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| 模糊商空间理论(模糊粒度计算方法) |
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张铃1,2, 张钹1,2
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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
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| 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,所有模糊粒度世界全体,构成一个完备半序格.这些结论为粒度计算提供了一个强有力的数学模型和工具. |
| 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 |
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| 基金项目:Supported by the National Natural Science Foundation of China under Grant Nos.60135010, 60175010 (国家自然科学基金) |
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| Theory of Fuzzy Quotient Space (Methods of Fuzzy Granular Computing) |
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ZHANG Ling,ZHANG Bo
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| 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 |
