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关于二型模糊集合的一些基本问题

王飞跃 莫红

王飞跃, 莫红. 关于二型模糊集合的一些基本问题. 自动化学报, 2017, 43(7): 1114-1141. doi: 10.16383/j.aas.2017.c160638
引用本文: 王飞跃, 莫红. 关于二型模糊集合的一些基本问题. 自动化学报, 2017, 43(7): 1114-1141. doi: 10.16383/j.aas.2017.c160638
WANG Fei-Yue, MO Hong. Some Fundamental Issues on Type-2 Fuzzy Sets. ACTA AUTOMATICA SINICA, 2017, 43(7): 1114-1141. doi: 10.16383/j.aas.2017.c160638
Citation: WANG Fei-Yue, MO Hong. Some Fundamental Issues on Type-2 Fuzzy Sets. ACTA AUTOMATICA SINICA, 2017, 43(7): 1114-1141. doi: 10.16383/j.aas.2017.c160638

关于二型模糊集合的一些基本问题

doi: 10.16383/j.aas.2017.c160638
基金项目: 

国家自然科学基金 61473048

国家自然科学基金 71232006

国家自然科学基金 61074093

国家自然科学基金 61233001

国家自然科学基金 61533019

详细信息
    作者简介:

    莫红 长沙理工大学电气与信息工程学院教授.2004年获中国科学院研究生院工学博士学位.主要研究方向为语言动力系统与智能计算.E-mail:mohong198@163.com

    通讯作者:

    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研究员.国防科学技术大学军事计算实验与平行系统技术研究中心主任.主要研究方向为智能系统和复杂系统的建模、分析与控制.本文通信作者. E-mail:feiyue.wang@ia.ac.cn

Some Fundamental Issues on Type-2 Fuzzy Sets

Funds: 

National Natural Science Foundation of China 61473048

National Natural Science Foundation of China 71232006

National Natural Science Foundation of China 61074093

National Natural Science Foundation of China 61233001

National Natural Science Foundation of China 61533019

More Information
    Author Bio:

      Associate professor at the School of Electric and Information Engineering, Changsha University of Science and Technology. She received her Ph. D. degree from Chinese Academy of Sciences in 2004. Her research interest covers linguistic dynamic systems and intelligent computing

    Corresponding author: WANG Fei-Yue  Professor at the State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences. Director of the Research Center for Computational Experiments and Parallel Systems Technology, National University of Defense Technology. His research interest covers modeling, analysis, and control of intelligent systems and complex systems. Corresponding author of this paper. E-mail:feiyue.wang@ia.ac.cn
  • 摘要: 采用集合论的方法给出了单位模糊集合和二型模糊集合及其在一点的限制等定义,使得二型模糊集合更易于理解.通过定义嵌入单位模糊集合来描述一般二型模糊集合,并给出离散、半连通二型模糊集合的表达式.根据论域、主隶属度及隶属函数的特性将二型模糊集合分为四种类型:离散、半连通、连通及复合型,并根据连通的特点将连通二型模糊集合分为单连通及多连通两类.利用支集的闭包(Closure of support,CoS)划分法表述主隶属度及区间二型模糊集合.提出了CoS二、三次划分法分别来表述单、复连通二型模糊集合,并使每一个子区域的上下边界及次隶属函数在该子区域上的限制分别具有相同的解析表述式.最后,探讨了二型模糊集合在一点的限制、主隶属度、支集、嵌入单位模糊集合之间的关系.
  • 图  1  单位模糊集合

    Fig.  1  Unit fuzzy set

    图  2  嵌入单位模糊集合

    Fig.  2  Embedded unit fuzzy set

    图  5  离散二型模糊集合

    Fig.  5  Discrete type-2 fuzzy set

    图  6  半连通二型模糊集合

    Fig.  6  Partially connected T2 fuzzy set

    图  3  单连通CoS

    Fig.  3  Single connected CoS

    图  4  多连通CoS

    Fig.  4  Multi-connected CoS

    图  19  线连通二型模糊集合的CoS

    Fig.  19  CoS of linear connected T2 fuzzy set

    图  7  半连通二型模糊集合

    Fig.  7  Partially connected T2 fuzzy set

    图  8  半连通二型模糊集合

    Fig.  8  Partially connected T2 fuzzy set

    图  9  单连通三角二型模糊集合CoS的第一次划分

    Fig.  9  The first partition for CoS of simply connected triangular T2 FS

    图  10  单连通三角二型模糊集合CoS的第二次划分

    Fig.  10  The second partition for CoS of simply connected triangular T2 FS

    图  11  单连通三角二型模糊集合

    Fig.  11  imply connected triangular T2 FS

    图  12  单连通梯形二型模糊集合CoS的第一次划分

    Fig.  12  The first partition for CoS of simply connected trapezoidal T2 FS

    图  13  单连通梯形二型模糊集合CoS的第二次划分

    Fig.  13  The second partition for CoS of simply connected trapezoidal T2 FS

    图  14  单连通梯形二型模糊集合

    Fig.  14  Simply connected trapezoidal T2 FS

    图  15  单连通高斯二型模糊集合的CoS

    Fig.  15  CoS of simply connected Gaussian T2 FS

    图  16  单连通高斯二型模糊集合

    Fig.  16  Simply connected Gaussian T2 FS

    图  17  多连通二型模糊集合CoS的第三次划分

    Fig.  17  The third partition for multi-connected T2 FS

    图  18  多连通二型模糊集合

    Fig.  18  Multi-connected T2 FS

    图  20  线连通二型模糊集合

    Fig.  20  Linear connected T2 fuzzy set

    图  21  复合二型模糊集合

    Fig.  21  Compounded T2 FS

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  • 收稿日期:  2016-09-14
  • 录用日期:  2017-04-21
  • 刊出日期:  2017-07-20

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