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

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

1.
华中科技大学人工智能与自动化学院图像信息处理与智能控制教育部重点实验室武汉 430074
2.
长沙理工大学电气与信息工程学院长沙 410114
3.
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北京 100190

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

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- 被引次数: 0
出版历程
- 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

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

1.
Ministry of Education Key Laboratory on Image Information Processing and Intelligent Control, School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074
2.
School of Electric and Information Engineering, Changsha University of Science and Technology, Changsha 410114
3.
The State Key Laboratory for Management and Control of Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190

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

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.
- 区间二型模糊集 /
- 区间二型模糊系统 /
- 模糊控制 /
- 感知计算
Abstract: Type-1 fuzzy sets can model the linguistic uncertainty from a single user, i.e., intra-personal uncertainty. Type-1 fuzzy systems have been widely used in controls and machine learning applications. Interval type-2 fuzzy sets can simultaneously model both intra-personal uncertainty and inter-personal uncertainty, and hence have demonstrated better performance than type-1 fuzzy systems in many applications, becoming a hot research topic recently. This paper first introduces main concepts and theoretical research progresses of interval type-2 fuzzy sets, summarizes their successful applications in decision-making and machine learning, then introduces basic operations and theoretical research progresses of interval type-2 fuzzy systems, and reviews their typical applications in controls and machine learning. Finally, it points out several future research directions on interval type-2 fuzzy sets and systems.
- Interval type-2 fuzzy set /
- interval type-2 fuzzy system /
- fuzzy control /
- perceptual computing

HTML全文

图 1 “高温”的不同集合表示

Fig. 1 Different representations of “High temperature”

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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

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图 3 二型模糊集

Fig. 3 Type-2 fuzzy sets

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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.)

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图 5 各种不同的加权平均

Fig. 5 Various weighted averages

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图 6 感知计算机

Fig. 6 Perceptual computer

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图 7 区间二型模糊系统

Fig. 7 Interval type-2 fuzzy system

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图 8 转换点

Fig. 8 The switch points

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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

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图 10 区间二型模糊系统的不连续性

Fig. 10 Discontinuity of interval type-2 fuzzy systems

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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

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图 12 式$(25)\sim (27) $决定的输入区域

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

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图 13 $\alpha$, $\beta$和$\dot{e}$的关系

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

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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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