摘要
不确定性决策是目前管理科学研究和应用中的一个热点问题。客观世界的实际问题往往涉及众多相互联系又相互影响的因素,这些因素本身及其相互之间的关系都存在大量的不确定性,而不确定性可分为两类,一类是反映客观事物内在本质的随机不确定性,一类是反映由于人们对客观世界的认识不足、信息缺失或知识缺乏而导致的认知不确定性。如何描述各种不确定性,如何在复杂关系分析中对问题有效的建模,如何综合定量数据和定性知识而做出科学的决策,都对不确定性管理决策问题的研究提出了新的挑战。
为应对上述挑战,本文在定性定量综合集成方法论的指导下,通过对D-S证据理论和图模型基础理论的研究,借鉴贝叶斯网络模型的研究思路,提出了证据网络模型。证据网络模型是D-S证据理论和图模型的结合,其可以充分发挥D-S证据理论在不确定性信息处理,尤其是认知不确定性的建模和分析上的理论优势,发挥图模型在问题描述、关系分析上的语义优势,在理论上扩展不确定性建模与分析的研究思路和方法,为定性经验知识与定量数据的统一建模和综合处理提供技术手段,在实践上为不确定性管理问题的分析、建模、推理以及评估、决策提供技术方法与工具支撑。
为建立一套完善的证据网络理论和方法体系,本文对证据网络的定义、结构建模、参数表示、不同参数模型下的推理、以及证据网络参数学习的相关理论和方法开展了深入研究。
首先,定义了证据网络模型的基本概念、关键要素、基本特点和建模流程。证据网络模型通过定性层面的有向无环图描述变量之间的相互关系,定量层面的信度函数刻画变量之间影响模式和程度,综合了证据理论和图模型的特点,为系统分析和建模提供了一种描述不确定性,建模相互影响关系及综合处理信息的技术手段;为了构建证据网络的结构和参数模型,提出基于树模型和基于因果图的证据网络拓扑结构建模方法,定义了证据理论框架下知识描述的两种规范化证据网络参数模型——条件信度模型和信度规则模型。
其次,研究并建立了以条件信度和信度规则为参数模型的证据网络推理策略与推理方法。其中,为解决条件信度参数模型下的证据网络推理问题,在条件信度函数计算理论基础上,提出了证据网络模型的正向因果推理和反向诊断推理方法;并通过对证据冲突悖论的分析,提出了一种基于冲突度量的证据网络信度合成算法,解决了证据网络结点信息融合问题。在以信度规则为参数模型的证据网络推理研究中,为分析结点之间的相互重要度,提出了不完全信息情况下的证据网络结点权重获取方法;并在证据推理算法的基础上,结合信度结构数据处理方法和信度规则激活算法,实现了数据与证据网络模型的对接,建立了基于信度规则的证据网络推理与结果分析方法。
接着,构建了证据网络参数学习的数学模型并设计了基于投影梯度法的证据网络参数学习算法。针对以信度规则为参数的证据网络模型,分析建立其参数学习问题的非线性目标优化模型,提出以信度结构模型差距度量准则作为优化模型的目标函数,并证明了其合理性;通过推导模型解析表达式函数的梯度,设计基于投影梯度法的证据网络参数学习求解算法,从而建立起从历史数据和经验知识信息学习证据网络参数的技术和方法。
最后,将上述证据网络推理和学习研究中提出的求解策略和方法,应用到航天系统安全性分析、军事威胁评估与预测、交通事故风险预警等管理决策问题中,以实际案例展示证据网络方法应用的过程,验证方法的可行性和有效性,说明证据网络模型理论及方法在系统分析与管理决策中的实际应用价值。
Uncertainty decision making is a very important research field in management science and applications. The real-world probems often involve many components and elements, which are interrelated and interactional. At the same time, large numbers of uncertainty exact among these elements and their relation. The uncertainty includes alearoty and epistemic uncertainty. The former is referred to as variability, irreducible and stochastic uncertainty. The later is also refered to as reducible, subjective and state-of-knowledge uncertainty, which is due to lack of knowledge or ambiguity. So, the new challenges in uncertainty management and decision research are how to describe various types of uncertainties, how to analyze and model complex relation of system, and how to aggregate quantitative data and qualitative knowledge for making correct decision.
In order to meet the above challenges, the Evidential Network model is proposed, which follows the methodology of qualitative and quantitative information integration and research road of Bayesian network, on the basis of Dempster-Shafer theory of evidence and graph theory. The Evidential Network is a combination of and graph model. It has the capability, which comes from D-S theory, to deal uncertain information, especially the epistemic uncertainty. It also has advantages of discirbing problems and analyzing relationship, which comes from graph theory. In theoretical prospect, the Evidential Network will develop research ideas and methods for modeling and analyzing uncertainty, and develop technology and tools which build a uniform treatment framework for aggregating quantitative data and qualitative knowledge. In application prospect, it will provide technology and methods for analyzing, modeling, inference, assessment, and decision making in uncertainty management problems.
For completing the theorerical and technical framework of Evidential Network model, this paper focuses on the research works of definition, topology constructing, parameter formulation, reasoning under different parameter models, and parameter learning as follows.
Firstly, the basic concept of Evidential Network is defined, including elements, characteristics, and modeling process. The Evidential Network can describe the relations among variables using the directed acyclic graph under qualitative views, and denote the influence modes and degree under qualitative views. It has the advantages of D-S theory and graph theory, and provides a technical tool for describing uncertainty, modeling relations, and dealinig with information. The construction methods based on tree model and causal network are proposed for constructing the topology of Evidential Network. The parameter models of Evidential Network are formulated with knowledge description under framework of D-S theory, which consiste of two types: Conditional Belief Function (CBF) and Belief Rule Model (BRM).
Secondly, the Evidential Network reasoning frameworks and approach with CBF and BRM parameter model are respectively analyzed. The forward causal and backward diagnosis reasoning for Evidential Network with CBF are solved using conditional belief inference and computing algorithms. A new belief combination algorithm is proposed based on a new belief conflict measurement, which avoids the conflict paradox of Dempster combination rule, to combine nodes’information of Evidential Network. In Evidential Network reasoning with BRM, a weight generating method based on goal programming is proposed to obtain EN nodes’priority under incomplete information environment. The EN reasoning with BRM is accomplished following several steps: belief structure data transformation, action weights of belief rule, evidetnaitl reasoning algorithms, and belief structure result analysis.
Then, the mathematic formulations for EN parameters learning is constructed, and learning algorithms are proposed based on Rosen projection grads method. For Evidential Network with BRM, the parameters learning problem is transformed to an nonlinear objective optimization problems. The objective function of optimization problems is constructed by using a belief structure distance measurement, which defines the difference between belief structure models and has some basic property of distance measurement. The grads of objective function needs to be gotten when the projection grads method is used to solve optimation problems. The whole solution process is proposed steps by steps for EN parameters learning from historical data or experience knowledge.
Finally, the solution process and approaches to Evidential Network, which are proposed in this paper, are used to deal with safety analysis and evaluation of aerospace system, military threat assessment and prediction, and risk forecasting of traffic accidents. These applications are examined to illustrate and show the feasibility and validity of the Evidential Network model, and to indicate the research and application value in the future system analysis, management, and uncertainty decision.
引文
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