【作者】 刘永刚；

【导师】 徐玖平；

【作者基本信息】 四川大学 ， 管理科学与工程， 2007， 硕士

【摘要】 多目标决策是现代决策科学的重要组成部分，是运筹学的重要分支。通常人们所面临的实际决策问题包含若干个相互矛盾且不可公度的决策目标。如何在有限资源的限制下，同时使得多个目标函数达到最优或找到决策者的满意解是确定多目标决策要研究的问题。然而，由于人为因素或客观因素的影响，实际的多目标决策问题常常伴随着许多不确定性，而不确定常常包含多种形式，如单重的随机、模糊；双重的双重模糊、模糊随机；以及多重不确定变量等。模糊随机变量是双重不确定变量的一种，在很多实际决策问题中，某些模糊变量的隶属函数是完全已知的，但是其中的某些参数是未知的。如果根据数据分析和经验积累，专家或者决策者将这些不确定参数描述为模糊变量或随机变量，则这些变量就成为双重模糊变量或模糊随机变量。对于含有双重模糊变量或模糊随机变量的优化问题，需分别利用双重模糊规划或模糊随机规划进行建模。这种更加柔性的数据结构与灵活的选择方式将会大大增强模型的表现力和适应性。但是，在处理这些不确定信息时，人们总是习惯地用确定的量来代替不确定的量，用单重不确定代替多重不确定，从而会损失掉很多有价值的信息，不能真实反映问题本质。本文主要从双重模糊和模糊随机两个角度出发，研究带有双重不确定系数的多目标规划问题，并实际应用到库存问题中。解决了一类带有双重不确定系数的多目标库存问题。同时，在同等的约束条件下，给出了模糊环境下的多目标规划模型的结果。通过比较这两种不同环境下的模型结果，我们发现双重不确定多目标规划更能反映问题的本质，更符合实际问题，而且其计算结果更能使决策者满意。本文在比较系统地总结国内外学者已有研究成果的基础上，提出了一整套求解一类带有双重不确定系数的多目标规划问题的方法，并将双重不确定系数的多目标规划模型应用到库存问题中。主要成果如下：(1)理论方面给出了双重模糊变量和模糊随机变量α-截集的概念．并提出了双重模糊变量和模糊随机变量转化为梯形模糊数的方法；给出了带有双重不确定系数的多目标规划的一般模型，并证明了求解这类模型(α，β)-满意解的方法。(2)应用方面把带有双重不确定系数的规划模型引入到库存问题中。利用双重模糊参数和模糊随机参数来体现决策者或专家的管理经验。在此基础上，对双重不确定环境下的库存问题做出精确的数学描述并给出模型的解，通过与模糊规划模型所得的结果比较发现，双重不确定环境下的结果更能使决策者满意。本文对促进不确定性理论和多目标理论的研究具有参考意义。更多还原

【Abstract】 Multi-objective decision-making is an important part of modern decision-making science and an important branch of operational research. We usually face these practical decision-making problems which include some conflictive and unmeasured each other decision-making objective. It is the problem of certain multi-objective decision-making that how to optimize some objective functions or find the satisfied solution under finite resource. But as a result of some artificial or external factors, practical multi-objective decision-making problems are often with much uncertainy which usually exist many kinds of uncertainties, such as fuzzy, random, bifuzzy, fuzzy random and multifold uncertain variables.Fuzzy random variable is a kind of twofold uncertain variables. In many practical decision-making problems, the membership functions of some random variables is know, but some parameters about these membership functions are unknown. Based on the data analysis and experience accumulation, the experts and decision-makers make the uncertain parameters be fuzzy variables or random variables, and then they would become bifuzzy variables or fuzzy random variables. Bifuzzy programming or fuzzy random programming are for the problems which include bifuzzy variables or fuzzy random variables respectively. The elastic data structure and choice pattern will boost the descriptive and adaptive capability of programming models. When dealing with these multifold uncertain information, people are used to replacing uncertain parameters with deterministic quantities and replacing multifold uncertain parameters with onefold uncertain parameters, which may leave out much valuable information and can not reflect the essence of problems. In this paper, from two points of view about bifuzzy variables and fuzzy random variables, we have studied multi-objective programming problems with twofold uncertain coefficients and have been applied to practical inventory problems; and have solved a class of multi-objective inventory problems with twofold uncertain coefficients. On the other hand, we have gave the results of the fuzzy multi-objective programming problems under the same restrictive conditions. By comparing the two different results under different environment, we find that the multi-objective programming with twofold uncertain coefficients are much practical than that with fuzzy parameters, and the results of the multi-objective programming with twofold uncertain coefficients are satisfied by the decision-makers.In this paper, on the basis of summarizing the known researches, we propose a system of solutions for a class of multi-objective inventory problems with twofold uncertain coefficients and apply them to the practical inventory problems. The major achievements as follows:(1) The theory aspectWe propose theα-cut set of the bifuzzy variables and fuzzy random variables, and propose the solution of transforming bifuzzy variables and fuzzy random variables to trapezoidal fuzzy numbers, and propose a generic multi-objective programming with twofold uncertain coefficients and proved the method of solving (α,β)-satisfied solution.(2) The application aspectWe apply the programming model with twofold uncertain coefficients to the practical inventory problem. The bifuzzy and fuzzy random parameters reflect the management experience of the decision-makers and experts. On the basis of these, we propose the precise mathematics model about inventory problem and the solution about mathematics model. By comparing the results with that under fuzzy environment, we find the results under towfold uncertain environment make the decision-makers satisfied.This paper has referenced significance to accelerate the research of bifuzzy theory and fuzzy random theory.更多还原