中 文 摘 要模糊性与随机性经常出现在同一个决策过程中, 这种现象称为双重不确定性. 本论文将分两部分讨论双重不确定系统优化理论.第一部分讨论了随机模糊系统优化理论. 这是一个新的研究领域. 该部分以概率论和非可加测度论为工具, 首先提出了模糊变量与随机模糊变量期望值的新概念, 并证明了两种期望值算子的线性. 然后利用随机模糊变量期望值算子, 建立了一类新的期望值模型. 此外, 本部分还提出了随机模糊事件的平衡机会测度和平均机会测度, 并讨论了这两种机会的对称性和对偶性. 以平均机会测度为指标, 提出了一类新的随机模糊平均机会规划模型. 为了求解上述两类模型, 首先设计了一种随机模糊模拟方法来估计期望值和平均机会函数, 然后再训练一个前馈型神经网络去逼近这两种不确定函数, 最后将训练好的神经网络嵌入到一个遗传算法中, 从而得到一个搜索最优解的混合智能算法. 大量的数值实验表明, 该算法是可行且有效的.第二部分讨论了模糊随机系统优化理论. 该部分首先提出了模糊随机规划中几个新的基本概念, 包括模糊随机变量、模糊随机变量的期望值、模糊随机事件的平衡机会测度和平均机会测度, 以及模糊随机变量的独立同分布. 然后证明了一类模糊随机变量序列的强大数定律. 此外, 以平衡机会测度为指标，建立了一类新的模糊随机规划模型. 对其中的线性模型, 讨论了它们的凸性定理, 这些结果为将原模糊随机线性规划问题转化为等价的随机凸规划问题提供了方法; 对其中的非线性模型, 设计了一种混合智能算法进行求解, 并通过数值例子说明该算法的可行性和有效性.综上, 本论文的创新点包括: (1) 提出了模糊变量期望值的概念; (2) 提出了随机模糊变量的期望值、随机模糊事件的平衡机会测度和平均机会测度的概念; (3) 证明了一类模糊随机变量序列的强大数定律; (4) 建立了一类新的模糊随机规划模型.关键词: 随机模糊变量, 模糊随机变量, 机会测度, 期望值算子, 不确定规划

AbstractFuzziness and randomness usually coexist in a real decision process. This phenomena is refereed to as twofold uncertainty. In order to model twofold uncertain systems, this dissertation provides a practical optimization theory.The first part deals with random fuzzy optimization theory. This is a new research area. First, taking probability theory and fuzzy integral as the research tools, the novel concepts of expected value of fuzzy variable as well as random fuzzy variable are presented. The linearity of the two expected value operators is also proved. Then, by employing the expected value operator of random fuzzy variable, a new class of expected value models is established. Besides, equilibrium and mean chance measures of random fuzzy event are introduced, and the symmetry and duality of the two chance measures are also discussed. By using the mean chance measures, a new class of random fuzzy mean chance programming models is presented. In order to solve the two classes of models, random fuzzy simulation is first designed to estimate the expected value and mean chance functions; then a feedforward neural network is trained to approximate the two kinds of uncertain functions; finally, the trained neural network is embedded into a genetic algorithm to produce a hybrid intelligent algorithm to search for the optimal solutions. The feasibility and effectiveness of the proposed algorithm are illustrated via many numerical experiments.The second part deals with fuzzy random optimization theory. In this part, several new concepts in fuzzy random programming are first presented, including fuzzy random variable, expected value operator, equilibrium and mean chance measures, and independent and identically distributed fuzzy random variables. Then, a type of strong law of large numbers of fuzzy random variable sequence is proved. Besides, a new spectrum of fuzzy random programming models is formulated via the equilibrium chance. For fuzzy random linear programming problems, several convexity theorems are proved, which provide us approaches to convert primal fuzzy random linear programming problem to its equivalent stochastic convex programming. For general nonlinear programming models, a hybrid intelligent algorithm is designed to solve them. The feasibility and effectiveness of the algorithm are shown by a set of numerical examples. In conclusion, this dissertation brings forth the following new ideas in the twofold uncertain optimization theory: (i) the concept of the expected value of fuzzy variable is presented; (ii) the concepts of the expected value of random fuzzy variable, the equilibrium and mean chance measures of random fuzzy event are presented; (iii) a type of strong law of large numbers of fuzzy random sequence is proved, and (iv) a spectrum of fuzzy random programming models is established.Key words: Random fuzzy variable, Fuzzy random variable, Chance measure, Expected value operator, Uncertain programming