基于决策粗糙集的模糊多分类三支决策方法与应用研究

The problem of uncertainty and complexity in decision making is always treated as one of the hot topics in decision analysis. This project considers the fuzzy uncertainty and complexity of multi-category simultaneously, and proposes a new decision-theoretic rough set model (DTRSM). On the one hand, we utilize the fuzzy loss functions to describe the decision risk; on the another hand, we use the multi-category situation to represent the complexity of decision systems. The methodologies and applications of fuzzy multi-category three-way decisions (FMTWD) based on DTRS are investigated via Bayesian decision procedure. The main contents of this project are as follows: 1. A new fuzzy multi-category three-way decision model (FMTWDM) is constructed, the properties and principles of FMTWDM are analyzed, the similarity and difference between FMTWDM and DTRS are discussed. 2. By considering four types of fuzzy loss functions, the attribute reduction in FMTWDM and the integrated mechanism of decision rules with three different regions are investigated. 3. Under group decision environment, the causes of inconsistency generated by fuzzy multi-category three-way group decisions are discussed. Furthermore, the conflict mechanisms in group decision with the viewpoint of optimizations are investigated. 4. The applications of the new group decision model in risk benefit management and emergency management are studied. This project can enrich the theory and methodology of three-way decisions, make the decision-making process more close to the realistic decision environment, and further promote the development of decision analysis based on rough sets.

决策的不确定性和复杂性问题一直以来是决策分析研究的热点。本项目同时将模糊不确定性和多分类复杂性引入到决策粗糙集中，一方面利用模糊损失函数来刻画决策不确定风险；另一方面利用多分类状态来描述决策系统的复杂性，进而探讨在贝叶斯决策过程下，基于决策粗糙集的模糊多分类三支决策理论与方法。具体研究内容为：1. 构建模糊多分类三支决策基本模型，分析其数学性质，讨论新模型与决策粗糙集的继承和拓展关系；2. 考虑四种类型模糊损失函数时，不同模糊多分类三支决策的属性约简方法，研究三个决策区域生成决策规则的融合机理；3. 研究群决策下模糊多分类三支群决策模型产生不一致规则的原因，并从优化的角度讨论相应的冲突协调机制；4. 探讨模糊多分类三支群决策在风险收益、应急管理等实际问题中的应用。本项目不仅丰富了三支决策现有理论和方法，使决策过程更符合现实决策环境，而且可推动粗糙集理论在决策分析领域的发展。

决策的复杂性一直以来是决策分析研究的热点之一，多分类决策正是研究这类复杂问题的典型代表。作为一种新的处理复杂决策问题的方法，本项目引入决策粗糙集理论来研究多分类决策问题。考虑到决策环境的不确定性，利用模糊损失函数来刻画决策风险，探讨贝叶斯决策过程下，模糊决策环境和多分类决策情形下模糊多分类三支决策理论与方法。具体研究内容为：1.构建模糊三支决策和模糊多分类三支决策基本模型，分析其数学性质，讨论新模型与决策粗糙集的继承和拓展关系；2.考虑不同类型模糊损失函数时，不同模糊多分类三支决策的属性约简方法，研究三个决策区域生成决策规则的融合机理；3.研究群决策下模糊多分类三支群决策模型产生不一致规则的原因，并从优化的角度讨论相应的冲突协调机制；4.探讨模糊多分类三支群决策在管理问题中的应用。本项目从三支决策的视角来研究模糊多分类问题，不仅丰富了多分类决策理论和方法，而且可推动三支决策理论在决策分析领域的发展。