【作者】 李德顺；

【导师】 许开立；

【作者基本信息】 东北大学 ， 安全技术及工程， 2010， 博士

【摘要】 本文探讨了现阶段SPA理论在系统危险性评价及多属性决策中应用时所存在的问题,提出了基于广义集对分析（General Set Pair Analysis,GSPA）的系统危险性评价及其多属性决策理论。（1）分析了现有的指标线性标准化方法的优缺点。提出了一种改进的线性比例变换方法。该方法不仅保持了原有指标的大小关系,也避免了原线性比例变换方法无法处理x_ij＜0的情况。通过图形与公式相结合的方法详细地讨论了极差变换法的推导过程。考虑到系统危险性在一定状态下,提高相同安全水平的难度会有所不同的特点,提出了可变指数函数型非线性标准化方法与可变抛物线函数型非线性标准化方法,并得出了后者比前者离散化程度更大的结论,更适合指标的标准化处理。（2）讨论了现有权重确定方法。引入GSPA方法,从确定与不确定性两方面讨论了区间权重转化为精确权重值的过程。提出了GSPA-IAHP主观赋权法,避免了单个专家因专业水平、个人偏好等因素的影响。为充分利用专家给出的区间不确定判断信息来确定专家权重,提出了一种基于区间不确定信息的专家后验权重确定方法。并通过分析,得出其同样适用于基于精确型判断信息的专家后验权重确定的结论。（3）针对SPA理论中的相关概念存在的不足,提出了GSPA理论及其相关的概念,主要包括广义集对（General Set Pair,GSP）、广义集对势（General Set Pair Posture,GSPP）,广义集对悲观势（General Set Pair Pessimistic Posture,GSPPP）、广义集对乐观势（GeneralSet Pair Optimistic Posture,GSPOP）及广义态势图（General Posture Figure,GPF）。同时,讨论了几种特殊联系度的GSPP分级情况,使GSPA的有关概念和理论得到进一步丰富和完善。（4）分析了SPA在系统危险性评价应用中存在的不足。讨论了同异反（IdentityDifference Opposition,IDO）联系测度确定方法,提出了一种新的基于三角函数变化的IDO联系测度确定方法。为了衡量联系测度确定方法的优劣,提出了广义联系熵的概念。广义联系熵越小,系统危险性级别的不确定性就越小,该IDO联系测度确定方法就越好。探讨了单层次GSPA评价模型、多层次GSPA评价模型。提出了IDO最优模式识别模型,并通过IDO最优模式识别模型的综合指数判断系统危险性级别,为系统危险性评价提供了新的途径。（5）讨论了GSPA在聚类方面所存在的问题,提出了一种新的联系度IDO相似性测度方法。探讨了一种基于IDO相似性测度的IDO动态聚类方法,为多指标样本聚类分析提供了新的方法。（6）讨论了SPA在多属性决策中存在的不足,提出了基于GSPA-TOPSIS的多属性决策模型、基于GSPA的相对从属度多属性决策模型,并将二者进行了比较,得出了后者较前者离散化程度更高、更易于作出决策的结论。讨论了在权重缺损情况下的多属性决策方法,提出了IDO交叉迭代多属性决策模型,使多属性决策理论更为全面、完善。（7）提出了一种基于GSPA-MARKOV的系统危险性动态评价模型。该模型通过MARKOV链动态地对系统危险性进行评价,从而确定系统不同时刻的危险性。更多还原

【Abstract】 In the dissertation, the open problems on the application of the system risk assessment and the multi-attribute decision-making in the SPA theory are addressed. The theories of GSPA in the system risk assessment and the multi-attribute decision-making are also proposed.(1) Advantages and disadvantages of the existing linear standardization methods of index are analyzed. A modified linear scale transformed method is proposed. It not only maintains the original index size, but also avoids the situation where the index is unable to the linear standardization method when the index is negative. The process of range transformation is discussed in detail. Considering the situation that the characteristic differs when the difficulty of the same safety level is enhanced under a certain condition, the nonlinear standardization methods based on the variable index function and the variable parabola function are proposed. It is concluded that the latter is bigger on the discretization degree than the former, and the latter is more suitable for the index standardization.(2) The existing weight determination methods are discussed. The process that the sector weight is transformed to the precise weigh process is discussed from certainty and uncertainty aspects with the GSPA method. The GSPA-IAHP subjective weight is proposed. It avoids disadvantages of the single expert that is affected by the professional standard, individual hobby and so on. In view of the characteristics that documents of determining the expert weight by the sector uncertainty judgment information are fewer, a new determining expert weight method by the sector uncertainty judgment information is proposed. By the analysis, it is suitable also for the determining expert weight method by the precise judgment information.(3) In view of the existing insufficiencies of the SPA theory in related concepts, the GSPA theory and the related concepts are proposed, mainly including GSP, GSPP, GSPPP, GSPOP, and GPF. The GSPP graduation situations of several special connection degrees have been also discussed. It enhances the related concepts of GSPA. (4) The SPA insufficiencies in the system risk assessment application are analyzed. Determination methods of IDO connection degree are discussed. A new method of IDO connection degree based on the trigonometric function change is proposed. In order to weigh the disadvantages and advantages of determining IDO connection degree methods, the concept of generalized connection entropy is put forward. The generalized connection entropy is smaller. The uncertainty of the system risky grade is smaller. The IDO connection degree determination method is better. The single level GSPA assessment model and multi-level GSPA assessment model are discussed. The IDO most superior pattern recognition model is proposed, and system risky grade is judged by the IDO most superior pattern recognition model composite index, which provides a new way for the system risk assessment.(5) The GSPA applicability in the cluster aspect is discussed. A new measuring method for connection degree similarity is proposed. The IDO dynamic cluster method based on the measure method of connection degree similarity is put forward. It provides a new method for the multi-index sample cluster analysis.(6) Disadvantages of SPA in the multi-attribute decision making are discussed. The multi-attribute decision making model based on the GSPA-TOPSIS and relative subordinate multi-attribute decision making model based on the GSPA are proposed Two comparisons are conducted, It is concluded that the latter is higher in the discretization degree, apt to make a decision to the former. The weight multi-attribute decision making method in the defectiveness is discussed. The IDO overlapping iteration multi-objective decision-making model is proposed. It is more comprehensive.(7) The system risk dynamic assessment model based on the GSPA-MARKOV is proposed. The model assesses the system risk dynamically by the MARKOV chain, and the final system risky is determined.更多还原