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区间二型模糊集和模糊系统: 综述与展望

伍冬睿 曾志刚 莫红 王飞跃

伍冬睿, 曾志刚, 莫红, 王飞跃. 区间二型模糊集和模糊系统: 综述与展望. 自动化学报, 2020, 46(8): 1539−1556 doi: 10.16383/j.aas.c200133
引用本文: 伍冬睿, 曾志刚, 莫红, 王飞跃. 区间二型模糊集和模糊系统: 综述与展望. 自动化学报, 2020, 46(8): 1539−1556 doi: 10.16383/j.aas.c200133
Wu Dong-Rui, Zeng Zhi-Gang, Mo Hong, Wang Fei-Yue. Interval type-2 fuzzy sets and systems: Overview and outlook. Acta Automatica Sinica, 2020, 46(8): 1539−1556 doi: 10.16383/j.aas.c200133
Citation: Wu Dong-Rui, Zeng Zhi-Gang, Mo Hong, Wang Fei-Yue. Interval type-2 fuzzy sets and systems: Overview and outlook. Acta Automatica Sinica, 2020, 46(8): 1539−1556 doi: 10.16383/j.aas.c200133

区间二型模糊集和模糊系统: 综述与展望

doi: 10.16383/j.aas.c200133
基金项目: 国家自然科学基金(61873321, U1913207), 湖北省技术创新专项资助项目(2019AEA171), NSFC-深圳机器人基础研究中心重点项目(U1913207), 科技部政府间国际科技创新合作重点专项(2017YFE0128300)资助
详细信息
    作者简介:

    伍冬睿:华中科技大学人工智能与自动化学院教授. 主要研究方向为机器学习, 脑机接口, 计算智能, 情感计算. 本文通信作者.E-mail: drwu@hust.edu.cn

    曾志刚:华中科技大学人工智能与自动化学院院长, 教授. 主要研究方向为神经网络理论与应用, 动力系统稳定性, 联想记忆.E-mail: zgzeng@mail.hust.edu.cn

    莫红:长沙理工大学电气与信息工程学院教授. 2004年获中国科学院自动化研究所工学博士学位. 主要研究方向为模糊AI, 智慧医疗, 复杂系统的管理与控制. E-mail: mohong198@163.com

    王飞跃:中国科学院自动化研究所复杂系统管理与控制国家重点实验室主任, 国防科技大学军事计算实验与平行系统技术研究中心主任, 中国科学院大学中国经济与社会安全研究中心主任, 青岛智能产业技术研究院院长. 主要研究方向为平行系统的方法与应用, 社会计算, 平行智能以及知识自动化. E-mail: feiyue.wang@ia.ac.cn

Interval Type-2 Fuzzy Sets and Systems: Overview and Outlook

Funds: Supported by National Natural Science Foundation of China (61873321, U1913207), Technology Innovation Project of Hubei Province of China (2019AEA171), NSFC-Shenzhen Robotics Basic Research Center (U1913207), and International Science and Technology Cooperation Program of China (2017YFE0128300)
  • 摘要: 一型模糊集可以建模单个用户的语义概念中的不确定性, 即个体内不确定性. 一型模糊系统在控制和机器学习中得到了大量成功应用. 区间二型模糊集能同时建模个体内不确定性和个体间不确定性, 因而在很多应用中显示了比一型模糊系统更好的性能, 是近年来的研究热点. 本文首先介绍了区间二型模糊集的重要概念和理论研究进展, 总结了其在决策和机器学习中的成功应用, 然后介绍了区间二型模糊系统的基本操作和理论研究进展, 并回顾了其在控制和机器学习中的典型应用. 最后, 对区间二型模糊集和模糊系统未来的研究方向进行了展望.
  • 图  1  “高温”的不同集合表示

    Fig.  1  Different representations of “High temperature”

    图  2  谷歌学术中包含“type-2 fuzzy”的论文数量

    Fig.  2  Number of publications on “type-2 fuzzy” in Google Scholar

    图  3  二型模糊集

    Fig.  3  Type-2 fuzzy sets

    图  4  根据不同的表示定理, 计算区间二型模糊集质心所用到的嵌入一型模糊集(左边的点是由实线嵌入一型模糊集决定的质心的下界, 右边的点是由虚线嵌入一型模糊集决定的质心的上界.)

    Fig.  4  Embedded type-1 fuzzy sets in computing the centroid of the interval type-2 fuzzy set, according to different representation theorems (The left dot is the lower bound of the centroid determined by the solid embedded type-1 fuzzy set, and the right dot is the upper bound determined by the dashed embedded type-1 fuzzy set.)

    图  5  各种不同的加权平均

    Fig.  5  Various weighted averages

    图  6  感知计算机

    Fig.  6  Perceptual computer

    图  7  区间二型模糊系统

    Fig.  7  Interval type-2 fuzzy system

    图  8  转换点

    Fig.  8  The switch points

    图  9  简化的区间二型模糊系统输入域中使用的模糊集示例

    Fig.  9  MFs in a simplified interval type-2 fuzzy system

    图  10  区间二型模糊系统的不连续性

    Fig.  10  Discontinuity of interval type-2 fuzzy systems

    图  11  区间二型模糊控制器的隶属度函数

    Fig.  11  MFs of the interval type-2 fuzzy controller

    图  12  $(25)\sim (27) $决定的输入区域

    Fig.  12  Input region determined by $(25)\sim (27) $

    图  13  $\alpha$, $\beta$$\dot{e}$的关系

    Fig.  13  Relationship between $\alpha$, $\beta$ and $\dot{e}$

    图  14  对于区间二型模糊系统初学者的建议

    Fig.  14  Recommendations on designing interval type-2 fuzzy system for beginners

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  • 收稿日期:  2020-03-16
  • 录用日期:  2020-05-12
  • 网络出版日期:  2020-08-26
  • 刊出日期:  2020-08-26

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