定性概率网整合
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摘要
概率网是人工智能学科表示并处理概率知识的一类图模型方法.多源概率网整合是全面进行概率知识表示和推理研究中的重要问题.已有工作大多限于贝叶斯网、影响图和可能性网等定量概率网的整合,较少考虑到概率知识只能定性表示或只需定性表示时的定性概率网(Qualitative Probabilistic Networks, QPNs)整合.
基于上述问题,本文结合不完整数据,研究QPNs符号整合方法和三种情况下的QPNs结构整合方法.具体内容包括：
1.提出基于定性互信息的歧义性约简方法.严格定义定性互信息,在此基础上提出可区分影响强度的增强QPN,并证明其性质,给出多项式时间的歧义性约简方法.
2.设计并实现基于定性互信息的QPNSI符号整合算法.将歧义性约简方法扩展到多个结构相同的QPNs符号整合中,提出QPNSI整合算法,分析了算法的时间复杂性.
3.设计并实现具有相同节点的SNQPNI结构整合算法.基于粗糙集理论,采用概率正域求解属性依赖度作为定性影响的强度,解决整合时涉及到的关键问题,提出SNQPNI整合算法,分析了算法的时间复杂性.
4.设计并实现时序环境具有相同节点的TQPNI结构整合算法.定义时变QPN(TQPN),通过考虑其中的自身环等问题,提出基于粗糙集理论的TQPNI整合算法,分析了算法的时间复杂性.
5.设计并实现具有不同节点的DNQPNI结构整合算法.由SNQPNI算法整合思想,得出合并后的初始QPN,基于粗糙集理论,通过向其中添加缺失边和删除冗余边,提出DNQPNI整合算法,分析了算法的时间复杂性.
Probabilistic network is the important approach to represent and deal with prob-abilistic knowledge in artificial intelligence. The integration of multiple-source prob-abilistic networks is crucial to research comprehensively on representation and rea-soning of probabilistic knowledge. However, in many previous researches, these inte-gration methods are proposed mostly for quantitative probabilistic networks, such asBayesian networks, influence diagrams and possibilistic networks, but less for takinginto account to integrate multiple Qualitative Probabilistic Networks (QPNs) by whichprobabilistic knowledge only can be represented or be needed to represent qualitatively.
In this paper, the sign integration method and three structure integration meth-ods are proposed by combining domain expert knowledge and incomplete data. Mainresults are as follows.
1. Ambiguity reduction method is proposed based on qualitative mutual information.The definition of qualitative mutual information is first given. Using the definitionan enhanced QPN is proposed. Specifically, symmetry, transitivity, parallel com-position of qualitative influences, geometric properties in the enhanced QPN areanalyzed. Furthermore, ambiguity reduction method in polynomial time for QPNinference is proposed.
2. The sign integration method named QPNSI algorithm is designed and implementedbased on qualitative mutual information. The above ambiguity reduction method isfurther extended to the integration of multiple QPNs that have the same structures.QPNSI algorithm is proposed and its time complexity is analyzed.
3. The structure integration method named SNQPNI algorithm is designed and im-plemented based on rough set theory. Probabilistic positive region is adopted tocompute attribute dependency degree that regarded as the strength of qualitative in-fluence. SNQPNI integration algorithm of multiple QPNs that have the same nodesis proposed by addressing some key problems and its time complexity is analyzed.
4. The structure integration method named TQPNI algorithm is designed and imple-mented based on rough set theory. The definition of temporal QPN (TQPN) is firstgiven, and then TQPNI algorithm of multiple TQPNs in time serial environment isproposed by removing self loop. The time complexity is analyzed.
5. The structure integration method named DNQPNI algorithm is designed and im-plemented based on rough set theory. The initial union of QPNs is obtained basedon the idea of SNQPNI algorithm. Furthermore, the missing edges are added to itaccording to attribute dependency degree and the redundant edges are removed byattribute relative necessity and relative reduction. DNQPNI integration algorithm ofmultiple QPNs that have the diferent nodes is proposed and its time complexity isanalyzed.
基于上述问题,本文结合不完整数据,研究QPNs符号整合方法和三种情况下的QPNs结构整合方法.具体内容包括：
1.提出基于定性互信息的歧义性约简方法.严格定义定性互信息,在此基础上提出可区分影响强度的增强QPN,并证明其性质,给出多项式时间的歧义性约简方法.
2.设计并实现基于定性互信息的QPNSI符号整合算法.将歧义性约简方法扩展到多个结构相同的QPNs符号整合中,提出QPNSI整合算法,分析了算法的时间复杂性.
3.设计并实现具有相同节点的SNQPNI结构整合算法.基于粗糙集理论,采用概率正域求解属性依赖度作为定性影响的强度,解决整合时涉及到的关键问题,提出SNQPNI整合算法,分析了算法的时间复杂性.
4.设计并实现时序环境具有相同节点的TQPNI结构整合算法.定义时变QPN(TQPN),通过考虑其中的自身环等问题,提出基于粗糙集理论的TQPNI整合算法,分析了算法的时间复杂性.
5.设计并实现具有不同节点的DNQPNI结构整合算法.由SNQPNI算法整合思想,得出合并后的初始QPN,基于粗糙集理论,通过向其中添加缺失边和删除冗余边,提出DNQPNI整合算法,分析了算法的时间复杂性.
Probabilistic network is the important approach to represent and deal with prob-abilistic knowledge in artificial intelligence. The integration of multiple-source prob-abilistic networks is crucial to research comprehensively on representation and rea-soning of probabilistic knowledge. However, in many previous researches, these inte-gration methods are proposed mostly for quantitative probabilistic networks, such asBayesian networks, influence diagrams and possibilistic networks, but less for takinginto account to integrate multiple Qualitative Probabilistic Networks (QPNs) by whichprobabilistic knowledge only can be represented or be needed to represent qualitatively.
In this paper, the sign integration method and three structure integration meth-ods are proposed by combining domain expert knowledge and incomplete data. Mainresults are as follows.
1. Ambiguity reduction method is proposed based on qualitative mutual information.The definition of qualitative mutual information is first given. Using the definitionan enhanced QPN is proposed. Specifically, symmetry, transitivity, parallel com-position of qualitative influences, geometric properties in the enhanced QPN areanalyzed. Furthermore, ambiguity reduction method in polynomial time for QPNinference is proposed.
2. The sign integration method named QPNSI algorithm is designed and implementedbased on qualitative mutual information. The above ambiguity reduction method isfurther extended to the integration of multiple QPNs that have the same structures.QPNSI algorithm is proposed and its time complexity is analyzed.
3. The structure integration method named SNQPNI algorithm is designed and im-plemented based on rough set theory. Probabilistic positive region is adopted tocompute attribute dependency degree that regarded as the strength of qualitative in-fluence. SNQPNI integration algorithm of multiple QPNs that have the same nodesis proposed by addressing some key problems and its time complexity is analyzed.
4. The structure integration method named TQPNI algorithm is designed and imple-mented based on rough set theory. The definition of temporal QPN (TQPN) is firstgiven, and then TQPNI algorithm of multiple TQPNs in time serial environment isproposed by removing self loop. The time complexity is analyzed.
5. The structure integration method named DNQPNI algorithm is designed and im-plemented based on rough set theory. The initial union of QPNs is obtained basedon the idea of SNQPNI algorithm. Furthermore, the missing edges are added to itaccording to attribute dependency degree and the redundant edges are removed byattribute relative necessity and relative reduction. DNQPNI integration algorithm ofmultiple QPNs that have the diferent nodes is proposed and its time complexity isanalyzed.
引文
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