【作者】 张娜；

【导师】 刘思峰；

【作者基本信息】 南京航空航天大学 ， 管理科学与工程， 2010， 硕士

【摘要】 基于经典概率描述的GERT网络理论已经相对比较成熟,其应用范围十分广泛,几乎涵盖了包括资源规划、应急计划、地震分析、产品开发试制及改进计划等许多行业和领域。它是处理经典的概率网络关系的强有力工具。然而,现实世界中除了概率的不确定性以外,还存在着大量的非概率不确定性问题,如模糊不确定性和灰色不确定性等。模糊现象几乎渗透到了所有的科学和技术领域,可信性理论是完整地研究模糊性的理论。因此,有效的把GERT网络技术与可信性理论进行结合,建立基于可信性理论的模糊GERT网络技术(简称F-GERT)既有重要的理论价值,又具有潜在的应用前景。本文首次将GERT网络研究的范围从传统的随机环境拓展至模糊环境,将可信性理论引入了GERT网络领域。针对含有模糊信息参量的随机网络,提出了一种新的考虑模糊信息的F-GERT网络的建模技术,构造了F-GERT网络的矩、矩母函数,对其4个方面的重要的数学性质做了详细的讨论;在此基础上,利用信号流图原理研究了F-GERT网络的仿真算法。然后,对含有模糊信息的F-GERT网络要素重复执行次数的模型构建问题进行了研究,定义了反馈网络的基本单元、多重反馈网络、多重反馈递进网络、多重反馈并进网络、多重反馈混合网络以及模糊反馈网络,并对模型网络简化的规则做了研究;在F-GERT网络的重复执行次数的求解思路的基础上,对重复执行次数的F-GERT网络的执行次数算法、条件矩母函数、过程到达时间进行了研究。最后,用信号流图的拓扑方程确定F-GERT网络的等价模糊传递函数和等价模糊概率,根据WF函数的定义,将等价模糊传递函数转为等价模糊矩母函数。通过等价模糊矩母函数逆向推导F-GERT网络的各项基本参数,基于模糊信息的F-GERT网络模型设计了结合模糊模拟和遗传算法的混合智能算法,并通过数值试验验证了算法的有效性。更多还原

【Abstract】 The GERT network based on classical probability theory has been relatively mature, and its scope of application is very extensive, including almost resource planning, contingency planning, seismic analysis, product development, trial and improvement plans, and many other industries and fields. However, there is also a large number of non-probabilistic uncertainty outside of the probability of uncertainty, such as the fuzzy uncertainty and grey uncertainty. Fuzziness infiltrate into almost all fields of science and technology, and credibility theory is a complete study of the theory of ambiguity. Thus, it has important theoretical value and potential applications to combine the GERT network technology with the credibility theory effectively and establish credibility based on the theory of GERT network technology (referred to F-GERT) .It is the first time extending GERT network study range from the traditional random environment to fuzzy environment. In view of random network with the fuzzy information parameter, a new F-GERT network modeling technique which considers the fuzzy information is proposed in this thesis. Moreover, the moments and moment generating function of F-GERT network are constructed and the important mathematical nature of its four aspects is discussed in detail. On this basis, the simulation algorithm of F-GERT network is studied using signal flow graph principle.Then, it studied the moedl of fuzzy information of the F-GERT network with the number of times repeated questions. The thesis has defined the basic unit of feedback network, multi-feedback network, multi-feedback progressive network, multi-hand feedback network, multi-feedback hybrid networks and fuzzy feedback network, and examined the rules of the network model simplified. On this basis, the number of times to repeat the implementation of ideas for solving based on the number of pairs of repeated F-GERT network, the implementation of the number of algorithms, conditional moment generating function, the process arrival time were studied.Finally, fuzzy equivalent transfer function and equivalent to fuzzy probabilit were determined by the signal flow graph of the topological equations to F-GERT networks. The transfer function was equivalent to fuzzy moment generating function according to the definition of WF function. It anti-derivated the basic parameters of F-GERT network by the equivalent fuzzy moment generating function and designed hybrid intelligent algorithm based on fuzzy simulation and genetic algorithm of F-GERT network model.Numerical tests were given in detail . Through simulating we know that the effect is good.更多还原