基于区间数的决策粗糙集模型与方法研究

In realistic decision process, some challenging factors impact people to make reasonable decisions, e.g., the complexity and dynamic variation of decision environment, the limited knowledge of decision maker, etc. Decision-theoretic rough sets (DTRS) theory is a new method in dealing with uncertainty decision problem. Its feature is to take into account the effect of Bayesian decision risk to decision results. It better serve to our decision making. Interval-value uses an interval to measure uncertainty. It is in line with the need of real decisions. This project intends to construct an extended model of DTRS by the interval-value, research on its attribute reduction, rule induction and methods for dynamically updating rules. The main contents of this project are organized as follows: 1. With the minimum expected overall risk, Interval decision-theoretic rough sets (IDTRS) model is constructed and analyzed its property and principle, which are the basis of attribute reduction and rule induction. 2. Based on the IDTRS model, the mechanisms of attribute reduction are studied in the viewpoint of positive region and the minimization of the decision cost, and the two corresponding optimization algorithms are designed, respectively. 3. By analyzing the conflict mechanisms of derived rules in the positive region, negative region and boundary region, the approach for inducing rules in IDTRS is discussed. Furthermore, considering the dynamic variation of interval-value, the approach for dynamically updating decision rules is analyzed. This project can enrich the theory and methodology of DTRS, and further push the application and development of decision analysis based on rough sets.

决策环境的复杂性、动态性，以及决策者所具备知识的有限性等都是影响人们作出合理决策所面临的挑战性因素。决策粗糙集理论是一种新的处理不确定性决策问题的方法，其特点是考虑到贝叶斯决策风险对决策结果的影响，可更好为人们决策服务。区间数利用一个区间来对不确定性进行度量，符合实际决策需要。本项目基于区间数来构建决策粗糙集扩展模型，研究其属性约简、规则推导及动态获取方法。主要内容包括：1.在期望贝叶斯风险最小情形下，基于区间数构建区间决策粗糙集模型，分析其数学性质，为属性约简和规则推导奠定基础；2.在区间决策粗糙集理论模型下，研究基于正域最大化和基于决策风险最小化的属性约简机理并设计优化算法；3.研究区间决策粗糙集正域、负域和边界域所导出决策规则的冲突机理，讨论相应决策规则推导方法,并研究区间数变化下，动态决策规则的获取。本项目不仅丰富了决策粗糙集理论和方法，而且可推动粗糙集在决策分析领域的应用和发展。

复杂的决策环境、实时变化的决策信息，以及决策者的有限理性和不同偏好等都是影响人们作出合理决策所面临的挑战性因素。决策粗糙集理论是一种近二十年来新起的处理不确定性决策问题的方法，其特点是考虑贝叶斯决策风险对决策结果的影响。区间数利用一个区间来对不确定性进行度量，符合实际决策的需要。本项目基于区间数来构建决策粗糙集扩展模型，研究其属性约简、规则推导及动态获取方法。. 通过三年来的研究，项目组已发表与项目紧密相关的高水平研究论文20余篇，出版专著《三支决策与粒计算》1部。本项目主要研究内容有：1.在期望贝叶斯风险最小情形下，基于区间数构建区间决策粗糙集模型，分析其数学性质，为属性约简和规则推导奠定基础；2.在区间决策粗糙集理论模型下，研究基于正域最大化和基于决策风险最小化的属性约简机理并设计优化算法；3.研究区间决策粗糙集正域、负域和边界域所导出决策规则的冲突机理，讨论相应决策规则推导方法,并研究区间数变化下，动态决策规则的获取。此外，本项目的相关应用成果获得了四川省哲学社科优秀成果二等奖，项目已得到高质量地完成。. 本项目的研究成果不仅丰富了决策粗糙集理论和方法，推动了粗糙集在决策分析领域的应用和发展，而且对于不确定决策粗糙集理论、方法和应用的后续研究有一定的借鉴意义。