forms a structure-less network associated with wireless links.But,the node movement is the key feature of MANETs;hence,the quick action of the nodes ...A Mobile Ad-hoc NETwork(MANET)contains numerous mobile nodes,and it forms a structure-less network associated with wireless links.But,the node movement is the key feature of MANETs;hence,the quick action of the nodes guides a link failure.This link failure creates more data packet drops that can cause a long time delay.As a result,measuring accurate link failure time is the key factor in the MANET.This paper presents a Fuzzy Linear Regression Method to measure Link Failure(FLRLF)and provide an optimal route in the MANET-Internet of Things(IoT).This work aims to predict link failure and improve routing efficiency in MANET.The Fuzzy Linear Regression Method(FLRM)measures the long lifespan link based on the link failure.The mobile node group is built by the Received Signal Strength(RSS).The Hill Climbing(HC)method selects the Group Leader(GL)based on node mobility,node degree and node energy.Additionally,it uses a Data Gathering node forward the infor-mation from GL to the sink node through multiple GL.The GL is identified by linking lifespan and energy using the Particle Swarm Optimization(PSO)algo-rithm.The simulation results demonstrate that the FLRLF approach increases the GL lifespan and minimizes the link failure time in the MANET.展开更多
Aiming at the problems of output voltage fluctuation and current total harmonic distortion(THD)in the front stage totem-pole bridgeless PFC of two-stage V2G(Vehicle to Grid)vehicle-mounted bi-directional converter,a f...Aiming at the problems of output voltage fluctuation and current total harmonic distortion(THD)in the front stage totem-pole bridgeless PFC of two-stage V2G(Vehicle to Grid)vehicle-mounted bi-directional converter,a fuzzy linear active disturbance rejection control strategy for V2G front-stage AC-DC power conversion system is proposed.Firstly,the topologicalworkingmode of the totem-pole bridgeless PFC is analyzed,and themathematical model is established.Combined with the system model and the linear active disturbance rejection theory,a double closed-loop controller is designed with the second-order linear active disturbance rejection control as the voltage outer loop and PI control as the current inner loop.The controller can realize self-adaptive tuning of the proportional gain coefficient of the active disturbance rejection controller through fuzzy reasoning and realize self-adaptive control.Simulation and experimental results show that this method can better solve the problems of slow system response and high total harmonic distortion rate of input current and effectively improve the system’s robustness.展开更多
Planning and production optimization within multiple mines or several work sites (entities) mining systems by using fuzzy linear programming (LP) was studied. LP is the most commonly used operations research metho...Planning and production optimization within multiple mines or several work sites (entities) mining systems by using fuzzy linear programming (LP) was studied. LP is the most commonly used operations research methods in mining engineering. After the introductory review of properties and limitations of applying LP, short reviews of the general settings of deterministic and fuzzy LP models are presented. With the purpose of comparative analysis, the application of both LP models is presented using the example of the Bauxite Basin Niksic with five mines. After the assessment, LP is an efficient mathematical modeling tool in production planning and solving many other single-criteria optimization problems of mining engineering. After the comparison of advantages and deficiencies of both deterministic and fuzzy LP models, the conclusion presents benefits of the fuzzy LP model but is also stating that seeking the optimal plan of production means to accomplish the overall analysis that will encompass the LP model approaches.展开更多
A multi-objective linear programming problem is made from fuzzy linear programming problem. It is due the fact that it is used fuzzy programming method during the solution. The Multi objective linear programming probl...A multi-objective linear programming problem is made from fuzzy linear programming problem. It is due the fact that it is used fuzzy programming method during the solution. The Multi objective linear programming problem can be converted into the single objective function by various methods as Chandra Sen’s method, weighted sum method, ranking function method, statistical averaging method. In this paper, Chandra Sen’s method and statistical averaging method both are used here for making single objective function from multi-objective function. Two multi-objective programming problems are solved to verify the result. One is numerical example and the other is real life example. Then the problems are solved by ordinary simplex method and fuzzy programming method. It can be seen that fuzzy programming method gives better optimal values than the ordinary simplex method.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
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
A new fully fuzzy linear programming (FFLP) problem with fuzzy equality constraints is discussed. Using deviation degree measures, the FFLP problem is transformed into a crisp 6-parametric linear programming (LP) ...A new fully fuzzy linear programming (FFLP) problem with fuzzy equality constraints is discussed. Using deviation degree measures, the FFLP problem is transformed into a crisp 6-parametric linear programming (LP) problem. Giving the value of deviation degree in each constraint, the 6-fuzzy optimal solution of the FFLP problem can be obtained by solving this LP problem. An algorithm is also proposed to find a balance-fuzzy optimal solution between two goals in conflict: to improve the values of the objective function and to decrease the values of the deviation degrees. A numerical example is solved to illustrate the proposed method.展开更多
In this paper, the statistical averaging method and the new statistical averaging methods have been used to solve the fuzzy multi-objective linear programming problems. These methods have been applied to form a single...In this paper, the statistical averaging method and the new statistical averaging methods have been used to solve the fuzzy multi-objective linear programming problems. These methods have been applied to form a single objective function from the fuzzy multi-objective linear programming problems. At first, a numerical example of solving fuzzy multi-objective linear programming problem has been provided to validate the maximum risk reduction by the proposed method. The proposed method has been applied to assess the risk of damage due to natural calamities like flood, cyclone, sidor, and storms at the coastal areas in Bangladesh. The proposed method of solving the fuzzy multi-objective linear programming problems by the statistical method has been compared with the Chandra Sen’s method. The numerical results show that the proposed method maximizes the risk reduction capacity better than Chandra Sen’s method.展开更多
The Robogymnast is a highly complex,three-link system based on the triple-inverted pendulum and is modelled on the human example of a gymnast suspended by their hands from the high bar and executing larger and larger ...The Robogymnast is a highly complex,three-link system based on the triple-inverted pendulum and is modelled on the human example of a gymnast suspended by their hands from the high bar and executing larger and larger upswings to eventually rotate fully.The links of the Robogymnast correspond respectively to the arms,trunk,and lower limbs of the gymnast,and from its three joints,one is under passive operation,while the remaining two are powered.The passive top joint poses severe challenges in attaining the smooth movement control needed to operate the Robogymnast effectively.This study assesses four types of controllers used for systems operation and identifies how far response stabilisation is achieved with each.The system is simulated using MATLAB Simulink,with findings generated regarding rising and settling time,as well as overshoot.The research primarily seeks to exam-ine the application of a linear quadratic regulator controller,proportional-integral-derivative controller,fuzzy linear quadratic regulator controller and linear quadratic regulator-proportional-integral-derivative controller for this type of system and comparisons between the different controllers to demon-strate successful performance,which highlights the claimed advantages of the proposed system.展开更多
The objective of this paper is to deal with a kind of fuzzy linear programming problem based on interval\|valued fuzzy sets (IVFLP) through the medium of procedure that turns IVFLP into parametric linear programming v...The objective of this paper is to deal with a kind of fuzzy linear programming problem based on interval\|valued fuzzy sets (IVFLP) through the medium of procedure that turns IVFLP into parametric linear programming via the mathematical programming.Some useful results for the benefit of solving IVFLP are expounded and proved,developed and discussed.Furthermore,that the proposed techniques in this paper allow the decision\|maker to assign a different degree of importance can provide a useful way to efficiently help the decision\|maker make their decisions.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 the present study the MOFLP models have been developed for the optimal cropping pattern planning which maximizes the four objectives such as Net Benefits (NB), Crop Production (CP), Employment Generation (EG) and M...In the present study the MOFLP models have been developed for the optimal cropping pattern planning which maximizes the four objectives such as Net Benefits (NB), Crop Production (CP), Employment Generation (EG) and Manure Utilization (MU) under conflicting situation and also, for maximization of Releases for Irrigation (RI) and Releases for Power (RP) simultaneously under uncertainty by considering the fuzziness in the objective functions. The developed models have been applied using the LINGO 13 (Language for Interactive General Optimization) optimization software to the case study of the Jayakwadi Project Stage-II across Sindhphana River, in the State of Maharashtra India. The various constraints have been taken into consideration like sowing area, affinity to crop, labour availability, manure availability, water availability for optimal cropping pattern planning. Similarly constraints to find the optimal reservoir operating policy are releases for power and turbine capacity, irrigation demand, reservoir storage capacity, reservoir storage continuity. The level of satisfaction for a compromised solution of optimal cropping pattern planning for four conflicting objectives under fuzzy environment is worked out to be λ = 0.68. The MOFLP compromised solution provides NB = 1088.46 (Million Rupees), CP = 241003 (Tons), EG = 23.13 (Million Man days) and MU = 111454.70 (Tons) respectively. The compromised solution for optimal operation of multi objective reservoir yields the level of satisfaction (λ) = 0.533 for maximizing the releases for irrigation and power simultaneously by satisfying the constraint of the system under consideration. The compromised solution provides the optimal releases, i.e. RI = 348.670 Mm3 and RP = 234.285 Mm3 respectively.展开更多
Purpose-The purpose of this paper is to stabilize the type-2 Takagi-Sugeno(T-S)fuzzy systems with the sufficient and guaranteed stability conditions.The given conditions efficaciously handle parameter uncertainties by...Purpose-The purpose of this paper is to stabilize the type-2 Takagi-Sugeno(T-S)fuzzy systems with the sufficient and guaranteed stability conditions.The given conditions efficaciously handle parameter uncertainties by the upper and lower membership functions of the type-2 fuzzy sets(FSs).Design/methodology/approach-This paper reports on a relevant study of stable fuzzy controllers and type-2 T-S fuzzy systems and reported that the synthesis of controller for nonlinear systems described by the type-2 T-S fuzzy model is a key problem and it can be resolve to convex problems via linear matrix inequalities(LMIs).Findings-The multigain fuzzy controllers are established to improve the solvability of the stability conditions,and the authors design multigain fuzzy controllers which have extensive information of upper and lower membership grades.Consequently,the authors derive the traditional stability condition in terms of LMIs.One simulation examples illustrate the effectiveness and robustness of the derived stabilization conditions.Originality/value-The uncertain MIMO nonlinear system described by Type-2 Takagi-Sugeno(T-S)fuzzy model,and successively LMI approach used to determine the system stability conditions.The proposed control approach will give superior fault-tolerant control permanence under the actuator fault[partial loss of effectiveness(LOE)].Also the controller robust against the unmeasurable process disturbances.Additionally,the statistical z-test are carried out to validate the proposed control approach against the control approach proposed by Himanshukumar and Vipul(2019a).展开更多
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Purpose–The purpose of this paper is to study a nascent theory and an emerging concept of solving a fully fuzzy linear system(FFLS)with no non negative restrictions on the triangular fuzzy numbers chosen as parameters.Two new simplified computational methods are proposed to solve a FFLS without any sign restrictions.The first method eliminates the non-negativity constraint from the coefficient matrix while the second method eliminates the constraint of non-negativity on the solution vector.The methods are introduced with an objective to broaden the domain of fuzzy linear systems to encompass a wide range of problems occurring in reality.Design/methodology/approach–The design of numerical methods is motivated by decomposing the fuzzy based linear system into its equivalent crisp linear form which can be further solved by variety of classical methods to solve a crisp linear system.Further the paper investigates Schur complement technique to solve the crisp equivalent of the FFLS.Findings–The results that are obtained reveal interesting properties of a FFLS.By using the proposed methods,the authors are able to check the consistency of the fuzzy linear system as well as obtain the nature of obtained solutions,i.e.trivial,unique or infinite.Further it is also seen that an n£n FFLS may yield finitely many solutions which may not be entirely feasible(strong).Also the methods successfully remove the non-negativity restriction on the coefficient matrix and the solution vector,respectively.Research limitations/implications–Evolving methods with better computational complexity and that which remove the non-negativity restriction jointly on all the parameters are left as an open problem.Originality/value–The proposed methods are new and conceptually simple to understand and apply in several scientific areas where fuzziness persists.The methods successfully remove several constraints that have been employed exhaustively by researchers and thus eventually tend to widen the breadth of applicability and usability of fuzzy linear models in real life situations.Heretofore,the usability of FFLS is largely dormant.
文摘A Mobile Ad-hoc NETwork(MANET)contains numerous mobile nodes,and it forms a structure-less network associated with wireless links.But,the node movement is the key feature of MANETs;hence,the quick action of the nodes guides a link failure.This link failure creates more data packet drops that can cause a long time delay.As a result,measuring accurate link failure time is the key factor in the MANET.This paper presents a Fuzzy Linear Regression Method to measure Link Failure(FLRLF)and provide an optimal route in the MANET-Internet of Things(IoT).This work aims to predict link failure and improve routing efficiency in MANET.The Fuzzy Linear Regression Method(FLRM)measures the long lifespan link based on the link failure.The mobile node group is built by the Received Signal Strength(RSS).The Hill Climbing(HC)method selects the Group Leader(GL)based on node mobility,node degree and node energy.Additionally,it uses a Data Gathering node forward the infor-mation from GL to the sink node through multiple GL.The GL is identified by linking lifespan and energy using the Particle Swarm Optimization(PSO)algo-rithm.The simulation results demonstrate that the FLRLF approach increases the GL lifespan and minimizes the link failure time in the MANET.
基金supported by the Science and Technology Project of State Grid Corporation of China(W22KJ2722005)Tianyou Innovation Team of Lanzhou Jiaotong University(TY202009).
文摘Aiming at the problems of output voltage fluctuation and current total harmonic distortion(THD)in the front stage totem-pole bridgeless PFC of two-stage V2G(Vehicle to Grid)vehicle-mounted bi-directional converter,a fuzzy linear active disturbance rejection control strategy for V2G front-stage AC-DC power conversion system is proposed.Firstly,the topologicalworkingmode of the totem-pole bridgeless PFC is analyzed,and themathematical model is established.Combined with the system model and the linear active disturbance rejection theory,a double closed-loop controller is designed with the second-order linear active disturbance rejection control as the voltage outer loop and PI control as the current inner loop.The controller can realize self-adaptive tuning of the proportional gain coefficient of the active disturbance rejection controller through fuzzy reasoning and realize self-adaptive control.Simulation and experimental results show that this method can better solve the problems of slow system response and high total harmonic distortion rate of input current and effectively improve the system’s robustness.
文摘Planning and production optimization within multiple mines or several work sites (entities) mining systems by using fuzzy linear programming (LP) was studied. LP is the most commonly used operations research methods in mining engineering. After the introductory review of properties and limitations of applying LP, short reviews of the general settings of deterministic and fuzzy LP models are presented. With the purpose of comparative analysis, the application of both LP models is presented using the example of the Bauxite Basin Niksic with five mines. After the assessment, LP is an efficient mathematical modeling tool in production planning and solving many other single-criteria optimization problems of mining engineering. After the comparison of advantages and deficiencies of both deterministic and fuzzy LP models, the conclusion presents benefits of the fuzzy LP model but is also stating that seeking the optimal plan of production means to accomplish the overall analysis that will encompass the LP model approaches.
文摘A multi-objective linear programming problem is made from fuzzy linear programming problem. It is due the fact that it is used fuzzy programming method during the solution. The Multi objective linear programming problem can be converted into the single objective function by various methods as Chandra Sen’s method, weighted sum method, ranking function method, statistical averaging method. In this paper, Chandra Sen’s method and statistical averaging method both are used here for making single objective function from multi-objective function. Two multi-objective programming problems are solved to verify the result. One is numerical example and the other is real life example. Then the problems are solved by ordinary simplex method and fuzzy programming method. It can be seen that fuzzy programming method gives better optimal values than the ordinary simplex method.
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.
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.
基金supported by the National Natural Science Foundation of China(71202140)the Fundamental Research for the Central Universities(HUST:2013QN099)
文摘A new fully fuzzy linear programming (FFLP) problem with fuzzy equality constraints is discussed. Using deviation degree measures, the FFLP problem is transformed into a crisp 6-parametric linear programming (LP) problem. Giving the value of deviation degree in each constraint, the 6-fuzzy optimal solution of the FFLP problem can be obtained by solving this LP problem. An algorithm is also proposed to find a balance-fuzzy optimal solution between two goals in conflict: to improve the values of the objective function and to decrease the values of the deviation degrees. A numerical example is solved to illustrate the proposed method.
文摘In this paper, the statistical averaging method and the new statistical averaging methods have been used to solve the fuzzy multi-objective linear programming problems. These methods have been applied to form a single objective function from the fuzzy multi-objective linear programming problems. At first, a numerical example of solving fuzzy multi-objective linear programming problem has been provided to validate the maximum risk reduction by the proposed method. The proposed method has been applied to assess the risk of damage due to natural calamities like flood, cyclone, sidor, and storms at the coastal areas in Bangladesh. The proposed method of solving the fuzzy multi-objective linear programming problems by the statistical method has been compared with the Chandra Sen’s method. The numerical results show that the proposed method maximizes the risk reduction capacity better than Chandra Sen’s method.
文摘The Robogymnast is a highly complex,three-link system based on the triple-inverted pendulum and is modelled on the human example of a gymnast suspended by their hands from the high bar and executing larger and larger upswings to eventually rotate fully.The links of the Robogymnast correspond respectively to the arms,trunk,and lower limbs of the gymnast,and from its three joints,one is under passive operation,while the remaining two are powered.The passive top joint poses severe challenges in attaining the smooth movement control needed to operate the Robogymnast effectively.This study assesses four types of controllers used for systems operation and identifies how far response stabilisation is achieved with each.The system is simulated using MATLAB Simulink,with findings generated regarding rising and settling time,as well as overshoot.The research primarily seeks to exam-ine the application of a linear quadratic regulator controller,proportional-integral-derivative controller,fuzzy linear quadratic regulator controller and linear quadratic regulator-proportional-integral-derivative controller for this type of system and comparisons between the different controllers to demon-strate successful performance,which highlights the claimed advantages of the proposed system.
文摘The objective of this paper is to deal with a kind of fuzzy linear programming problem based on interval\|valued fuzzy sets (IVFLP) through the medium of procedure that turns IVFLP into parametric linear programming via the mathematical programming.Some useful results for the benefit of solving IVFLP are expounded and proved,developed and discussed.Furthermore,that the proposed techniques in this paper allow the decision\|maker to assign a different degree of importance can provide a useful way to efficiently help the decision\|maker make their decisions.
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.
文摘In the present study the MOFLP models have been developed for the optimal cropping pattern planning which maximizes the four objectives such as Net Benefits (NB), Crop Production (CP), Employment Generation (EG) and Manure Utilization (MU) under conflicting situation and also, for maximization of Releases for Irrigation (RI) and Releases for Power (RP) simultaneously under uncertainty by considering the fuzziness in the objective functions. The developed models have been applied using the LINGO 13 (Language for Interactive General Optimization) optimization software to the case study of the Jayakwadi Project Stage-II across Sindhphana River, in the State of Maharashtra India. The various constraints have been taken into consideration like sowing area, affinity to crop, labour availability, manure availability, water availability for optimal cropping pattern planning. Similarly constraints to find the optimal reservoir operating policy are releases for power and turbine capacity, irrigation demand, reservoir storage capacity, reservoir storage continuity. The level of satisfaction for a compromised solution of optimal cropping pattern planning for four conflicting objectives under fuzzy environment is worked out to be λ = 0.68. The MOFLP compromised solution provides NB = 1088.46 (Million Rupees), CP = 241003 (Tons), EG = 23.13 (Million Man days) and MU = 111454.70 (Tons) respectively. The compromised solution for optimal operation of multi objective reservoir yields the level of satisfaction (λ) = 0.533 for maximizing the releases for irrigation and power simultaneously by satisfying the constraint of the system under consideration. The compromised solution provides the optimal releases, i.e. RI = 348.670 Mm3 and RP = 234.285 Mm3 respectively.
基金The project outcome is Ph.D work of corresponding author of this article.This research received no external funding.The authors would also like to thank Department of Instrumentation and Control,Faculty of Technology,Dharmsinh Desai University,Nadiad 387001,Gujarat,India.
文摘Purpose-The purpose of this paper is to stabilize the type-2 Takagi-Sugeno(T-S)fuzzy systems with the sufficient and guaranteed stability conditions.The given conditions efficaciously handle parameter uncertainties by the upper and lower membership functions of the type-2 fuzzy sets(FSs).Design/methodology/approach-This paper reports on a relevant study of stable fuzzy controllers and type-2 T-S fuzzy systems and reported that the synthesis of controller for nonlinear systems described by the type-2 T-S fuzzy model is a key problem and it can be resolve to convex problems via linear matrix inequalities(LMIs).Findings-The multigain fuzzy controllers are established to improve the solvability of the stability conditions,and the authors design multigain fuzzy controllers which have extensive information of upper and lower membership grades.Consequently,the authors derive the traditional stability condition in terms of LMIs.One simulation examples illustrate the effectiveness and robustness of the derived stabilization conditions.Originality/value-The uncertain MIMO nonlinear system described by Type-2 Takagi-Sugeno(T-S)fuzzy model,and successively LMI approach used to determine the system stability conditions.The proposed control approach will give superior fault-tolerant control permanence under the actuator fault[partial loss of effectiveness(LOE)].Also the controller robust against the unmeasurable process disturbances.Additionally,the statistical z-test are carried out to validate the proposed control approach against the control approach proposed by Himanshukumar and Vipul(2019a).