基于三支决策的拟阵扩展理论研究

Using various mathematical tools to study rough sets are always hot topics in the research of rough set theory. Due to its rich axiom systems and algorithm properties, matroid theory now is an important tool for the research of rough sets. As an induced theory of rough sets, three-way decision theory becomes a new approach to decision and information processing in recent years. This project is expected to construct various generalized three-way decision models based on subset evaluation and focuses on the study of combination of three-way decisions and matroids. The main content is as follows. 1. To study generalized three-way decision models. We study mainly lattice-value three-way decision model and fuzzy three-way decision model, and focus on matroidal structures of these two models. 2. To study generalized matroids based on generalized three-way decision models. We emphasis on lattice-value three-way matroids and fuzzy three-way matroids, study axiom systems of these two generalized matroids and connections with other generalized matroids. 3. To study algorithm properties of lattice-value three-way matroids and fuzzy three-way matroids. We consider mainly the problems of maximum weight basis and maximum common independent set in these two generalized matroids. This project may help to promote the development of three-way decisions, enrich the theory of generalized matroids and extend the application background for algorithms in combinatorial optimization.

运用各种数学工具和方法来研究粗糙集一直是粗糙集理论研究的热点。拟阵理论由于其丰富的公理系统和算法性质，现已成为粗糙集研究的重要工具。作为粗糙集理论的延伸，三支决策理论近年来逐渐发展成为一种新的决策和信息处理方法。本项目拟建立基于子集评价的各种三支决策扩展模型并致力于三支决策理论和拟阵理论的融合研究。主要内容如下：1. 研究三支决策扩展模型，重点研究格值三支决策模型、模糊三支决策模型及两种扩展模型的拟阵结构性质；2. 研究基于三支决策扩展模型的拟阵推广理论，重点研究格值三支拟阵和模糊三支拟阵，考察这两类扩展拟阵的公理系统及与其它拟阵推广理论的关系；3. 研究格值三支拟阵和模糊三支拟阵的算法性质，重点考察这两类基于三支决策的拟阵扩展理论中求解最大权基、最大公共独立集等问题的算法。本项目将推动三支决策理论的发展，丰富拟阵扩展理论，拓宽组合优化算法的应用范围。

本项目主要研究了三支决策扩展模型及其在拟阵推广和冲突分析等方面的应用。主要研究结果及进展如下：. （1）建立了面向一般信息表的三支决策扩展模型，提出了基于信息测度的模型求解方法，并将各种双论域粗糙集模型统一到该模型之下；（2）建立了基于模糊信息和子集评价的三支决策扩展模型，并应用于冲突分析研究，提出了模糊信息值态度下联盟建立方法及事件对联盟重要度分析方法；（3）提出了基于三支决策方法的拟阵推广结构：三支模糊拟阵，研究了三支模糊拟阵的性质，并且指出三支模糊拟阵为粒计算三元论提供了一个数学模型；（4）研究了信息表中基于拟阵方法的概念近似，提出了一种基于几何格和划分格的双拟阵结构。. 上述研究成果已在本领域国内外期刊上发表论文35篇，其中SCI检索论文24篇。此外，出版学术著作1部，举办学术会议3次。这些工作不仅对三支决策及拟阵的推广理论的发展起到了积极的推动作用，在粒计算研究领域也产生了重要影响。