基于模糊化邻域系的粗糙近似算子(Ⅰ)  

Fuzzifying Neighborhood Systems-based Rough Approximation Operators(Ⅰ)

作　　者：金秋[1] 蒋惜珂 李令强[1] JIN Qiu;JIANG Xi-ke;LI Ling qiang(Department of Mathematics,Liaocheng University,Liaocheng Shandong 252059,China)

机构地区：[1]聊城大学数学科学学院,山东聊城252059

出　　处：《大学数学》2018年第4期1-5,共5页College Mathematics

基　　金：国家自然科学基金资助课题(11501278,11471152);山东省自然科学基金资助课题(ZR2013AQ011,ZR2014AQ011);聊城大学成人教育科研立项项目(ldcj201216);聊城大学大学生科技文化创新基金(26312170714)

摘　　要：模糊化邻域系源自模糊化拓扑空间.以模糊化邻域系为工具,定义了一对粗糙近似算子,研究了其基本性质.证明了这对算子涵盖一些常见粗糙近似算子作为其特殊情形,从而扩大了粗糙集理论的研究范围.此外,还研究了由串行的、反身的、一元的和传递的模糊化邻域系生成的粗糙近似算子.The notion of fuzzifying neighborhood systems is initiated from the notion of fuzzifying topological spaces. In this paper, we introduce a pair of rough approximation operators by the notion of fuzzifying neighborhood systems, and then study their basic properties. We prove that this pair of approximation operators includes many well known rough approximation operators as their special case. Therefore, it enlarges the research scope of rough set theory. Furthermore, we also study the approximation operators generated by serial, reflexive, unary and transitive fuzzifying neighborhood systems.

关 键 词：粗糙集 模糊集 模糊化邻域系 近似算子 

分 类 号：O159.1[理学—数学] TP18[理学—基础数学]