| 模糊度的结构分析 |
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| 引用本文： | 张铃,张钹,张燕平.模糊度的结构分析[J].中国科学：信息科学,2011(7). |
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| 作者姓名： | 张铃 张钹 张燕平 |
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| 作者单位： | 安徽大学计算机学院;清华信息科学与技术国家实验室智能技术与系统国家重点实验室清华大学信息学院计算机系; |
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| 基金项目： | 国家自然科学基金(批准号:90820305,61073117); 国家基础研究发展计划(批准号:2007CB311003)资助项目 |
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| 摘 要： | 从商空间的粒度计算理论出发,本文讨论模糊集的模糊度量问题,即模糊度的定义.根据模糊集的结构分析,我们提出各向同性的假设,在这个假设下得出以下结果:(1)在有限完备半序集上具有各向同性的模糊度是唯一的.(2)得出模糊数学中的模糊度函数同构的充分必要条件.(3)得出模糊度具有模糊单调性和粒度单调性的充分必要条件.(4)在一定的假设下,给出模糊度的解析表达式.这些结果阐明了模糊度与粒计算的关系,揭示了模糊度的本质,同时提供一种构造模糊度的简易方法.
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| 关 键 词： | 商空间 模糊集 模糊度 粗糙集 结构分析 |
The structural analysis of fuzzy measures |
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| ZHANG Ling,ZHANG Bo & ZHANG YanPing Computer Science College,Anhui University,Hefei ,China, State Key Lab of Intelligent Technology & Systems,Tsinghua National Lab for Information Science & Technology,Information Science & Technology College,Computer Science & Technology.The structural analysis of fuzzy measures[J].Scientia Sinica Informationis,2011(7). |
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| Authors: | ZHANG Ling ZHANG Bo & ZHANG YanPing Computer Science College Anhui University Hefei China State Key Lab of Intelligent Technology & Systems Tsinghua National Lab for Information Science & Technology Information Science & Technology College Computer Science & Technology |
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| Affiliation: | ZHANG Ling~1,ZHANG Bo~(2*) & ZHANG YanPing~1 1 Computer Science College,Anhui University,Hefei 230039,China,2 State Key Lab of Intelligent Technology & Systems,Tsinghua National Lab for Information Science & Technology,Information Science & Technology College,Computer Science & Technology Department,Tsinghua University,Beijing 100084 |
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| Abstract: | From the quotient space based granular computing theory we explore the fuzzy measures of fuzzy sets. Based on the structural analysis of fuzzy sets,we present anisotropismassumption.Under the assumption we have the following results,(1) the uniqueness of the fuzzy measure having isotropic on a finite complete semi-order set;(2) the necessary and sufficient condition of the isomorphism of fuzzy measure functions in fuzzy mathematics;(3) the necessary and sufficient condition that fuzzy measures have fuzzy an... |
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| Keywords: | quotient space fuzzy set fuzzy measure rough set structural analysis |
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