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Solving Fuzzy Multi-Objective Linear Programming Problem by Applying Statistical Method 认领 引用 被引量：1
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作者 Samsun Nahar Marin Akter Md. Abdul Alim 《American Journal of Operations Research》 2022年第6期293-309,共17页
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
关键词 Fuzzy Multi-Objective Linear Programming Problem Fuzzy Linear Programming Problem Chandra Sen’s Method Statistical Averaging Method New Statistical Averaging Method
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Solving Multi-Objective Linear Programming Problem by Statistical Averaging Method with the Help of Fuzzy Programming Method 认领 引用
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作者 Samsun Nahar Marin Akter Md. Abdul Alim 《American Journal of Operations Research》 2023年第2期19-32,共14页
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
关键词 Fuzzy Programming Method Fuzzy Linear Programming Problem Multi-Objective Linear Programming Problem Statistical Averaging Method New Statistical Averaging Method
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Solving Intuitionistic Fuzzy Linear Programming Problem 认领 引用 被引量：4
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作者 Arpita Kabiraj Prasun Kumar Nayak Swapan Raha 《International Journal of Intelligence Science》 2019年第1期44-58,共15页
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
关键词 Intuitionistic Fuzzy Set Intuitionistic Index Intuitionistic Fuzzy Number Intuitionistic Fuzzy Linear Programming Problem Fuzzy Linear Programming Problem
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Solving Intuitionistic Fuzzy Linear Programming Problem—II 认领 引用 被引量：1
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作者 Arpita Kabiraj Prasun Kumar Nayak Swapan Raha 《International Journal of Intelligence Science》 2019年第4期93-110,共18页
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
关键词 Fuzzy Linear Programming Problem (FLPP) Intuitionistic Fuzzy Set (IFS) Intuitionistic Fuzzy Number (IFN) Intuitionistic Fuzzy Linear Programming Problem (IFLPP)
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Time variant multi-objective linear fractional interval-valued transportation problem 认领 引用 被引量：1
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作者 Dharmadas Mardanya Sankar Kumar Roy 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2022年第1期111-130,共20页
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
关键词 fractional transportation problem multi-objective optimization interval number time variant parameter fuzzy programming Pareto optimal solution
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Goal Programming for Solving Fractional Programming Problem in Fuzzy Environment 认领 引用 被引量：2
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作者 Anil Kumar Nishad Shiva Raj Singh 《Applied Mathematics》 2015年第14期2360-2374,共15页
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
关键词 Fuzzy Sets Trapezoidal Fuzzy Number (TFN) Multi-Objective Linear Programming Problem (MOLPP) Multi-Objective Linear Fractional Programming Problem (MOLFPP)
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An Approach to Solve a Possibilistic Linear Programming Problem 认领 引用
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作者 Ritika Chopra Ratnesh R. Saxena 《Applied Mathematics》 2014年第2期226-233,共8页
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
关键词 Multi Objective Linear Programming Problem Fuzzy Set Theory Trapezoidal Fuzzy Numbers Possibilistic Linear Programming Problem
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Sustainable Multi-Objective Multi-Reservoir Optimization Considering Environmental Flow 认领 引用 被引量：1
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作者 Pushpak D. Dabhade Dattatray G. Regulwar 《Journal of Water Resource and Protection》 CAS 2021年第12期945-956,共12页
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
关键词 Optimization Multi-Objective Analysis Multi-Reservoir Reservoir Operation Environmental Flow Linear Programming Fuzzy Logic
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Improving Supply Chain Performance Through Supplier Selection and Order Allocation Problem 认领 引用
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作者 Chia-Nan Wang Ming-Cheng Tsou +2 位作者 Chih-Hung Wang Viet Tinh Nguyen Pham Ngo Thi Phuong 《Computers, Materials & Continua》 SCIE EI 2022年第1期1667-1681,共15页
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
关键词 Supplier selection multi-objective linear programming multiprice level multi-product fuzzy sets
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The Impact on the Environment and Economy Due to the Introduction of Electric Cars: Based on the Fuzzy Synthetical Evaluation Method 认领 引用 被引量：1
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作者 Heli Gao 《Journal of Applied Mathematics and Physics》 2016年第12期2172-2185,共14页
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
关键词 Electric Vehicle Fuzzy Comprehensive Evaluation Linear Regression Model Multi-Objective Programming Model
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一类模糊线性规划的求解方法及应用 认领 引用 被引量：22
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作者 高淑萍 刘三阳 《系统工程与电子技术》 EI 北大核心 2005年第8期1412-1415,共4页
利用一种新的模糊数排序准则,提出了约束条件中含有三角模糊数的模糊线性规划转化为经典的线性规划的方法。与其他方法相比,该方法从理论上证明了得到的解优于其它解,约束条件个数少。用该方法求解了具有模糊等式约束的运输问题。通过... 利用一种新的模糊数排序准则,提出了约束条件中含有三角模糊数的模糊线性规划转化为经典的线性规划的方法。与其他方法相比,该方法从理论上证明了得到的解优于其它解,约束条件个数少。用该方法求解了具有模糊等式约束的运输问题。通过数值算例,进一步表明了提出方法的有效性和应用的广泛性。 展开更多
关键词 三角模糊数 排序准则 模糊线性规划 运输问题
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具有弹性约束的模糊运输问题求解 认领 引用 被引量：3
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作者 郭嗣琮 张景姝 《运筹与管理》 CSSCI CSCD 北大核心 2012年第6期10-16,共7页
为了研究信息不完整、不确定条件下的运输问题,建立了目标函数费用系数为三角模糊数,约束条件为弹性约束的模糊运输问题的模型。首先,将约束条件中的弹性约束转化为两个经典的不等式约束,同时,利用结构元加权排序准则,将模糊目标函数转... 为了研究信息不完整、不确定条件下的运输问题,建立了目标函数费用系数为三角模糊数,约束条件为弹性约束的模糊运输问题的模型。首先,将约束条件中的弹性约束转化为两个经典的不等式约束,同时,利用结构元加权排序准则,将模糊目标函数转化为传统的目标函数。然后对转化后的目标函数和约束条件进行整合,从而建立与原模型等价的线性规划模型,进而求出其最优解及其满意度。最后通过具体算例,证明了模型求解方法的可行性。 展开更多
关键词 模糊运输问题 线性规划 弹性约束 最优解 模糊结构元
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多目标模糊运输问题的建模与求解 认领 引用 被引量：3
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作者 罗霞 廖勇 《西华大学学报（自然科学版）》 CAS 2010年第4期43-47,共5页
为了研究信息不完整、不确定条件下的运输问题,建立了目标函数费用系数、供应量和需求量均为三角模糊的多目标模糊运输问题(MOFTP)模型。通过选用三角模糊数的大小关系将模糊目标函数转化为传统的目标函数,同时根据模糊数的数学特征将... 为了研究信息不完整、不确定条件下的运输问题,建立了目标函数费用系数、供应量和需求量均为三角模糊的多目标模糊运输问题(MOFTP)模型。通过选用三角模糊数的大小关系将模糊目标函数转化为传统的目标函数,同时根据模糊数的数学特征将模糊等式约束转化为对应的不等式约束,然后对转化后的目标函数和约束条件进行整合,从而建立与多目标模糊运输问题等价的多目标线性规划模型,其最优解即为原多目标模糊运输问题的最优解。最后通过具体算例,证明了模型求解方法的可行性。 展开更多
关键词 三角模糊数 模糊运输问题 多目标 建模
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模糊线性规划中模糊目标系数的隶属函数的确定 认领 引用 被引量：1
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作者 魏本成 李钢 《信阳师范学院学报（自然科学版）》 CAS 北大核心 2007年第4期416-418,422,共3页
针对模糊线性规划问题中的模糊目标系数的确定,提出了一种两阶段方法.在第一阶段,利用线性插值技术得到一个粗糙的隶属函数;在第二阶段,利用决策者过去的决策来提高所得隶属函数的精确度.
关键词 模糊线性规划 隶属函数 模糊关系 反问题
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基于梯形模糊数的线性规划问题的求解方法 认领 引用
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作者 付云鹏 郭云峰 +1 位作者 宋琪 祝国君 《河北科技师范学院学报》 CAS 2013年第3期56-58,71,共3页
提出一种约束条件和目标系数中均含有梯形模糊数的模糊线性规划问题,并通过梯形模糊数的排序关系准则,将问题的求解转化为一个经典线性规划问题,进而利用经典线性规划进行求解。
关键词 模糊线性规划 模糊数 梯形模糊数
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含有三角模糊数的模糊线性规划问题的求解方法 认领 引用
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作者 付云鹏 郭云峰 祝国君 《河北科技师范学院学报》 CAS 2013年第4期37-40,共4页
提出了一种含有三角模糊数的模糊线性规划问题,给出了该问题的求解方法,最后应用一个具体的实例来说明该方法的实际应用。
关键词 三角模糊数 模糊线性规划 模糊约束
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基于模糊多分配的辽宁煤炭枢纽站选址研究 认领 引用
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作者 赵宝福 徐雅臣 《统计与信息论坛》 CSSCI 2012年第3期50-55,共6页
提出一种模糊多分配p枢纽站中位问题,其中运输成本定义为模糊变量,问题的目标函数是在给定的可信性水平下,最小化总的运输成本。对于梯形和正态运输成本,问题等价于确定的混合整数线性规划问题。在实证分析中,选取了辽宁省煤炭产业的相... 提出一种模糊多分配p枢纽站中位问题,其中运输成本定义为模糊变量,问题的目标函数是在给定的可信性水平下,最小化总的运输成本。对于梯形和正态运输成本,问题等价于确定的混合整数线性规划问题。在实证分析中,选取了辽宁省煤炭产业的相关面板数据,分析计算在不同可信度水平下煤炭运输枢纽站设立的数量和位置,再利用传统的优化方法(如分枝定界法)求解。经计算,这一模型和求解方法可以用来解决辽宁省煤炭运输的选址问题。 展开更多
关键词 p枢纽中位问题 模糊运输成本 可信性 混合整数线性规划
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一类模糊线性规划模型及应用 认领 引用 被引量：2
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作者 靳晓 邱东 《陕西师范大学学报（自然科学版）》 CAS CSCD 北大核心 2023年第2期121-129,共9页
针对以模糊数为目标函数的模糊线性规划问题,建立了一种模糊数值目标函数的模糊线性规划新模型。该模型通过定义新的辅助函数将其转化为经典线性规划问题,再通过经典线性规划问题求解方法进行求解。与已有模型相比,该模型更具一般性,且... 针对以模糊数为目标函数的模糊线性规划问题,建立了一种模糊数值目标函数的模糊线性规划新模型。该模型通过定义新的辅助函数将其转化为经典线性规划问题,再通过经典线性规划问题求解方法进行求解。与已有模型相比,该模型更具一般性,且计算简单。选用投资问题对该模型进行验证,数值算例说明了该模型在实际应用中的有效性。 展开更多
关键词 模糊数 模糊线性规划 投资问题
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浅谈模糊数学和线性规划方法在决策问题中的应用 认领 引用
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作者 韩志伟 《科技与创新》 2014年第6期125-126,共2页
在日常生活和工作中,在解决问题时,我们需要对若干可行方法进行选择,以便能取得最佳效果。通过对具体问题进行分析,运用模糊数学和线性规划模型研究,将实际问题转化成数学问题,并用数学方法实现求解。
关键词 模糊数学 线性规划 决策问题 优化方案
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区间模糊环境下应急物资多式联运路径优化 认领 引用 被引量：3
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作者 孙岩 孙国华 +2 位作者 李民 卢越 董坤祥 《综合运输》 2025年第4期140-145,共6页
以运输时间最短为目标研究应急物资多式联运路径优化问题。为了提高应急物资运输的可靠性,从速度、时间和能力出发系统规划了多式联运网络的不确定性。在采用区间模糊数刻画不确定性的基础上,构建应急物资多式联运路径优化的模糊线性规... 以运输时间最短为目标研究应急物资多式联运路径优化问题。为了提高应急物资运输的可靠性,从速度、时间和能力出发系统规划了多式联运网络的不确定性。在采用区间模糊数刻画不确定性的基础上,构建应急物资多式联运路径优化的模糊线性规划模型,进而对模型进行去模糊化处理,得到其等价可解形式,从而使问题优化可采用数学规划软件运行精确求解算法得到问题的全局最优解。采用算例分析验证了数学模型的可行性,同时通过分析优化结果对满足水平的敏感性,揭示应急物资多式联运的运输时效性和运输可靠性之间的矛盾对立关系,指出运输组织者可以通过合理确定满足水平取值得到符合具体决策情景的应急物资多式联运最优路径。 展开更多
关键词 应急物资 多式联运 路径优化 区间模糊环境 模糊线性规划模型
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