模糊商空间理论(模糊粒度计算方法).pdf

1000-9825/2003/14(04)0770 ©2003 Journal of Software 软 件 学 报 Vol.14, No.4 ∗ 模糊商空间理论(模糊粒度计算方法) 1,2+ 2,3 张 铃 , 张 钹 1(安徽大学 人工智能研究所,安徽 合肥 230039) 2(清华大学 智能技术与系统国家重点实验室,北京 100084) 3(清华大学 计算机科学与技术系,北京 100084) Theory of Fuzzy Quotient Space (Methods of Fuzzy Granular Computing) ZHANG Ling1,2+, ZHANG Bo2,3 1(Artificial Intelligence Institute, Anhui University, Anhui 230039, China) 2(State Key Laboratory of Intelligent Technology and System, Tsinghua University, Beijing 100084, China) 3(Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China) + Corresponding author: Phn: 86-551-5107664, E-mail: zling@ ; Received 2002-07-29; Accepted 2002-09-30 Zhang L, Zhang B. Theory of fuzzy quotient space (methods of fuzzy granular computing). Journal of Software, 2003,14(4):770~776. Abstract: In this paper, the quotient space model is 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 in X . Second, the whole world with different fuzzy granularities composes a complete semi-order lattice. The results provide a powerful mathematical model and tool for granule computing. Key words: granule computing; 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,并给出了两个基本结论.一个结论是,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) 给定一个X 的模糊知识基.另一个结论是,所有模糊粒度世