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
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
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
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 comprised of the modeling and optimization of a multi objective linear programming problem in fuzzy environment in which some goals are fractional and some are linear. Here, we present a new approach for...This paper is comprised of the modeling and optimization of a multi objective linear programming problem in fuzzy environment in which some goals are fractional and some are linear. Here, we present a new approach for its solution by using α-cut of fuzzy numbers. In this proposed method, we first define membership function for goals by introducing non-deviational variables for each of objective functions with effective use of α-cut intervals to deal with uncertain parameters being represented by fuzzy numbers. In the optimization process the under deviational variables are minimized for finding a most satisfactory solution. The developed method has also been implemented on a problem for illustration and comparison.展开更多
This paper studies a time-variant multi-objective linear fractional transportation problem. In reality, transported goods should reach in destinations within a specific time. Considering the importance of time, a time...This paper studies a time-variant multi-objective linear fractional transportation problem. In reality, transported goods should reach in destinations within a specific time. Considering the importance of time, a time-variant multi-objective linear fractional transportation problem is formulated here. We take into account the parameters as cost, supply and demand are interval valued that involved in the proposed model, so we treat the model as a multi-objective linear fractional interval transportation problem. To solve the formulated model, we first convert it into a deterministic form using a new transformation technique and then apply fuzzy programming to solve it. The applicability of our proposed method is shown by considering two numerical examples. At last, conclusions and future research directions regarding our study is included.展开更多
The objective of the paper is to deal with a kind of possibilistic linear programming (PLP) problem involving multiple objectives of conflicting nature. In particular, we have considered a multi objective linear progr...The objective of the paper is to deal with a kind of possibilistic linear programming (PLP) problem involving multiple objectives of conflicting nature. In particular, we have considered a multi objective linear programming (MOLP) problem whose objective is to simultaneously minimize cost and maximize profit in a supply chain where cost and profit coefficients, and related parameters such as available supply, forecast demand and budget are fuzzy with trapezoidal fuzzy numbers. An example is given to illustrate the strategy used to solve the aforesaid PLP problem.展开更多
Increasing demand for water from all sectors presents a challenge for policy makers to improve water allocation policies for storage reservoirs. In addition, there are many other organisms and species present in river...Increasing demand for water from all sectors presents a challenge for policy makers to improve water allocation policies for storage reservoirs. In addition, there are many other organisms and species present in river waters that also require water for their survival. Due to the lack of awareness many times the minimum required quantity and quality of water for river ecosystem is not made available at downstream of storage reservoirs. So, a sustainable approach is required in reservoir operations to maintain the river ecosystem with environmental flow while meeting the other demands. Multi-objective, multi-reservoir operation model developed with Python programming using Fuzzy Linear Programing method incorporating environmental flow requirement of river is presented in this paper. Objective of maximization of irrigation release is considered for first run. In second run maximization of releases for hydropower generation is considered as objective. Further both objectives are fuzzified by incorporating linear membership function and solved to maximize fuzzified objective function simultaneously by maximizing satisfaction level indicator (λ). The optimal reservoir operation policy is presented considering constraints including Irrigation release, Turbine release, Reservoir storage, Environmental flow release and hydrologic continuity. Model applied for multi-reservoir system consists of four reservoirs, i.e., Jayakwadi Stage-I Reservoir (R1), Jayakwadi Stage-II Reservoir (R2), Yeldari Reservoir (R3), Siddheshwar Reservoir (R4) in Godavari River sub-basin from Marathwada region of Maharashtra State, India.展开更多
In this paper, we establish a model to analyze the influence of widespread use of electric vehicle on environment, society and economist based on Fuzzy Comprehensive Evaluation method. We set the fuzzy objects are int...In this paper, we establish a model to analyze the influence of widespread use of electric vehicle on environment, society and economist based on Fuzzy Comprehensive Evaluation method. We set the fuzzy objects are internal combustion engine vehicles, pure electric vehicles and hybrid electric vehicles. Considering the difference of environment, society and economics, we use of three different kinds to define the fuzzy evaluation factor sets. According to the data and calculating results, we finally obtain fuzzy synthetical evaluation matrix. Through comparing and analysis, we draw such conclusion that the widespread using of electric vehicle is benefit for both environment and economics, while has disadvantageous influence for some aspects on society. In Section 3, we establish a model to estimate the influence of widespread use of electric vehicles on energy saving. According to the proportion of coal resources in the whole energies, we use Linear Regression Model to forecast the development situation in the following several years. Contrasting energy consumptions of electric vehicles and internal combustion engine vehicles, we calculate the whole energies saved by widespread use of electric vehicles. In Section 4, we establish a multi-objective programming model to plan the number and type of power station. Considering the thermal power, hydropower, nuclear power and solar power as four ways, combined with the funds of setting up power station, running funds and the cost of dealing with the pollutants, we find the objective function and four constraints, and finally we reach optimal solution using lingo software.展开更多
Suppliers play the vital role of ensuring the continuous supply of goods to themarket for businesses.If businesses do not maintain a strong bond with their suppliers,they may not be able to secure a steady supply of g...Suppliers play the vital role of ensuring the continuous supply of goods to themarket for businesses.If businesses do not maintain a strong bond with their suppliers,they may not be able to secure a steady supply of goods and products for their customers.As a result of failure to deliver products,the production and business activities of the business can be delayed which leads to the loss of customers.Normally,each trading enterprise will have a variety of commodity supply chains withmultiple suppliers.Suppliers play an important role and contribute to the value of the entire supply chain.Should any supplier encounters a problem,the whole supply chain of businesses will be affected and could lead to not guaranteeing the stable supply to the market.Thus,suppliers can be seen as a threat to businesses where they have the ability to increase input prices or decrease the quality of the required products and services they provide.The quantity of the business,and the supply lead time directly affect the operations and reduce the profitability of the business.The paper mainly focuses on the supplier selection problemunder a variety of price level and product families when using a two-phase fuzzy multi-objective linear programming.The objectives of the proposed model are to minimize the total purchasing and ordering cost in order to reduce the quantity of defective materials and the late-delivery components from suppliers.Moreover,the piecewise linear membership function is applied in themodel to determine an optimal solution which is based on the requirement of decision makers under their fuzzy environment.The results of this study can be applied in various business environment and provide a reliable decision tool for choosing potential suppliers relating to these objectives.Based on the results,the company canmake a good decision on supplier selection;therefore,the company can improve the quality and quantity of their final product.This is because,the best supplier can supply raw material using just-in-time application and reduce production risk on the manufacturing process.展开更多
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.
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.
文摘This paper is comprised of the modeling and optimization of a multi objective linear programming problem in fuzzy environment in which some goals are fractional and some are linear. Here, we present a new approach for its solution by using α-cut of fuzzy numbers. In this proposed method, we first define membership function for goals by introducing non-deviational variables for each of objective functions with effective use of α-cut intervals to deal with uncertain parameters being represented by fuzzy numbers. In the optimization process the under deviational variables are minimized for finding a most satisfactory solution. The developed method has also been implemented on a problem for illustration and comparison.
文摘This paper studies a time-variant multi-objective linear fractional transportation problem. In reality, transported goods should reach in destinations within a specific time. Considering the importance of time, a time-variant multi-objective linear fractional transportation problem is formulated here. We take into account the parameters as cost, supply and demand are interval valued that involved in the proposed model, so we treat the model as a multi-objective linear fractional interval transportation problem. To solve the formulated model, we first convert it into a deterministic form using a new transformation technique and then apply fuzzy programming to solve it. The applicability of our proposed method is shown by considering two numerical examples. At last, conclusions and future research directions regarding our study is included.
文摘The objective of the paper is to deal with a kind of possibilistic linear programming (PLP) problem involving multiple objectives of conflicting nature. In particular, we have considered a multi objective linear programming (MOLP) problem whose objective is to simultaneously minimize cost and maximize profit in a supply chain where cost and profit coefficients, and related parameters such as available supply, forecast demand and budget are fuzzy with trapezoidal fuzzy numbers. An example is given to illustrate the strategy used to solve the aforesaid PLP problem.
文摘Increasing demand for water from all sectors presents a challenge for policy makers to improve water allocation policies for storage reservoirs. In addition, there are many other organisms and species present in river waters that also require water for their survival. Due to the lack of awareness many times the minimum required quantity and quality of water for river ecosystem is not made available at downstream of storage reservoirs. So, a sustainable approach is required in reservoir operations to maintain the river ecosystem with environmental flow while meeting the other demands. Multi-objective, multi-reservoir operation model developed with Python programming using Fuzzy Linear Programing method incorporating environmental flow requirement of river is presented in this paper. Objective of maximization of irrigation release is considered for first run. In second run maximization of releases for hydropower generation is considered as objective. Further both objectives are fuzzified by incorporating linear membership function and solved to maximize fuzzified objective function simultaneously by maximizing satisfaction level indicator (λ). The optimal reservoir operation policy is presented considering constraints including Irrigation release, Turbine release, Reservoir storage, Environmental flow release and hydrologic continuity. Model applied for multi-reservoir system consists of four reservoirs, i.e., Jayakwadi Stage-I Reservoir (R1), Jayakwadi Stage-II Reservoir (R2), Yeldari Reservoir (R3), Siddheshwar Reservoir (R4) in Godavari River sub-basin from Marathwada region of Maharashtra State, India.
文摘In this paper, we establish a model to analyze the influence of widespread use of electric vehicle on environment, society and economist based on Fuzzy Comprehensive Evaluation method. We set the fuzzy objects are internal combustion engine vehicles, pure electric vehicles and hybrid electric vehicles. Considering the difference of environment, society and economics, we use of three different kinds to define the fuzzy evaluation factor sets. According to the data and calculating results, we finally obtain fuzzy synthetical evaluation matrix. Through comparing and analysis, we draw such conclusion that the widespread using of electric vehicle is benefit for both environment and economics, while has disadvantageous influence for some aspects on society. In Section 3, we establish a model to estimate the influence of widespread use of electric vehicles on energy saving. According to the proportion of coal resources in the whole energies, we use Linear Regression Model to forecast the development situation in the following several years. Contrasting energy consumptions of electric vehicles and internal combustion engine vehicles, we calculate the whole energies saved by widespread use of electric vehicles. In Section 4, we establish a multi-objective programming model to plan the number and type of power station. Considering the thermal power, hydropower, nuclear power and solar power as four ways, combined with the funds of setting up power station, running funds and the cost of dealing with the pollutants, we find the objective function and four constraints, and finally we reach optimal solution using lingo software.
文摘Suppliers play the vital role of ensuring the continuous supply of goods to themarket for businesses.If businesses do not maintain a strong bond with their suppliers,they may not be able to secure a steady supply of goods and products for their customers.As a result of failure to deliver products,the production and business activities of the business can be delayed which leads to the loss of customers.Normally,each trading enterprise will have a variety of commodity supply chains withmultiple suppliers.Suppliers play an important role and contribute to the value of the entire supply chain.Should any supplier encounters a problem,the whole supply chain of businesses will be affected and could lead to not guaranteeing the stable supply to the market.Thus,suppliers can be seen as a threat to businesses where they have the ability to increase input prices or decrease the quality of the required products and services they provide.The quantity of the business,and the supply lead time directly affect the operations and reduce the profitability of the business.The paper mainly focuses on the supplier selection problemunder a variety of price level and product families when using a two-phase fuzzy multi-objective linear programming.The objectives of the proposed model are to minimize the total purchasing and ordering cost in order to reduce the quantity of defective materials and the late-delivery components from suppliers.Moreover,the piecewise linear membership function is applied in themodel to determine an optimal solution which is based on the requirement of decision makers under their fuzzy environment.The results of this study can be applied in various business environment and provide a reliable decision tool for choosing potential suppliers relating to these objectives.Based on the results,the company canmake a good decision on supplier selection;therefore,the company can improve the quality and quantity of their final product.This is because,the best supplier can supply raw material using just-in-time application and reduce production risk on the manufacturing process.
