【作者】 顾秀梅；

【导师】 秦克云；

【作者基本信息】 西南交通大学 ， 应用数学， 2007， 硕士

【摘要】 粗糙集理论是Pawlak于1982年提出的一种处理不确定性知识的数学工具，现在已发展成为人工智能的一个重要研究方向，在数据挖掘(data mining)与知识发现(KDD)中具有非常广泛的应用背景，并已获得许多成功的应用。Pawlak粗糙集模型是建立在等价关系基础上的。为推广粗糙集理论的应用范围，Pawlak粗糙集模型被推广为多种形式，包括模糊粗糙集模型、概率粗糙集模型、变精度粗糙集模型以及一般二元关系下的粗糙集模型等。本文研究基于逻辑算子的模糊粗糙集模型，具体做了如下研究工作：(1)给出了两类基于逻辑算子的模糊粗糙集模型：利用连续三角模t给出论域中模糊集合的上近似算子的定义，再分别利用t的剩余蕴涵算子φ和t的对偶余模φ给出了模糊集合的两类下近似算子的定义。(2)讨论了这两类近似算子的基本性质，特别研究了特殊的模糊关系R近似算子之间的联系。(3)通过闭包与内部算子研究模糊粗糙集的拓扑性质，证明了在自反且t传递的模糊关系R下的近似空间中，上、下近似算子分别为一个模糊拓扑的闭包，内部算子。更多还原

【Abstract】 Rough set theory is a mathematical tool of dealing with uncertain information, and Pawlak put forward this theory at 1982. At present, it has developed to be an important research direction of artificial intelligent, it has very extensive latent applying background at the field of Data Mining.Pawlak rough set was established at the base of equivalent relation. For generalizing the application area of rough set theory, Pawlak rough set model is generalized to many models included fuzzy rough set model、probability rough set model、alterable precision rough set model and the rough set model under the generic binary relation etc. In this paper, fuzzy rough sets based on logical operators are researched. Material work is done as follows:Firstly, a general formula norm is given for the approximation operators of fuzzy sets using the triangular norm and its co-nom. And another general formula norm is given using a triangular norm and an implicator. Basic properties of fuzzy rough sets are investigated.Secondly, the connections between fuzzy relations and fuzzy rough approximation operators are examined.Finally, based on closure and interior operators , we discusses the topological structure of fuzzy rough sets. In a approximation space which is based on a reflexive and t-transitive fuzzy relation, it is proved that the upper and lower approximations of fuzzy sets are closure and interior operators of a fuzzy topology respectively.更多还原