| 二叉树型分层模糊系统的等效性分析 |
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| 引用本文： | 杜新宇,张乃尧.二叉树型分层模糊系统的等效性分析[J].清华大学学报(自然科学版),2004,44(7):993-996. |
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| 作者姓名： | 杜新宇 张乃尧 |
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| 作者单位： | 清华大学,自动化系,北京,100084 |
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| 基金项目： | 国家自然科学基金资助项目(60174015) |
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| 摘 要： | 为进一步研究分析多变量模糊系统以及分层模糊系统的数学机理,解决多变量模糊系统的"维数灾"问题,该文对一类广泛应用的多输入单输出模糊系统(MISO-FS)进行了解析分析,提出了一类二叉树型分层模糊系统(HFS),并推导了其解析表达式。从而证明了HFS和MISO-FS具有等效性。在此基础上分析了HFS的规则数,证明了HFS的规则数随输入变量数线性增长,因此HFS是解决模糊多变量系统"维数灾"问题的一个很好的实用方案。
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| 关 键 词： | 模糊系统 分层模糊系统 结构分析 等效性 |
| 文章编号： | 1000-0054(2004)07-0993-04 |
| 修稿时间： | 2002年5月7日 |
Equivalence analysis of binary-tree-type hierarchical fuzzy systems |
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| DU Xinyu,ZHANG Naiyao.Equivalence analysis of binary-tree-type hierarchical fuzzy systems[J].Journal of Tsinghua University(Science and Technology),2004,44(7):993-996. |
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| Authors: | DU Xinyu ZHANG Naiyao |
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| Abstract: | This paper analyzes multiple-input-single-output fuzzy systems (MISO-FS) with unequally spaced, fully-overlapped, triangular membership functions for the input variables and equally spaced, singleton membership functions for the output variable. The Sum-Product inference method, linearization rules and the center of gravity method are used for defuzzification. Explicit analytical expressions are given for the MISO-FS along with explicit analytical expressions for binary-tree-type hierarchical fuzzy systems (HFS) to prove the equivalence between MISO-FS and HFS. Since the number of rules in HFS linearly increases with the number of input variables, HFS can be used to replace MISO-FS to solve the "dimensional disaster" problem in fuzzy multi-variable systems with large numbers of input variables. |
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| Keywords: | fuzzy systems hierarchical fuzzy systems structure analysis equivalence |
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