贝叶斯网建模技术及其在决策中的应用
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摘要
决策问题往往具有一定的不确定性，其根源主要来自问题本身的模糊性、随机性，决策信息的不完备性、不精确性，人类认知能力的有限性以及主观认识和客观实际之间存在的差异性。这些不确定性使得决策的难度大大增加，因此，不确定环境下的决策理论与决策方法成为决策科学研究的重要内容之一。
近年来，随着数学理论与人工智能技术的发展，出现了多种不确定性问题的处理方法，如证据理论、贝叶斯网、模糊集和粗糙集等。在这些方法中，贝叶斯网络是以概率论为数学基础的图形模式，具有直观的表达能力和强大的知识推理能力等诸多优越性，在不确定推理方面具有较强的优势，因此成为不确定理论研究的热点。
本文针对贝叶斯网络存在学习效率不高、建模困难的缺陷，重点研究了贝叶斯网建模技术及其在管理决策中的应用，具体内容如下：
(1) 综述了不确定性问题的分类，贝叶斯网的诞生发展过程和研究现状，贝叶斯网在管理决策及智能决策支持系统中的应用前景。阐述了贝叶斯网的结构和特点，常用的推理方法，以及贝叶斯网的各种扩展模型。
(2) 研究了贝叶斯网的结构学习，提出了一种知识和数据融合的贝叶斯网结构学习方法。首先由专家给出对网络结构的信度分配，采用证据理论进行证据合成，合成后具有最高信度的结构被认为是正确的，然后再使用机器学习算法从专家选出的结构中求出最优的一个。这种方法利用专家知识剔除了大量无意义的网络结构，避免了学习算法的穷举搜索，加快了学习速度。
(3) 研究了基于知识的建模理论，提出了基于案例和规则推理的贝叶斯网建模方法。将历史贝叶斯网模型作为案例保存到案例库中，设计了相似度和偏离度两个指标，当面临新的问题时，利用案例推理进行模型匹配，得到相同或相似的案例，并进行案例修正。如果案例推理没有结果，系统转向规则推理继续建模过程。这种方法将贝叶斯网作为整体进行复用，提高了贝叶斯网的建模效率。
(4) 阐述了贝叶斯网的建模原则，建立了面向复杂问题的贝叶斯网建模流程。分为问题分析、模型设计和模型测试三个阶段。问题分析阶段通过对问题的分析，选择领域专家，对复杂的问题进行任务分解。模型设计阶段首先确定相关的变量，然后分别建模网络结构，确定节点的概率分布。最后用测试方法测试模型，修正错误，直到模型较为准确为止。同时还讨论了简化模型的方法。
(5) 研究了定性贝叶斯网的特点，针对其推理过程不精确的缺点，提出了带权重的定性贝叶斯网，使用一个数值权重描述节点之间影响力的强弱，在推理时可以通过权重之间的运
Decision problems are always uncertain due to their ambiguity and randomicity, imperfection and nonproficiency of decision information, finity of human's cognitive abilities and otherness of subjective cognizance from objective realities. The existence of uncertainty raises the difficulty in making decisions. Therefore, decision theories and methods in uncertain circumstances is the frontier area in decision-science.
In recent years, many of resolvents to uncertain problems have appeared such as evidence theory, Bayesian Network, fuzzy set and rough set with the development of mathematical theory and artificial intelligence. Among these methods, Bayesian Network has a good many advantages such as intuitionistic expression abilities and strong knowledge reasoning especially at uncertain reasoning which make it a hot topic in uncertain theory.
Aiming at Bayesian Network's shortage of low study efficiency and difficult to be constructed, this dissertation mainly discusses Bayesian Network modeling techniques and its application in decision-making, including:
(1) The dissertation summarizes the categories of uncertain problems, the development of Bayesian Network and research has been made on it, its prospect of being applied in management decision and intelligent decision support system. It also expatiates on Bayesian Network's structure and characteristics, reasoning methods and all kinds of expanding models of Bayesian Networks.
(2) The structural learning methods of Bayesian Network are discussed. A constructing method of Bayesian Network combining knowledge with data is presented. Firstly, the experts assign belief of networks structure, which is combined by evidence theory. The structures with highest belief are considered as correct ones. Secondly, we select the best one from those structures given by the experts using a learning arithmetic. Eliminating insignificant structures of network by expert knowledge, this method can avoid mass blindly hunting and speed up study rate.
(3) The knowledge-based modeling method of Bayesian Network is discussed. A modeling method based on case and rule reasoning is presented. By saving historical Bayesian models to case-base and designing two indexes: degree of similarity and degree of irrelevance, we can match models with case-based reasoning when encounter with a new problem, and get a same or similar case. If the cased-based reasoning proved to be resultless , the system will continue modeling procedure by rule-based reasoning .This method reuses Bayesian Network as a whole, thus to improve the modeling efficiency .
(4) The Bayesian Network modeling principles are summarized, and the modeling course for
近年来，随着数学理论与人工智能技术的发展，出现了多种不确定性问题的处理方法，如证据理论、贝叶斯网、模糊集和粗糙集等。在这些方法中，贝叶斯网络是以概率论为数学基础的图形模式，具有直观的表达能力和强大的知识推理能力等诸多优越性，在不确定推理方面具有较强的优势，因此成为不确定理论研究的热点。
本文针对贝叶斯网络存在学习效率不高、建模困难的缺陷，重点研究了贝叶斯网建模技术及其在管理决策中的应用，具体内容如下：
(1) 综述了不确定性问题的分类，贝叶斯网的诞生发展过程和研究现状，贝叶斯网在管理决策及智能决策支持系统中的应用前景。阐述了贝叶斯网的结构和特点，常用的推理方法，以及贝叶斯网的各种扩展模型。
(2) 研究了贝叶斯网的结构学习，提出了一种知识和数据融合的贝叶斯网结构学习方法。首先由专家给出对网络结构的信度分配，采用证据理论进行证据合成，合成后具有最高信度的结构被认为是正确的，然后再使用机器学习算法从专家选出的结构中求出最优的一个。这种方法利用专家知识剔除了大量无意义的网络结构，避免了学习算法的穷举搜索，加快了学习速度。
(3) 研究了基于知识的建模理论，提出了基于案例和规则推理的贝叶斯网建模方法。将历史贝叶斯网模型作为案例保存到案例库中，设计了相似度和偏离度两个指标，当面临新的问题时，利用案例推理进行模型匹配，得到相同或相似的案例，并进行案例修正。如果案例推理没有结果，系统转向规则推理继续建模过程。这种方法将贝叶斯网作为整体进行复用，提高了贝叶斯网的建模效率。
(4) 阐述了贝叶斯网的建模原则，建立了面向复杂问题的贝叶斯网建模流程。分为问题分析、模型设计和模型测试三个阶段。问题分析阶段通过对问题的分析，选择领域专家，对复杂的问题进行任务分解。模型设计阶段首先确定相关的变量，然后分别建模网络结构，确定节点的概率分布。最后用测试方法测试模型，修正错误，直到模型较为准确为止。同时还讨论了简化模型的方法。
(5) 研究了定性贝叶斯网的特点，针对其推理过程不精确的缺点，提出了带权重的定性贝叶斯网，使用一个数值权重描述节点之间影响力的强弱，在推理时可以通过权重之间的运
Decision problems are always uncertain due to their ambiguity and randomicity, imperfection and nonproficiency of decision information, finity of human's cognitive abilities and otherness of subjective cognizance from objective realities. The existence of uncertainty raises the difficulty in making decisions. Therefore, decision theories and methods in uncertain circumstances is the frontier area in decision-science.
In recent years, many of resolvents to uncertain problems have appeared such as evidence theory, Bayesian Network, fuzzy set and rough set with the development of mathematical theory and artificial intelligence. Among these methods, Bayesian Network has a good many advantages such as intuitionistic expression abilities and strong knowledge reasoning especially at uncertain reasoning which make it a hot topic in uncertain theory.
Aiming at Bayesian Network's shortage of low study efficiency and difficult to be constructed, this dissertation mainly discusses Bayesian Network modeling techniques and its application in decision-making, including:
(1) The dissertation summarizes the categories of uncertain problems, the development of Bayesian Network and research has been made on it, its prospect of being applied in management decision and intelligent decision support system. It also expatiates on Bayesian Network's structure and characteristics, reasoning methods and all kinds of expanding models of Bayesian Networks.
(2) The structural learning methods of Bayesian Network are discussed. A constructing method of Bayesian Network combining knowledge with data is presented. Firstly, the experts assign belief of networks structure, which is combined by evidence theory. The structures with highest belief are considered as correct ones. Secondly, we select the best one from those structures given by the experts using a learning arithmetic. Eliminating insignificant structures of network by expert knowledge, this method can avoid mass blindly hunting and speed up study rate.
(3) The knowledge-based modeling method of Bayesian Network is discussed. A modeling method based on case and rule reasoning is presented. By saving historical Bayesian models to case-base and designing two indexes: degree of similarity and degree of irrelevance, we can match models with case-based reasoning when encounter with a new problem, and get a same or similar case. If the cased-based reasoning proved to be resultless , the system will continue modeling procedure by rule-based reasoning .This method reuses Bayesian Network as a whole, thus to improve the modeling efficiency .
(4) The Bayesian Network modeling principles are summarized, and the modeling course for
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