文档介绍：, ?2003 Journal of Software 软件学报 1000-9825/2003/14(04)0770 模糊商空间理论(模糊粒度计算方法) ?张铃, 张钹(安徽大学人工智能研究所,安徽合肥230039) (清华大学智能技术与系统国家重点实验室,北京 100084) (清华大学计算机科学与技术系,北京 100084) Theory of Fuzzy Quotient Space (Methods of Fuzzy puting) ZHANG Ling 1,2+, ZHANG Bo 2,3 (Artificial Intelligence Institute, Anhui University, Anhui 230039, China) (State Key Laboratory of Intelligent Technology and System, Tsinghua University, Beijing 100084, China) (Department puter Science and Technology, Tsinghua University, Beijing 100084, China) + Corresponding author: Phn: 86-551-5107664, E-mail: ******@ahu. ; Received 2002-07-29; Accepted 2002-09-30 Zhang L, Zhang B. Theory of fuzzy quotient space (methods of fuzzy puting). Journal of Software, 2003,14(4):770~776. Abstract: In this paper, the quotient space modelis extended to the fuzzy granular world and two main conclusions are given. First, the following four statements are equivalent: (1) a fuzzy equivalence relation given in universe X, (2) a normalized isosceles distance given in quotient space [X], (3) a hierarchical structure given in X, (4) a fuzzy knowledge base given inX. Second, the whole world with different fuzzy poses plete semi-order lattice. The results provide a powerful mathematical model and tool for puting. Key words: puting; quotient space theory of problem solving; rough set theory; fuzzy set theory; quotient space model 摘要: 把商空间模型推广到模糊粒度世界,,下面4种提法等价:(1)在论域X上给定一个模糊等价关系;(2)给定X的商空间上的一个归一化等腰距离;(3)给定X的一个分层递阶结构;(4),所有模糊粒度世界全体,. 关键词: 粒度计算;问题求解的商空间理论;粗糙集理论;模糊集理论;商空间模型中图法分类号:TP18 文献标识码: A 波兰学者Pawlak [1]提出了一个假设:人的智能(知识),但却?Supported by the National Natural Science Foundation of China under Grant , 60175010 (国家自然科学基金) 第一作者简介:张铃(1937 ),男,福建福清人,教授,博士生导师,主要研究领域为人工智能理论,机器学习理论和方法,粒度计算. 万方数据张铃等:模糊商空间理论(模糊粒度计算方法) 771 ,,在论域中给定一个等价关系以后,就为论域给定了一个知识基(X,R).然后,讨论一个一般的概念x如何用知识基中的知识来表示,即用知识基中的集合的并来表示,对于那些无法