| 引用本文: | 游文虎,王茂,施佳.PIE+MOM的Mamdani模糊系统通用逼近性充要条件[J].哈尔滨工业大学学报,2014,46(11):1.DOI:10.11918/j.issn.0367-6234.2014.11.001 |
| YOU Wenhu,WANG Mao,SHI Jia.Sufficient and necessary condition of Mamdani fuzzy systems with PIE and MOM as universal approximators[J].Journal of Harbin Institute of Technology,2014,46(11):1.DOI:10.11918/j.issn.0367-6234.2014.11.001 |
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| 摘要: |
| 为了解决如何构造具有通用逼近性能的Mamdani模糊系统问题,提出一类Mamdani模糊系统具有通用逼近性的充要条件. 该模糊系统采用乘积推理机(product inference engine, PIE)和最大值平均(mean of maximum, MOM)解模糊器,按模糊规则后件分为单点规则后件和模糊数规则后件两种情况,分别根据Weierstrass第一定理和隶属度函数性质给出了严格证明. 最后通过示例证明该充要条件的有效性. |
| 关键词: Mamdani模糊系统 乘积推理机 MOM 通用逼近性 |
| DOI：10.11918/j.issn.0367-6234.2014.11.001 |
| 分类号:TP273.4 |
| 基金项目:国家自然科学基金(61004038). |
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| Sufficient and necessary condition of Mamdani fuzzy systems with PIE and MOM as universal approximators |
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YOU Wenhu1, WANG Mao1,SHI Jia2
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(1. Space Control and Inertial Technology Research Center, Harbin Institute of Technology, 150001 Harbin, China; 2.China Aeronautical Radio Electronics Research Institute, 200241 Shanghai, China)
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| Abstract: |
| Focusing on whether fuzzy system can approximate any given function, the sufficient and necessary theory of one type of fuzzy systems as universal approximators was investigated. Mamdani fuzzy systems with product inference engine (PIE) and mean of maximum (MOM) defuzzificator can be classified two cases according to rule consequent: simple point rule consequent and fuzzy set rule consequent. Based on Weierstrass's first theorem and properties of membership functions, sufficient and necessary condition is proved respectively. A simulation example is given to show the effectiveness of the proposed method. |
| Key words: mamdani fuzzy system PIE MOM approximation |
