一类系数为梯形模糊数的两层多随从线性规划模型

针对一类系数为梯形模糊数的两层多随从线性规划问题,利用模糊结构元理论定义了模糊结构元加权序,证明了一类系数为梯形模糊数的两层多随从线性规划问题的最优解等价于两层多随从线性规划问题的最优解.根据线性规划的对偶定理和互补松弛性质,得到了两层多随从线性规划模型的最优化条件.最后,利用两层多随从线性规划模型的最优化条件,设计了求解一类系数为梯形模糊数的两层多随从线性规划问题的算法,并通过算例验证了该方法的可行性和合理性.     

区间目标规划与模糊目标规划

从区间数与模糊数的序关系出发讨论了一类目标函数含区间数系数的非线性规划和目标函数中含有模糊数系数的线性规划问题,提出将相应的规划问题等价地转化为两个依次求解的经典数学规划问题来求最优解.     

求解上层含约束条件的模糊二层线性规划的结构元方法

讨论了一类上层含约束条件的模糊二层线性规划模型,利用结构元方法,证明了模型最优解等价于二层线性规划模型最优解,并通过Kuhn-Tucker方法得到了模型最优解,最后通过数值算例验证了方法的可行性.     

求解上层含约束条件且具有模糊决策变量二层线性规划的结构元方法

讨论一类含模糊决策变量二层线性规划模型,利用模糊结构元理论,证明该模型最优解等价于二层线性规划模型最优解,并通过极点搜索法得到该模型最优解,最后通过数值算例验证该方法的可行性。     

含直觉模糊弹性约束的多目标模糊线性规划求解

基于模糊结构元方法构建并讨论了一类含有直觉模糊弹性约束的多目标模糊线性规划问题.通过引入模糊数的加权特征数,定义了一种序关系并拓展了Verdegay的模糊线性规划方法,将上述多目标模糊线性规划问题转化成两个等价含参数约束条件的清晰多目标线性规划模型,并应用一种线性加权函数法给出了此类线性规划模型的对比最优可行解.最后通过一个数值实例来说明此类问题的一般求解方法.     

含弹性约束的多目标模糊线性规划求解

本文讨论了一类含弹性约束的多目标模糊线性规划问题.利用模糊结构元方法引入模糊数的加权特征数概念和序关系,应用Verdegay的模糊线性规划方法及模糊数的加权特征数将此类多目标模糊线性规划问题转化成一类含参数约束条件的清晰多目标线性规划模型,并应用一种基于线性加权函数的规划算法求其α-拟最优可行解.最后,给出了一个数值实例来说明如何求解此类多目标模糊线性规划问题.     

一类全系数模糊线性规划的求解方法

利用结构元方法定义一种模糊数排序准则,提出将目标函数和约束条件中都含有三角模糊数的全系数模糊线性规划等价转化为经典线性规划的方法,并证明其合理性.与其它方法相比较,该方法证明了得到的解优于已有其它方法的解,并且约束条件少,运算方法简便.将本文的方法运用到数值算例中,进一步表明了提出方法的有效性和广泛性.     

全系数模糊两层线性规划

利用结构元方法定义一种模糊数排序准则,对模糊系数(目标函数与约束条件中系数为有界模糊数情形)的隶属函数为非单调函数的情形,给出将全系数模糊两层线性规划等价转化为经典的线性规划的方法,并证明了其合理性.与其它方法相比较,该方法不仅约束条件少,而且运算方法简便.最后,将本文的方法运用到数值算例中,进一步表明该提法的有效性和广泛性.     

具有模糊变量的线性规划问题

讨论含模糊变量的线性规划问题，研究了其求解方法。利用新定义的模糊数序关系，将它转换成一个多目标线性规划问题，然后进一步转换成两层多目标线性规划问题，进而利用分层规划法求解。     

一般梯形模糊逼近算子及其在模糊运输问题中的应用

研究运输成本信息为一般模糊数的模糊运输问题.首先,在保持一般模糊数的核不变的条件下,建立一般模糊数与一般梯形模糊数的距离最小优化模型,通过求解模型得到一般模糊数的一般梯形模糊逼近算子,并给出该逼近算子具有的性质如数乘不变性、平移不变性、连续性等.然后利用该逼近算子将一般模糊运输信息表转换成一般梯形模糊运输信息表,再根据已有GFLCM和GFMDM算法得到模糊运输问题的近似最优解,最后给出具体算例分析说明方法的有效性和合理性.     

梯形模糊数的有序表示及中心平均排序方法

模糊数的排序在决策分析和优化问题中占有十分重要的地位,而一般模糊数均可近似分解为若干分片小梯形的叠加形式,故梯形模糊数的排序问题至关重要!本文首先引入等距分片方法对梯形模糊数实施纵向分割,进而获得梯形模糊数的有序表示。其次,依中心平均加权准则改进梯形模糊数的横向和纵向中心坐标公式,并提出新的指标排序准则。最后,通过实例分析考证了新的排序方法的有效性。     

Possibility linear programming with trapezoidal fuzzy numbers

Fuzzy linear programming with trapezoidal fuzzy numbers (TrFNs) is considered and a new method is developed to solve it. In this method, TrFNs are used to capture imprecise or uncertain information for the imprecise objective coefficients and/or the imprecise technological coefficients and/or available resources. The auxiliary multi-objective programming is constructed to solve the corresponding possibility linear programming with TrFNs. The auxiliary multi-objective programming involves four objectives: minimizing the left spread, maximizing the right spread, maximizing the left endpoint of the mode and maximizing the middle point of the mode. Three approaches are proposed to solve the constructed auxiliary multi-objective programming, including optimistic approach, pessimistic approach and linear sum approach based on membership function. An investment example and a transportation problem are presented to demonstrate the implementation process of this method. The comparison analysis shows that the fuzzy linear programming with TrFNs developed in this paper generalizes the possibility linear programming with triangular fuzzy numbers.     

Some new results in linear programs with trapezoidal fuzzy numbers: Finite convergence of the Ganesan and Veeramani’s method and a fuzzy revised simplex method

In a recent paper, Ganesan and Veermani [K. Ganesan, P. Veeramani, Fuzzy linear programs with trapezoidal fuzzy numbers, Ann. Oper. Res. 143 (2006) 305–315] considered a kind of linear programming involving symmetric trapezoidal fuzzy numbers without converting them to the crisp linear programming problems and then proved fuzzy analogues of some important theorems of linear programming that lead to a new method for solving fuzzy linear programming (FLP) problems. In this paper, we obtain some another new results for FLP problems. In fact, we show that if an FLP problem has a fuzzy feasible solution, it also has a fuzzy basic feasible solution and if an FLP problem has an optimal fuzzy solution, it has an optimal fuzzy basic solution too. We also prove that in the absence of degeneracy, the method proposed by Ganesan and Veermani stops in a finite number of iterations. Then, we propose a revised kind of their method that is more efficient and robust in practice. Finally, we give a new method to obtain an initial fuzzy basic feasible solution for solving FLP problems.     

A revisit of numerical approach for solving linear fractional programming problem in a fuzzy environment

In the article, Veeramani and Sumathi [10] presented an interesting algorithm to solve a fully fuzzy linear fractional programming (FFLFP) problem with all parameters as well as decision variables as triangular fuzzy numbers. They transformed the FFLFP problem under consideration into a bi-objective linear programming (LP) problem, which is then converted into two crisp LP problems. In this paper, we show that they have used an inappropriate property for obtaining non-negative fuzzy optimal solution of the same problem which may lead to the erroneous results. Using a numerical example, we show that the optimal fuzzy solution derived from the existing model may not be non-negative. To overcome this shortcoming, a new constraint is added to the existing fuzzy model that ensures the fuzzy optimal solution of the same problem is a non-negative fuzzy number. Finally, the modified solution approach is extended for solving FFLFP problems with trapezoidal fuzzy parameters and illustrated with the help of a numerical example.     

Fuzzy linear programs with trapezoidal fuzzy numbers

The objective of this paper is to deal with a kind of fuzzy linear programming problem involving symmetric trapezoidal fuzzy numbers. Some important and interesting results are obtained which in turn lead to a solution of fuzzy linear programming problems without converting them to crisp linear programming problems.     

含直觉模糊弹性约束的广义模糊变量线性规划

本文基于模糊结构元方法建立并讨论了一类含有直觉模糊弹性约束的广义模糊变量线性 规划问题。首先,简单介绍了结构元方法并对结构元加权排序中权函数表征决策者风险态度进行了深入分析。然后,通过选取风险中立型决策态度来定义序关系并拓展Verdegay模糊线性规划方法,将新型模糊变量线性规划问题转化为两个含一般模糊弹性约束的模糊变量线性规划模型,给出了此类规划最优直觉模糊解的求法。最后,通过数值算例进一步说明该方法的有效性。     

目标系数模糊型模糊关系线性规划

提出了目标系数模糊型模糊关系线性规划问题,这是传统模糊关系线性规划的扩展.以三角模糊数为例,基于它的一种排序方法给出了求解该类规划的一个算法.最后,为了说明算法的有效性给出了两个数值例子.     

The dual simplex method and sensitivity analysis for fuzzy linear programming with symmetric trapezoidal numbers

In this paper, we first extend the dual simplex method to a type of fuzzy linear programming problem involving symmetric trapezoidal fuzzy numbers. The results obtained lead to a solution for fuzzy linear programming problems that does not require their conversion into crisp linear programming problems. We then study the ranges of values we can achieve so that when changes to the data of the problem are introduced, the fuzzy optimal solution remains invariant. Finally, we obtain the optimal value function with fuzzy coefficients in each case, and the results are described by means of numerical examples.     

A redundancy detection algorithm for fuzzy stochastic multi-objective linear fractional programming problems

The computational complexity of linear and nonlinear programming problems depends on the number of objective functions and constraints involved and solving a large problem often becomes a difficult task. Redundancy detection and elimination provides a suitable tool for reducing this complexity and simplifying a linear or nonlinear programming problem while maintaining the essential properties of the original system. Although a large number of redundancy detection methods have been proposed to simplify linear and nonlinear stochastic programming problems, very little research has been developed for fuzzy stochastic (FS) fractional programming problems. We propose an algorithm that allows to simultaneously detect both redundant objective function(s) and redundant constraint(s) in FS multi-objective linear fractional programming problems. More precisely, our algorithm reduces the number of linear fuzzy fractional objective functions by transforming them in probabilistic–possibilistic constraints characterized by predetermined confidence levels. We present two numerical examples to demonstrate the applicability of the proposed algorithm and exhibit its efficacy.     

Approximation of fuzzy numbers by trapezoidal fuzzy numbers preserving the expected interval

The problem to find the nearest trapezoidal approximation of a fuzzy number with respect to a well-known metric, which preserves the expected interval of the fuzzy number, is completely solved. The previously proposed approximation operators are improved so as to always obtain a trapezoidal fuzzy number. Properties of this new trapezoidal approximation operator are studied.