模糊集和soft集描述了不同类型的不确定性，它们和粗糙集分别融合而得到的模糊粗糙集和soft粗糙集, 将知识粒度由等价类扩充为模糊化的集合类和参数化的集合类, 形成更强大的不确定性描述的数学工具, 使应用范围进一步扩大, 更有利于实际问题的解决。因此, 研究两类广义粗糙集(模糊粗糙集和soft粗糙集)对处理不确定性问题尤为重要。本项目拟利用粗糙集理论和soft集理论的最新研究成果, 使用一些数学方法, 力图探讨这两类广义粗糙集的拓扑结构、格结构、拟阵结构和信任结构等基本数学结构, 给出它们的刻划, 并探索将获得的成果应用到不确定决策、信息糸统、图论等实际问题中。

Fuzzy sets and soft sets describe the different types of uncertainty. Fuzzy rough sets and soft rough sets, the fusions of them and rough sets, expand knowledge granularity from equivalence classes to fuzzifying collections and parameterized collections, form a more powerful mathematical tool for uncertainty description and further enlarge the scope of applications. This is more advantageous to solve practical problems. So researching two types of generalized rough set (fuzzy rough sets and soft rough sets) for dealing with uncertainty problems is particularly important. This project intends to explore their basic mathematical structures such as topological structures, lattice structures, matroidal structures and belief structures so on, to give their depictions and to investigate that the research results are applied to uncertain decision, information systems, graph theory and other practical problems.