直觉模糊信息下的三支决策粗糙集方法及知识获取研究

Intuitionistic fuzzy set and decision-theoretic rough set are important methods for uncertain and imprecise problems. Considering the boundary region descriptions in subjective preference modeling and objective data driven analysis, respectively, intuitionistic fuzzy set and decision-theoretic rough set are both typical three-way decisions methodologies, and they received much attention in fuzzy rough decision research fields recently. Based on intuitionistic fuzzy set and decision-theoretic rough set theory, the main research objective of this proposal is to systematically study the decision-theoretic rough set methods under intuitionistic fuzzy preference information, in view of the fuzzy risk preference and the cost-sensitive characteristic of decision-makers in financial risk assessment problems. The main tasks of this project are to: (1) investigate the decision-theoretic rough set model in view of the intuitionistic fuzzy subjective preference, and establish a risk assessment decision mechanism by combining the subjective preference information and objective data information; and (2) study the attribute reduction and knowledge acquisition based on decision-theoretic rough set for intuitionistic fuzzy objective information systems, so as to discover the essential knowledge from massive data; and (3) investigate the group decision making methods using decision-theoretic rough set by integrating multi-decision-makers’ intuitionistic fuzzy preference and multi-attribute-reductions, which contributes to establish a methodology of group knowledge acquisition based on intuitionistic fuzzy decision-theoretic rough set. Besides the theory and methodology, the project also investigates the research fields of real-world applications. The applications of intuitionistic fuzzy decision-theoretic rough set in financial risk assessment areas will be further discussed based on the theoretical analysis, which provides an applicable decision support for scientific assessment on financial risk in real economical operation.

直觉模糊集与决策粗糙集均为处理不确定、不精确问题的重要方法，两者分别在主观偏好建模和客观数据分析中引入三支边界域表述，是典型的三支决策方法，目前正成为模糊粗糙决策研究领域的新亮点。本项目以金融风险评估问题为背景，以直觉模糊集和决策粗糙集为工具，针对决策者风险偏好的模糊性和误决策代价非平衡特点，系统研究直觉模糊信息下的决策粗糙集方法及应用。内容包括：（1）研究直觉模糊主观偏好信息下的决策粗糙集模型，建立基于主观偏好与客观数据的风险评估决策方法；（2）研究直觉模糊目标信息系统的决策粗糙集属性约简与知识获取方法，以实现海量数据中可用信息的精简；（3）研究群体代价损失函数的直觉模糊描述方法和多属性约简的集成方法，实现直觉模糊风险偏好下的决策粗糙集群决策与集成知识获取。在理论研究的同时，本项目将以金融评估为研究对象，依据理论方法研究结果，开展应用研究，为科学合理评估经济运行中的金融风险提供决策支持。

本项目以直觉模糊信息下的决策粗糙集方法及知识获取为研究对象，以决策粗糙集、直觉模糊集、三支决策为理论依据，系统研究了基于决策粗糙集的直觉模糊知识获取方法。主要研究成果包括：1、研究了直觉模糊主观偏好信息条件下的决策粗糙集方法。（1）引入了决策理论粗糙集和多粒度粗糙集之间的一种包含测度，该研究为从多粒度直觉模糊决策系统获取知识提供了一种多粒度直觉模糊决策粗糙集方法。（2）解决了基于优势的多尺度直觉模糊决策表中最佳尺度选择和规则获取的问题。（3）提出了一种基于模糊测度的新型优化模型，设计了一种粒子群算法来求解模型。2、研究了直觉模糊目标信息系统的决策粗糙集属性约简与规则提取。（1）提出了一种借助多粒度策略的新的代价敏感粗糙集模型。（2）定义了直觉模糊对象之间的相似度和发散度，给出了相关性质，并且利用定义的粗糙隶属函数推导出目标集的上下近似集。（3）研究了Local约简与Global约简之间的内在序贯性，并以此构建了具有约简特性的序贯信息粒。3、研究了直觉模糊风险偏好下的决策粗糙集群决策与集成属性约简。（1）基于归一化的汉明距离，定义了直觉模糊数之间的相似性度量，由此得到直觉模糊集之间的相似性度量。（2）根据合理粒度的原则，研究了一种新颖的分类算法，称为具有合理子空间的序贯三支分类器。4、研究了基于直觉模糊决策粗糙集模型的金融风险评估应用研究。（1）针对专家评价值为直觉模糊数时的情况，提出一种新的基于动态直觉模糊理想解法来评价智能体。（2）对于多源异构信息系统中的评估问题，采用基于TOPSIS的评估方法。（3）提出了基于前景理论的三支决策模型。使用前景理论来描述决策者的风险态度，并利用价值函数作为一种新的风险度量。（4）提出了一种基于累积前景理论的三支决策模型并证明了该模型阈值的存在性和唯一性。基于条件概率和阈值的数值解对决策规则进行了简化，构造了三支决策规则的推导算法。