论文标题:目标函数系数为模糊数的规划问题研究
Research on Programming Based on Objective Coefficients of Fuzzy Number
论文作者 卢伟
论文导师 黄天民,论文学位 硕士,论文专业 应用数学
论文单位 西南交通大学,点击次数 128,论文页数 54页File Size1563k
2003-03-01论文网 http://www.lw23.com/lunwen_704445472/ 最优化;区间线性规划;多目标规划;模糊优化;模糊变量
Optimization;interval linear programming;multiobjective programming;fuzzy optimization;fuzzy variable
在现实生活和工程领域中，存在着许多不确定性现象，这种不确定性现象主要表现在两个方面：一是随机性，二是模糊性。而在数学规划问题中，这种不确定性现象会给决策者作决策时带来很大的困难。因此对于研究这种在不确定环境下的最优化问题，具有很重要的理论和实际意义。本文讨论了一类不确定性线性规划问题——目标系数分别为区间数和模糊数的线性规划问题。全文主要内容如下： 首先，对目标函数中具有区间系数的线性规划问题进行了讨论。就最大化区间目标函数而言，通过在区间数之间的左端点、右端点、中点以及区间的半长度引入序关系，然后再通过所定义的这些序关系，可把问题转化为求解一个多目标问题。而对最小化问题，也可定义区间数之间的另一序关系，同样可把原问题转化为一个多目标问题，通过求此多目标问题得到原问题的解。 进一步，本文还就目标系数为三角型模糊数的多目标问题给出了—种解法，同时对目标系数为一般模糊数的多目标问题也作了重点讨论。从模糊数之间的序关系出发，分别定义了弱较优解和较优解，然后对模糊多目标问题引入模糊评价函数，将多目标化为单目标，在此也证明了求得的解为原问题的弱较优解。还讨论了系数为一般模糊数的多目标问题，通过模糊集的λ水平集可将多目标问题转化为区间数线性规划问题，并利用上一章所讲的方法，得到原问题的弱较优解。 最后，对变量为模糊数的线性规划问题也进行了讨论。实际上，在许多的数学规划问题中，所有决策变参量都为模糊数，对于此类问题通常采用可能性规划或多目标规划方法来解决，遗憾的是，所有这些方法均存在不足。因此在第四章中，为解决一类具有模糊变量的线性规划问题提出了一种切实可行的方法。
In realistic life and many fields including engineering technology, there exits a lot of uncertainty including stochastic and fuzzy. The uncertainty will bring about great difficulty in making decision for decision maker in mathematical programming. So under the uncertain environments research on optimal problems is very important from the theoretical as well as from the practical point view. The dissertation takes action about a kind of uncertain linear programming problem with interval numbers and fuzzy numbers in objective programming respectively. The main contributions of this dissertation can be summarized as follows:First of all, in the dissertation the linear programming problem whose objective function has interval coefficients is investigated. To maximize the interval objective function, the order relations are defined by the right limit, the left limit, the center and the half with of an interval. The maximization problem with the interval objective functions is converted into a multiobjective problem by using the order relations. Similarly, the minimization problem is also transformed into a multiobjective problem by using the other order relations, so by doing the multiobjective problem a solution of the primitive problem can be obtained.Further, this thesis brings forward a method based on multiobjective coefficients with triangular fuzzy numbers, and lays undue emphasis on the multiobjective problem with general fuzzy numbers in objective coefficients. According to order relations defined between fuzzy numbers, the Pareto less optimal solution and the Pareto optimal solution are defined, then a fuzzy evaluation function is introduced into a multiobjective programming problem, this method results in a multiobjective programming problem been converted into a one objective programming problem, accordingly the solution by this method is the Pareto less optimal solution to the primitive problem, which is given proof A multiobjective problem with general fuzzy number coefficients is also further discussed, by λ_ cutset of fuzzy sets a multiobjective problem can betransformed into a interval linear programming problem, and using the method of the previous chapter, we can obtain the Pareto less optimal solution.Lastly, in the thesis the fuzzy linear programming with fuzzy variables is discussed. In practice, there are many problems in which all decision parametersare fuzzy numbers, and either possibilistic programming or multiobjective programming methods usually solves such problems. Unfortunately, all these methods have shortcomings. So in the fourth chapter a practical method for solving linear programming problems with fuzzy variables is discussed.
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