| 模糊相容商空间与模糊子集 |
| |
| 引用本文： | 张铃,张钹.模糊相容商空间与模糊子集[J].中国科学：信息科学,2011(1). |
| |
| 作者姓名： | 张铃 张钹 |
| |
| 作者单位： | 安徽大学计算机学院;智能技术与系统国家重点实验室;清华大学信息科学与技术国家实验室;清华大学信息学院;清华大学计算机系; |
| |
| 基金项目： | 国家自然科学基金(批准号:60621062,61073117); 国家重点基础研究发展计划(批准号:2004CB318108,2007CB311003)资助项目 |
| |
| 摘 要： | 本文利用商空间理论中的粒度和层次概念来讨论模糊子集的结构和性质.首先将基于等价关系的商空间理论推广到基于模糊相容关系,接着讨论模糊相容关系的同构性及同构性的判别问题,最后利用模糊相容关系定义模糊子集,并讨论其性质.主要给出以下结果:(1)模糊相容关系的几种等价表示形式;(2)模糊相容关系的同构定义;(3)模糊相容关系同构的判别准则;(4)模糊相容关系下的模糊子集的定义及其相关性质;以及(5)模糊子集同构的充分必要条件.这些结果加深了我们对模糊相容关系和模糊集的理解.
|
| 关 键 词： | 模糊相容关系 商空间 同构 模糊子集 |
Fuzzy tolerance quotient spaces and fuzzy subsets |
| |
| ZHANG Ling & ZHANG Bo, Computer Science & Technology College,Anhui University,Anhui ,China, State Key Laboratory of Intelligent Technology , Systems,Beijing , Tsinghua National Laboratory of Information Science & Technology, Information Science & Technology College,Computer Science & Technology.Fuzzy tolerance quotient spaces and fuzzy subsets[J].Scientia Sinica Informationis,2011(1). |
| |
| Authors: | ZHANG Ling & ZHANG Bo Computer Science & Technology College Anhui University Anhui China State Key Laboratory of Intelligent Technology Systems Beijing Tsinghua National Laboratory of Information Science & Technology Information Science & Technology College Computer Science & Technology |
| |
| Affiliation: | ZHANG Ling1 & ZHANG Bo2,3,4 1 Computer Science & Technology College,Anhui University,Anhui 230039,China,2 State Key Laboratory of Intelligent Technology and Systems,Beijing 100084,3 Tsinghua National Laboratory of Information Science & Technology,4 Information Science & Technology College,Computer Science & Technology Department,Tsinghua University |
| |
| Abstract: | The structure and characteristic of fuzzy subsets are discussed by using the concepts of granulation and hierarchy in quotient space theory.First,the equivalence relation based quotient space theory is extended to the fuzzy tolerance relation.Second,the isomorphism and its discriminant of fuzzy tolerance relations are discussed.Finally,by using the fuzzy tolerance relation to define the fuzzy subset,its properties are addressed. The main results are given below:(1) several equivalent statements of fuzzy tol... |
| |
| Keywords: | fuzzy tolerance relation quotient space isomorphism fuzzy subset |
| 本文献已被 CNKI 等数据库收录！ |
|
