2.765

2022影响因子

(CJCR)

  • 中文核心
  • EI
  • 中国科技核心
  • Scopus
  • CSCD
  • 英国科学文摘

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

模糊认知图学习算法及应用综述

刘晓倩 张英俊 秦家虎 李卓凡 梁伟玲 李宗溪

刘晓倩, 张英俊, 秦家虎, 李卓凡, 梁伟玲, 李宗溪. 模糊认知图学习算法及应用综述. 自动化学报, 2024, 50(3): 1−24 doi: 10.16383/j.aas.c230120
引用本文: 刘晓倩, 张英俊, 秦家虎, 李卓凡, 梁伟玲, 李宗溪. 模糊认知图学习算法及应用综述. 自动化学报, 2024, 50(3): 1−24 doi: 10.16383/j.aas.c230120
Liu Xiao-Qian, Zhang Ying-Jun, Qin Jia-Hu, Li Zhuo-Fan, Liang Wei-Ling, Li Zong-Xi. A review of fuzzy cognitive map learning algorithms and applications. Acta Automatica Sinica, 2024, 50(3): 1−24 doi: 10.16383/j.aas.c230120
Citation: Liu Xiao-Qian, Zhang Ying-Jun, Qin Jia-Hu, Li Zhuo-Fan, Liang Wei-Ling, Li Zong-Xi. A review of fuzzy cognitive map learning algorithms and applications. Acta Automatica Sinica, 2024, 50(3): 1−24 doi: 10.16383/j.aas.c230120

模糊认知图学习算法及应用综述

doi: 10.16383/j.aas.c230120
基金项目: 中央高校基本科研业务费专项资金(2022YJS121), 中央高校基本科研业务费专项资金(科技领军人才团队项目) (2022JBQY009), 国家自然科学基金(62002148, 51827813) 资助
详细信息
    作者简介:

    刘晓倩:北京交通大学计算机与信息技术学院博士研究生. 主要研究方向为数据挖掘和不确定性人工智能. E-mail: 20112016@bjtu.edu.cn

    张英俊:北京交通大学计算机与信息技术学院副教授. 主要研究方向为数据挖掘与模糊推理. 本文通信作者. E-mail: zhangyj@bjtu.edu.cn

    秦家虎:中国科学技术大学自动化系教授. 主要研究方向为多智能体系统分布式决策与复杂网络理论. E-mail: jhqin@ustc.edu.cn

    李卓凡:北京交通大学计算机与信息技术学院硕士研究生. 主要研究方向为模糊认知图和进化学习. E-mail: 20120393@bjtu.edu.cn

    梁伟玲:北京交通大学计算机与信息技术学院硕士研究生. 主要研究方向为时间序列分析和模糊认知图. E-mail: 20120377@bjtu.edu.cn

    李宗溪:北京交通大学计算机与信息技术学院硕士研究生. 主要研究方向为模糊认知图和进化学习. E-mail: 22120402@bjtu.edu.cn

A Review of Fuzzy Cognitive Map Learning Algorithms and Applications

Funds: Supported by Fundamental Research Funds for the Central Universities (2022YJS121), Fundamental Research Funds for the Central Universities (Science and Technology Leading Talent Team Project) (2022JBQY009), and National Natural Science Foundation of China (62002148, 51827813)
More Information
    Author Bio:

    LIU Xiao-Qian Ph.D. candidate at the School of Computer and Information Technology, Beijing Jiaotong University. Her research interest covers data mining and uncertainty artificial intelligence

    ZHANG Ying-Jun Associate professor at the School of Computer and Information Technology, Beijing Jiaotong University. His research interest covers data mining and fuzzy reasoning. Corresponding author of this paper

    QIN Jia-Hu Professor in the Department of Automation, University of Science and Technology of China. His research interest covers distributed decision-making in multi-agent systems and complex network theory

    LI Zhuo-Fan Master student at the School of Computer and Information Technology, Beijing Jiaotong University. Her research interest covers fuzzy cognitive maps and evolution learning

    LIANG Wei-Ling Master student at the School of Computer and Information Technology, Beijing Jiaotong University. Her research interest covers time series analysis and fuzzy cognitive maps

    LI Zong-Xi Master student at the School of Computer and Information Technology, Beijing Jiaotong University. His research interest covers fuzzy cognitive maps and evolution learning

  • 摘要: 模糊认知图(Fuzzy cognitive map, FCM)是建立在认知图和模糊集理论上的一类代表性的软计算理论, 兼具神经网络和模糊决策两者的优势, 已成功地应用于复杂系统建模和时间序列分析等众多领域.学习权重矩阵是基于模糊认知图建模的首要任务, 是模糊认知图研究领域的焦点. 针对这一核心问题, 首先, 全面综述模糊认知图的基本理论框架, 系统地总结近年来模糊认知图的拓展模型.然后, 归纳、总结和分析模糊认知图学习算法的最新研究进展, 对学习算法进行重新定义和划分, 深度阐述各类学习算法的时间复杂度和优缺点.其次, 对比分析各类学习算法在不同科学领域的应用特点以及现有的模糊认知图建模软件工具. 最后, 讨论学习算法未来潜在的研究方向和发展趋势.
  • 图  1  模糊认知图研究框架

    Fig.  1  Research framework of fuzzy cognitive maps

    图  2  6节点的FCM案例

    Fig.  2  An FCM example with 6 concept nodes

    图  3  模糊认知图推理过程

    Fig.  3  Reasoning process of fuzzy cognitive maps

    图  4  专家知识驱动的学习算法的基本流程

    Fig.  4  The basic process of expert knowledge-driven learning algorithms

    图  5  自动学习算法的基本流程

    Fig.  5  The basic process of automatic learning algorithms

    图  6  半自动学习算法的基本流程

    Fig.  6  The basic process of semi-automatic learning algorithms

    表  1  拓展认知图模型对比

    Table  1  Comparison of fuzzy cognitive map expansion models

    类别名称特点优点缺点应用领域
    基于不同
    模糊理论
    的拓展
    认知图
    RBFCM[28] 引入模糊进位累加器计算因果权重 涵盖多种概念关系,具有
    多功能性和简单性
    建模要求高 决策支持
    FGCM[29] 引入灰色数衡量因果强度 建模概念之间的不确定信息 推理复杂 可靠性工程
    IFCM[30] 利用直觉模糊集建模因果关系 衡量了因果关系中的不确定性 推理复杂 时间序列预测
    IVFCM[31] 利用区间值描述因果关系的强度 考虑了非结构化环境相关的不确定性 依赖专家知识 决策支持时间
    序列预测
    ECM[32] 在因果推理中融入了证据理论 既能表示不确定性又能进行知识融合 依赖专家知识,
    推理复杂
    决策支持
    RCN[33] 利用粗糙集表示因果关系 解决了不确定情况下的决策问题 依赖专家知识 决策支持软件
    可靠性评估
    FRCN[34] 利用模糊粗糙结构构建神经网络 建模了因果关系的不确定性 推理复杂 决策支持
    zT2FSs-FCM[35] 引入二型模糊集建模节点间的
    因果权重
    捕获了概念间的不确定性关系 推理复杂 系统评估
    面向动态
    系统建模
    的拓展
    认知图
    DCN[37] 考虑了因果关系的时变性 结构上具有更高的可扩展性和灵活性 依赖拉普拉斯框架,
    建模复杂度高
    决策支持
    DRFCM[39] 推理过程中引入非线性动态函数 能够捕获动态因果关系,
    具有自适应性
    建模要求高 风险评估决策支持
    FTCM[40] 考虑了因果关系强度和时间滞后性 能够随时间推移分析系统的动态行为 建模复杂 时间序列预测
    E-FCM[41] 采用检查机制模拟动态因果关系 能够自我进化适应不断发展的行为 计算耗时 动态场景建模
    HFCM[42] 考虑了复杂系统建模过程中的
    多阶动态性
    准确地描述了系统行为 随着阶数增加,
    计算复杂度增加
    时间序列预测
    TAFCM[43] 引入了定时自动机理论建模
    系统的时间粒度
    推理过程具有动态性和自适应性 建模要求高 人类情绪建模
    DFCM[44] 嵌入在深度神经网络的框架中 构建可解释预测器, 挖掘隐藏的
    因果关系
    适应于大规模数据 时间序列预测
    AFCM[45] 构建基于趋势的信息粒引入
    自适应更新机制
    自适应权重长期预测 计算耗时 时间序列预测
    下载: 导出CSV

    表  2  基于学习范式的模糊认知图学习算法分类

    Table  2  Classification of fuzzy cognitive map learning algorithms based on the learning paradigm

    类别 学习方法 时间复杂度 优点 缺点 作者 发表年份
    专家知识驱动的方法 DHL[47] ${\rm{O}}(N^2)$ 简单, 易操作 只考虑了当前的一对概念 Dickerson等 1994
    BDA[48] ${\rm{O}}(N^2)$ 考虑多个概念的影响 只适用于二进制计算 Huerga等 2002
    AHL[49] ${\rm{O}}(N^2)$ 考虑了所有概念的影响 训练耗时 Papageorgiou等 2004
    NHL[50] ${\rm{O}}(N^2)$ 保留了原始的图结构, 具有合理的物理解释性 依赖专家标准 Papageorgiou等 2003
    INHL[51] ${\rm{O}}(N^2)$ 避免陷入局部最小值 需要先验知识 Li等 2004
    DDNHL[52] ${\rm{O}}(N^2)$ 数据驱动 依赖专家知识 Stach 等 2008
    FBN[54] ${\rm{O}}(N^2)$ 利用模糊因果规则推理 性能受激活参数的影响 Carvalho等 2007
    基于bagging增强的NHL算法[55] ${\rm{O}}(N^2)$ 泛化性能较好 依赖专家知识 Papageorgiou等 2012
    带终端约束的
    NHL算法[53]
    ${\rm{O}}(N^2)$ 提高结果的可行性 需要先验知识 Chen 等 2016
    自动学习
    算法
    GA[56] ${\rm{O}}(N^2)$ 数据驱动 受限于二进制编码 Mateou等 2005
    RCGA[57] ${\rm{O}}(N^2)$ 数据驱动, 实数编码 参数寻优耗时 Stach 等 2005
    PSO[58] ${\rm{O}}(N!)$ 数据驱动, 元启发式算法 依赖专家知识 Parsopoulos等 2003, 2013
    SOMA[60] ${\rm{O}}(N^2)$ 数据驱动 计算耗时 Vaščák等 2010
    ACO[61, 69] ${\rm{O}}(N^2)$ 概率型算法鲁棒性强 计算耗时容易早熟收敛 Chen等
    Hu 等
    2012, 2018
    ABC[62] ${\rm{O}}(N^2)$ 数据驱动 参数寻优耗时 Yesil等 2013
    分解RCGA[72] ${\rm{O}}(N^2)$ 分解并行计算 计算复杂 Chen 等 2015
    ICA[63] ${\rm{O}}(N^3)$ 数据驱动 计算复杂, 耗时 Ahmadi 等 2015
    DE[64] ${\rm{O}}(N^2)$ 容易理解计算简单 易局部收敛 Juszczuk等 2009
    SA[65] ${\rm{O}}(N^2)$ 计算简单 参数寻优耗时 Ghazanfari 等 2007, 2009
    BB-BC[67] ${\rm{O}}(N^2)$ 算法简单泛化能力较好 不适用于解决高维问题 Yesil等 2010
    CA[68] ${\rm{O}}(N^2)$ 全局搜索与局部搜索结合 参数寻优耗时对问题的依赖性强 Ahmadi等 2014
    D& C RCGA[74] ${\rm{O}}(N^2)$ 并行计算算法具有可扩展性 随着图的大小和处理器数量增加, 算法性能下降 Stach等 2007
    基于互信息的
    模因算法[70]
    ${\rm{O}}(N^2)$ 适用于大规模图学习 无法在搜索过程中
    关注图的稀疏性
    Zou等 2018
    MARO[71] ${\rm{O}}(N^2)$ 只需调用一次目标
    函数无需设置参数
    计算复杂, 易陷入局部最优 Salmeron等 2019
    dMAGA[75] ${\rm{O}}(N^2)$ 适用于大规模图学习
    具有鲁棒性
    受FCM节点的取值范围限制需在算法执行前进行数据归一化 Liu等 2015
    MA-NN[76] ${\rm{O}}(N^2)$ 分布式计算框架适用于
    大规模网络重建
    受FCM节点的取值范围限制需在算法执行前进行数据归一化 Chi等 2019
    MOEA[77, 80] ${\rm{O}}(N^2)$ 多目标进化考虑了图的稀疏性 不适用于大规模图学习 Chi等
    Liu等
    2015, 2019
    SRCGA[15] ${\rm{O}}(N^2)$ 考虑了图的稀疏性 不适用于处理大规模数据 Stach等 2012
    MMMA[17] ${\rm{O}}(N^2)$ 多图优化知识转移 有可能发生负信息迁移降低收敛速度 Shen等 2020
    CS[81] ${\rm{O}}(N^3)$ 适用于大规模稀疏图学习 参数寻优耗时 Wu等 2017
    Moore–Penrose逆[85] ${\rm{O}}(N^3)$ 参数较少 计算复杂 Vanhoenshoven等 2020
    内点法[82] ${\rm{O}}(N^4)$ 精度高, 可扩展性好 对初值敏感难以处理
    不等式约束问题
    Lu等 2020
    约束优化[83] ${\rm{O}}(N^3)$ 考虑了矩阵分布具有抗噪能力 仅适用于有监督学习 Feng等 2021
    近似梯度下降[84] ${\rm{O}}(N^3)$ 适用于解决大规模数据问题 对初始点敏感可能
    陷入局部最优
    Ding等 2021
    Lasso回归[86] ${\rm{O}}(N^3)$ 考虑了图的稀疏性适用于
    大规模图学习
    可能出现过拟合 Wu等 2016
    岭回归[87] ${\rm{O}}(N^3)$ 泛化性能较好适用于大
    规模图学习
    对特征的缩放敏感 Yang等 2018
    弹性网络回归[88] ${\rm{O}}(N^3)$ 增加了L1 和L2 正则化适用于大规模图学习 参数调节困难 Shen等 2020
    支持向量回归[89] ${\rm{O}}(N^4)$ 适用于高维非线性数据 对缺失数据敏感 Gao等 2020
    贝叶斯岭回归[90] ${\rm{O}}(N^4)$ 简单、模型适应性较强 对模型的假设较多依赖先验分布 Liu等 2020
    FTRL[91] ${\rm{O}}(N^3)$ 在线学习 计算、推理过程复杂 Wu 等 2021
    IMFPSO[78] ${\rm{O}}(N!)$ 优化过程考虑了知识迁移 算法易早熟, 过早收敛 Liang等 2022
    半自动学习算法 DE+NHL[92] ${\rm{O}}(N^2)$ 进化过程中保留了图的物理意义 依赖专家知识 Papageorgiou等 2005
    RCGA+NHL[93] ${\rm{O}}(N^2)$ 利用了遗传算法的全局优化能力 受限于专家经验 Zhu等 2008
    PSO+NHL[94] ${\rm{O}}(N!)$ 避免人为因素产生的训练误差 受限于专家经验 Yazdi等 2008
    EDGA+NHL[95] ${\rm{O}}(N^2)$ 全局搜索, 参数少 受限于专家经验 Ren 等 2012
    DDNHL+GA[96] ${\rm{O}}(N^3)$ 数据驱动分类推理能力强 受限于专家经验 Natarajan等 2016
    RCGA+DE+
    梯度下降[97]
    ${\rm{O}}(N^2)$ 全局搜索 参数寻优耗时 Madeiro 等 2012
    注: 时间复杂度为该算法更新一次FCM权重矩阵所需时间开销, 未考虑数据量大小及最大迭代次数. N表示节点个数.
    下载: 导出CSV

    表  3  大规模模糊认知图学习算法分类

    Table  3  Large-scale fuzzy cognitive map learning algorithm classification

    类别 方法 转换函数 最大FCM规模 发表年份
    基于暴力求解的方法 并行RCGA[74] Sigmoid 80 2007
    dMAGA[75] Sigmoid 200 2015
    MA-NN[76] Sigmoid 100 2019
    MOEA[80] Sigmoid 40 2015
    SRCGA[15] Sigmoid 40 2012
    D&C RCGA[73] Sigmoid 40 2010
    基于维度缩减的方法 Hatwagner等[101] Sigmoid 10 2015
    Hatwagner等[102] Sigmoid/Tanh 25 2018
    MIMA[103] Sigmoid 500 2017
    基于分解的方法 CS[81] Sigmoid 1 000 2017
    MMMA[17] Sigmoid/Tanh 600 2020
    内点法[82] Sigmoid/Tanh 200 2020
    约束优化[83] Sigmoid/Tanh 200 2021
    近似梯度下降[84] Sigmoid 200 2021
    Lasso回归[86] Sigmoid 500 2016
    弹性网络回归[88] Sigmoid 200 2020
    dMAGA-FCM$_D$[104] Sigmoid 500 2017
    NMM$_{\rm MAGA}$[105] Sigmoid 200 2019
    HTMA-DRA[99] Sigmoid 200 2022
    Parallel FCM[100] Sigmoid 1 000 2023
    下载: 导出CSV

    表  4  模糊认知图学习算法的应用文献总结

    Table  4  Literature review on the application of fuzzy cognitive map learning algorithms

    类别 应用领域 文献
    专家知识驱动的方法 模式分类 [55]
    前列腺癌诊断 [106]
    公司信用风险评估 [107]
    自闭症预测 [108]
    结构损伤检测 [109]
    帕金森病预测 [111]
    事故成因预测 [112]
    裂纹严重程度分级 [113]
    乳腺癌风险评估 [114]
    情景意识评估 [115]
    自动学习算法 病情趋势预测 [139]
    基因调控网络重建 [17, 7577, 82, 84, 86]
    前列腺癌预测 [140]
    日需水量预测 [141]
    电器能耗预测 [142]
    RFID物流操作评估 [143]
    多变量时间序列预测 [44, 45, 78, 85, 117120]
    单变量时间序列预测 [87, 89, 90, 121, 122, 123, 127129] [83, 91, 124, 125, 130]
    分类 [5, 133138]
    半自动学习算法 医学诊断 [144]
    甘蔗产量预测 [96]
    决策支持 [92]
    化学控制 [94]
    太阳能发电 [97]
    下载: 导出CSV

    表  5  模糊认知图建模工具对比

    Table  5  Comparison of fuzzy cognitive map modeling tools

    工具名称 受众定位 适用场景 应用形式 学习算法数量 图形页面 年份
    FCM Modeler[145] 学术研究 静态建模, 群体决策 Java Applet 1 1997
    FCMappers.net[146] 学术研究 网络分析, 系统建模 网站 2009
    FCM Tool[147] 商业产品, 学术研究 决策支持, 系统建模 软件 1 2011
    FCM Designer[148] 学术研究 系统建模 Java Applet 2010
    FCM Designer Version 2.0[149] 学术研究 医学诊断, 推荐系统建模 Java Applet 2016
    Mental Modeler[150] 商业产品, 学术研究 群体决策, 系统建模 Web 页面 2013
    JFCM[151] 教学工具, 学术研究 系统建模 Java开源库 2014
    ISEMK[153] 商业产品, 学术研究 决策支持, 时间序列预测 6 2015
    FCM Expert[155] 学术研究 决策支持, 系统建模 Java软件 4 2017
    FCMpy[159] 学术研究 系统建模 开源Python模块 5 2022
    注: —表示“无”或者未查询到.
    下载: 导出CSV
  • [1] 杨博帆, 张琳, 汪文峰, 唐东丽, 丁尔启, 项阳.复杂装备系统弹性度量方法研究.自动化学报, 2023, 1-11

    Yang Fu-Fan, Zhang Lin, Wang Wen-Feng, Tang Dong-Li, Ding Er-Qi, Xiang Yang. Research on resilience measurement method of complex equipment system. Acta Automatica Sinica, 2023, 1-11
    [2] 杨炳儒, 李晋宏, 宋威, 李欣.面向复杂系统的知识发现过程模型KD(D&K)及其应用.自动化学报, 2007, (02):151-155

    Liang Bing-Ru, Li Jin-Hong, Song Wei, Li Xin. KD(D&K): A new knowledge discovery process model for complex system. Acta Automatica Sinica, 2007, (02): 151-155
    [3] Kosko B. Fuzzy cognitive maps. International Journal of Man-Machine Studies. 1986, 24(1): 65-75. doi: 10.1016/S0020-7373(86)80040-2
    [4] Mls K, Cimler R, Vasvak J, Puheim M. Interactive evolutionary optimization of fuzzy cognitive maps. Neurocomputing. 2017, 232: 58-68 doi: 10.1016/j.neucom.2016.10.068
    [5] Homenda W, Jastrzebska A. Time-series classification using fuzzy cognitive maps. IEEE Transactions on Fuzzy Systems, 2019, 28(7): 1383-1394
    [6] Hajek P, Froelich W. Integrating topsis with interval-valued intuitionistic fuzzy cognitive maps for effective group decision making. Information Sciences. 2019, 485: 394-412 doi: 10.1016/j.ins.2019.02.035
    [7] Hoyos W, Aguilar J, Toro M. Prv-fcm: an extension of fuzzy cognitive maps for prescriptive modeling. Expert Systems with Applications. 2023, 231(30): Article No. 120729
    [8] Borrero-Domínguez C, Escobar-Rodríguez T. Decision support systems in crowdfunding: a fuzzy cognitive maps (fcm) approach. Decision Support Systems, 2023, Article No. 114000.
    [9] Nápoles G, Papageorgiou E, Bello R, Vanhoof K. Learning and convergence of fuzzy cognitive maps used in pattern recognition. Neural Processing Letters, 2017, 45(2): 431-444 doi: 10.1007/s11063-016-9534-x
    [10] Hoyos W, Aguilar J, Toro M. Federated learning approaches for fuzzy cognitive maps to support clinical decision-making in dengue. Engineering Applications of Artificial Intelligence, 2023, 123: Article No. 106371 doi: 10.1016/j.engappai.2023.106371
    [11] Ameli M, Esfandabadi Z S, Sadeghi S, Ranjbari M, Zanetti M C. Covid-19 and sustainable development goals (sdgs): scenario analysis through fuzzy cognitive map modeling. Gondwana Research, 2023, 114: 138-155 doi: 10.1016/j.gr.2021.12.014
    [12] Pérez Y F, Corona C C, Estrada A F. Fuzzy cognitive maps for evaluating software usability. Uncertainty Management with Fuzzy and Rough Sets: Recent Advances and Applications, 2019, 377: 141-155
    [13] Bertolini M, Bevilacqua M. Fuzzy cognitive maps for human reliability analysis in production systems. Production Engineering and Management under Fuzziness Studies in Fuzziness and Soft Computing. New York: Springer-Verlag. 2010. 381−415
    [14] Papageorgiou E I. Learning algorithms for fuzzy cognitive maps—a review study. IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), 2011, 42(2): 150-163
    [15] Stach W, Pedrycz W, Kurgan L A. Learning of fuzzy cognitive maps using density estimate. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 2012, 42: 900-912 doi: 10.1109/TSMCB.2011.2182646
    [16] Felix G, Nápoles G, Falcon R, Froelich W, Vanhoof K, Bello R. A review on methods and software for fuzzy cognitive maps. Artificial Intelligence Review, 2019, 52: 1707-1737 doi: 10.1007/s10462-017-9575-1
    [17] Shen F, Liu J, Wu K. Evolutionary multitasking fuzzy cognitive map learning. Knowledge-Based Systems, 2020, 192: Article No. 105294 doi: 10.1016/j.knosys.2019.105294
    [18] 林春梅. 模糊认知图模型方法及其应用研究[博士学位论文]. 东华大学, 中国, 2007

    Lin Chun-Mei. Model method and application study of fuzzy cognitive maps[Ph.D. dissertation]. Donghua University, China, 2007
    [19] Stylios C D, Groumpos P P. Modeling complex systems using fuzzy cognitive maps. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 2004, 34(1): 155-162 doi: 10.1109/TSMCA.2003.818878
    [20] Papageorgiou E I. A new methodology for decisions in medical informatics using fuzzy cognitive maps based on fuzzy rule-extraction techniques. Applied Soft Computing, 2011, 11(1): 500-513 doi: 10.1016/j.asoc.2009.12.010
    [21] Nápoles G, Grau I, Concepción L, Koutsoviti Koumeri L, Papa J P. Modeling implicit bias with fuzzy cognitive maps. Neurocomputing, 2022, 481: 33-45 doi: 10.1016/j.neucom.2022.01.070
    [22] Nair A, Reckien D, van Maarseveen M F. Generalised fuzzy cognitive maps: considering the time dynamics between a cause and an effect. Applied Soft Computing, 2020, 92: Article No. 106309 doi: 10.1016/j.asoc.2020.106309
    [23] Luo C, Wang H, Zheng Y. Controllability of k-valued fuzzy cognitive maps. IEEE Transactions on Fuzzy Systems, 2020, 28: 1694-1707 doi: 10.1109/TFUZZ.2019.2921263
    [24] Harmati I Á, Hatwagner M F, Kóczy L T. Global stability of fuzzy cognitive maps. Neural Computing & Application, 2023, 35: 7283-7295
    [25] Concepción L, Nápoles G, Falcon R, Vanhoof K, Bello R. Unveiling the dynamic behavior of fuzzy cognitive maps. IEEE Transactions on Fuzzy Systems, 2020, 29(5): 1252-1261
    [26] Bueno S, Salmeron J L. Benchmarking main activation functions in fuzzy cognitive maps. Expert systems with Applications, 2009, 36(3): 5221-5229 doi: 10.1016/j.eswa.2008.06.072
    [27] Papageorgiou E I, Salmeron J L. A review of fuzzy cognitive maps research during the last decade. IEEE Transactions on Fuzzy Systems, 2013, 21(1): 66-79 doi: 10.1109/TFUZZ.2012.2201727
    [28] Carvalho J P, Tome J A B. Rule based fuzzy cognitive maps-expressing time in qualitative system dynamics. In: Proceeding of the 10th IEEE International Conference on Fuzzy Systems, Melbourne, VIC, Australia: IEEE, 2001. 280−283
    [29] Salmeron J L. Modelling grey uncertainty with fuzzy grey cognitive maps. Expert Systems with Applications, 2010, 37(12): 7581-7588 doi: 10.1016/j.eswa.2010.04.085
    [30] Iakovidis D K, Papageorgiou E. Intuitionistic fuzzy cognitive maps for medical decision making. IEEE Transactions on Information Technology in Biomedicine, 2010, 15(1): 100-107
    [31] Hajek P, Prochazka O. Interval-valued fuzzy cognitive maps for supporting business decisions. In: Proceedings of the 2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), Vancouver, BC, Canada: IEEE, 2016. 531−536
    [32] Kang B, Deng Y, Sadiq R, Mahadevan S. Evidential cognitive maps. Knowledge-Based Systems, 2012, 35: 77-86 doi: 10.1016/j.knosys.2012.04.007
    [33] Nápoles G, Grau I, Papageorgiou E, Bello R, Vanhoof K. Rough cognitive networks. Knowledge-Based Systems, 2016, 91: 46-61 doi: 10.1016/j.knosys.2015.10.015
    [34] Nápoles G, Mosquera C, Falcon R, Grau I, Bello R, Vanhoof K. Fuzzy-rough cognitive networks. Neural Networks, 2018, 97: 19-27 doi: 10.1016/j.neunet.2017.08.007
    [35] Al Farsi A, Petrovic D, Doctor F. A non-iterative reasoning algorithm for fuzzy cognitive maps based on type 2 fuzzy sets. Information Sciences, 2023, 622: 319-336 doi: 10.1016/j.ins.2022.11.152
    [36] Li H, Xu W, Qiu C, Pei J. Fast markov clustering algorithm based on belief dynamics. IEEE Transactions on Cybernetics, 2023, 53(6): 3716-3725 doi: 10.1109/TCYB.2022.3141598
    [37] Miao Y, Liu Z Q, Siew C K, Miao C Y. Dynamical cognitive network-an extension of fuzzy cognitive map. IEEE Transactions on Fuzzy Systems, 2001, 9(5): 760-770 doi: 10.1109/91.963762
    [38] Miao Y, Miao C Y, Tao X H, Shen Z, Liu Z. Transformation of cognitive maps. IEEE Transactions on Fuzzy Systems, 2009, 18(1): 114-124
    [39] Aguilar J. A dynamic fuzzy-cognitive-map approach based on random neural networks. International Journal of Computational Cognition, 2003, 1(4): 91-107
    [40] Wei Z, Lu L, Yanchun Z. Using fuzzy cognitive time maps for modeling and evaluating trust dynamics in the virtual enterprises. Expert Systems with Applications, 2008, 35(4): 1583-1592 doi: 10.1016/j.eswa.2007.08.071
    [41] Andreou A S, Mateou N H, Zombanakis G A. Evolutionary fuzzy cognitive maps: a hybrid system for crisis management and political decision making. In: Proceedings of the Conference Proceedings on Computational Intelligence for Modelling Control and Automation, Vienna, Austria: 2003. 732−743
    [42] Stach W, Kurgan L, Pedrycz W. Higher-order fuzzy cognitive maps. In: Proceedings of the NAFIPS 2006 - 2006 Annual Meeting of the North American Fuzzy Information Processing Society, Montreal, QC, Canada: IEEE, 2006. 166−171
    [43] Acampora G, Loia V, Vitiello A. Distributing emotional services in ambient intelligence through cognitive agents. Service Oriented Computing and Applications, 2011, 5(1): 17-35 doi: 10.1007/s11761-011-0078-7
    [44] Wang J, Peng Z, Wang X, Li C, Wu J. Deep fuzzy cognitive maps for interpretable multivariate time series prediction. IEEE Transactions on Fuzzy Systems, 2020, 29(9): 2647-2660
    [45] Wang Y, Yu Y, Homenda W, Pedrycz W, Fellow L. The trend-fuzzy-granulation-based adaptive fuzzy cognitive map for long-term time series forecasting. IEEE Transactions on Fuzzy Systems. 2022, 30(12): 5166-5180 doi: 10.1109/TFUZZ.2022.3169624
    [46] Hebb D O. The organization of behavior: a neuropsychological theory. Science Editions, 1962
    [47] Dickerson J A, Kosko B. Virtual worlds as fuzzy cognitive maps. Presence: Teleoperators & Virtual Environments, 1994, 3(2): 173-189
    [48] Huerga A V. A balanced differential learning algorithm in fuzzy cognitive maps. In: Proceedings of the 16th International Workshop on Qualitative Reasoning, 2002. 1−7
    [49] Papageorgiou E I, Stylios C D, Groumpos P P. Active Hebbian learning algorithm to train fuzzy cognitive maps. International Journal of Approximate Reasoning, 2004, 37(3): 219-249 doi: 10.1016/j.ijar.2004.01.001
    [50] Papageorgiou E, Stylios C, Groumpos P. Fuzzy cognitive map learning based on nonlinear hebbian rule. AI 2003: Advances in Artificial Intelligence. Berlin, Heidelberg: Springer, 2003. 256−268
    [51] Li S J, Shen R M. Fuzzy cognitive map learning based on improved nonlinear hebbian rule. In: Proceedings of 2004 International Conference on Machine Learning and Cybernetics (IEEE Cat. No.04EX826), Shanghai, China: IEEE, 2004. 4: 2301−2306
    [52] Stach W, Kurgan L, Pedrycz W. Data-driven nonlinear hebbian learning method for fuzzy cognitive maps. In: Proceedings of the 2008 IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence). Hong Kong, China: IEEE, 2008. 1975−1981
    [53] 陈宁, 王磊, 彭俊洁, 刘波, 桂卫华. 基于模糊认知网络的改进非线性Hebbian算法. 控制理论与应用, 2016, 33(10): 1273-1280

    Chen Ning, Wang Lei, Peng Jun-Jie, Liu Bo, Gui Wei-Hua. Improved nonlinear hebbian learning algorithm based on fuzzy cognitive networks model. Control Theory & Applications, 2016, 33(10): 1273-1280
    [54] Carvalho J P, Tomé J. Qualitative optimization of fuzzy causal rule bases using fuzzy boolean nets. Fuzzy Sets and Systems, 2007, 158(17): 1931-1946 doi: 10.1016/j.fss.2007.04.018
    [55] Papageorgiou E I, Oikonomou P, Kannappan A. Bagged nonlinear hebbian learning algorithm for fuzzy cognitive maps working on classification tasks. In: Proceedings of the Hellenic Conference on Artificial Intelligence. Berlin, Heidelberg: Springer, 2012. 157−164
    [56] Mateou N H, Moiseos M, Andreou A S. Multi-objective evolutionary fuzzy cognitive maps for decision support. In: Proceedings of the 2005 IEEE Congress on Evolutionary Computation, Edinburgh, UK: IEEE, 2005. 824−830
    [57] Stach W, Kurgan L, Pedrycz W, Reformat M. Genetic learning of fuzzy cognitive maps. Fuzzy Sets and Systems, 2005, 153(3): 371-401 doi: 10.1016/j.fss.2005.01.009
    [58] Parsopoulos K E, Papageorgiou E I, Groumpos P P, Vrahatis M N. A first study of fuzzy cognitive maps learning using particle swarm optimization. In: Proceedings of the 2003 Congress on Evolutionary Computation, 2003. CEC '03., Canberra, ACT, Australia: IEEE, 2003. 2: 1440−1447
    [59] Oikonomou P, Papageorgiou E I. Particle swarm optimization approach for fuzzy cognitive maps applied to autism classification. In: Proceedings of the IFIP International Conference on Artificial Intelligence Applications and Innovations. Berlin, Heidelberg: Springer, 2013. 516−526
    [60] Vaščák J. Approaches in adaptation of fuzzy cognitive maps for navigation purposes. In: Proceedings of the 2010 IEEE 8th International Symposium on Applied Machine Intelligence and Informatics (SAMI), Herlany, Slovakia: IEEE, 2010. 31−36
    [61] Chen Y, Mazlack L, Lu L. Learning fuzzy cognitive maps from data by ant colony optimization. In: Proceedings of the 14th annual conference on Genetic and evolutionary computation, New York, USA: 2012. 9−16
    [62] Yesil E, Ozturk C, Furkan Dodurka M, Sakalli A. Fuzzy cognitive maps learning using artificial bee colony optimization. In: Proceedings of the 2013 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), Hyderabad, India: IEEE, 2013. 1−8
    [63] Ahmadi S, Forouzideh N, Alizadeh S, Papageorgiou E. Learning fuzzy cognitive maps using imperialist competitive algorithm. Neural Computing & Applications, 2015, 26(6): 1333-1354
    [64] Juszczuk P, Froelich W. Learning fuzzy cognitive maps using a differential evolution algorithm. Pol. J. Environ. Stud, 2009, 12(3B): 108
    [65] Ghazanfari M, Alizadeh S, Fathian M, Koulouriotis D E. Comparing simulated annealing and genetic algorithm in learning FCM. Applied Mathematics and Computation, 2007, 192(1): 56-68 doi: 10.1016/j.amc.2007.02.144
    [66] Alizadeh S, Ghazanfari M. Learning fcm by chaotic simulated annealing. Chaos, Solitons & Fractals, 2009, 41(3): 1182-1190
    [67] Yesil E, Urbas L. Big bang–big crunch learning method for fuzzy cognitive maps. International Journal of Computer and Information Engineering, 2010, 4(11): 1756-1765
    [68] Ahmadi S, Forouzideh N, Yeh C H, Martin R, Papageorgiou E. A first study of fuzzy cognitive maps learning using cultural algorithm. In: Proceedings of the 2014 9th IEEE Conference on Industrial Electronics and Applications, Hangzhou, China: 2014. 2023−2028
    [69] 胡运杰, 邓燕妮. 基于变异算子改进蚁群算法学习的模糊认知图. 科学技术与工程, 2018, 18(07): 203-207

    Hu Yun-jie, Deng Yan-Ni. Learning fuzzy cognitive maps by ant colony algorithm improved by mutation operator. Science Technology and Engineering, 2018, 18(07): 203-207
    [70] Zou X, Liu J. A autual information-based two-phase memetic algorithm for large-scale fuzzy cognitive map learning. IEEE Transactions on Fuzzy Systems, 2018, 26(4): 2120-2134 doi: 10.1109/TFUZZ.2017.2764445
    [71] Salmeron J L, Mansouri T, Moghadam M R S, Mardani A. Learning fuzzy cognitive maps with modified asexual reproduction optimisation algorithm. Knowledge-Based Systems, 2019, 163: 723-735 doi: 10.1016/j.knosys.2018.09.034
    [72] Chen Y, Mazlack L J, Minai A A, Lu L J. Inferring causal networks using fuzzy cognitive maps and evolutionary algorithms with application to gene regulatory network reconstruction. Applied Soft Computing, 2015, 37: 667-679 doi: 10.1016/j.asoc.2015.08.039
    [73] Stach W, Kurgan L, Pedrycz W. A divide and conquer method for learning large fuzzy cognitive maps. Fuzzy Sets and Systems, 2010, 161(19): 2515-2532 doi: 10.1016/j.fss.2010.04.008
    [74] Stach W, Kurgan L, Pedrycz W. Parallel learning of large fuzzy cognitive maps. 2007 International Joint Conference on Neural Networks, Orlando, FL, USA: 2007. 1584−1589
    [75] Liu J, Chi Y, Zhu C. A dynamic multiagent genetic algorithm for gene regulatory network reconstruction based on fuzzy cognitive maps. IEEE Transactions on Fuzzy Systems, 2015, 24(2): 419-431
    [76] Chi Y, Liu J. Reconstructing gene regulatory networks with a memetic-neural hybrid based on fuzzy cognitive maps. Natural Computing, 2019, 18(2): 301-312 doi: 10.1007/s11047-016-9547-4
    [77] Liu J, Chi Y, Liu Z, He S. Ensemble multi-objective evolutionary algorithm for gene regulatory network reconstruction based on fuzzy cognitive maps. CAAI Transactions on Intelligence Technology, 2019, 4: 24-36 doi: 10.1049/trit.2018.1059
    [78] Liang W, Zhang Y, Liu X, Yin H, Wang J, Yang Y. Towards improved multifactorial particle swarm optimization learning of fuzzy cognitive maps: a case study on air quality prediction. Applied Soft Computing, 2022, 130: Article No. 109708 doi: 10.1016/j.asoc.2022.109708
    [79] Poczeta K, Kubu U, Yastrebov A, Papageorgiou E I. Application of fuzzy cognitive maps with evolutionary learning algorithm to model decision support systems based on real-life and historical data. Recent Advances in Computational Optimization, Springer, Cham: 2018. 153−175
    [80] Chi Y, Liu J. Learning of fuzzy cognitive maps with varying densities using a multiobjective evolutionary algorithm. IEEE Transactions on Fuzzy Systems, 2015, 24(1): 71-81
    [81] Wu K, Liu J. Learning large-scale fuzzy cognitive maps based on compressed sensing and application in reconstructing gene regulatory networks. IEEE Transactions on Fuzzy Systems, 2017, 25(6): 1546-1560 doi: 10.1109/TFUZZ.2017.2741444
    [82] Lu W, Feng G, Liu X, Pedrycz W, Zhang L, Yang J. Fast and effective learning for fuzzy cognitive maps: a method based on solving constrained convex optimization problems. IEEE Transactions on Fuzzy Systems, 2019, 28(11): 2958-2971
    [83] Feng G, Lu W, Pedrycz W, Yang J, Liu X. The learning of fuzzy cognitive maps with noisy data: a rapid and robust learning method with maximum entropy. IEEE Transactions on Cybernetics, 2019, 51(4): 2080-2092
    [84] Ding F, Luo C. Structured sparsity learning for large-scale fuzzy cognitive maps. Engineering Applications of Artificial Intelligence, 2021, 105: Article No. 104444 doi: 10.1016/j.engappai.2021.104444
    [85] Vanhoenshoven F, Napoles G, Froelich W, Salmeron J L, Vanhoof K. Pseudoinverse learning of fuzzy cognitive maps for multivariate time series forecasting. Applied Soft Computing, 2020, 95: Article No. 106461 doi: 10.1016/j.asoc.2020.106461
    [86] Wu K, Liu J. Robust learning of large-scale fuzzy cognitive maps via the lasso from noisy time series. Knowledge-Based Systems, 2016, 113: 23-38 doi: 10.1016/j.knosys.2016.09.010
    [87] Yang S, Liu J. Time-series forecasting based on high-order fuzzy cognitive maps and wavelet transform. IEEE Transactions on Fuzzy Systems, 2018, 26(6): 3391-3402 doi: 10.1109/TFUZZ.2018.2831640
    [88] Shen F, Liu J, Wu K. Multivariate time series forecasting based on elastic net and high-order fuzzy cognitive maps: a case study on human action prediction through EEG signals. IEEE Transactions on Fuzzy Systems, 2020, 29(8): 2336-2348
    [89] Gao R, Du L, Yuen K F. Robust empirical wavelet fuzzy cognitive map for time series forecasting. Engineering Applications of Artificial Intelligence, 2020, 96: Article No. 103978 doi: 10.1016/j.engappai.2020.103978
    [90] Liu Z, Liu J. A robust time series prediction method based on empirical mode decomposition and high-order fuzzy cognitive maps. Knowledge-Based Systems, 2020, 203: Article No. 106105 doi: 10.1016/j.knosys.2020.106105
    [91] Wu K, Liu J, Liu P, Shen F. Online fuzzy cognitive map learning. IEEE Transactions on Fuzzy Systems, 2021, 29: 1885-1898 doi: 10.1109/TFUZZ.2020.2988845
    [92] Papageorgiou E I, Groumpos P P. A new hybrid method using evolutionary algorithms to train fuzzy cognitive maps. Applied Soft Computing, 2005, 5(4): 409-431 doi: 10.1016/j.asoc.2004.08.008
    [93] Zhu Y, Zhang W. An integrated framework for learning fuzzy cognitive map using rcga and nhl algorithm. In: Proceedings of the 2008 4th International Conference on Wireless Communications, Networking and Mobile Computing, Dalian, China: IEEE, 2008, 1−5
    [94] Yazdi M N, Lucas C. A hybrid method using pso and nhl algorithms to train fuzzy cognitive maps. In: Proceedings of the 2008 4th International IEEE Conference Intelligent Systems, Varna, Bulgaria: 2008. 8−13
    [95] Ren Z. Learning fuzzy cognitive maps by a hybrid method using nonlinear hebbian learning and extended great deluge algorithm. MAICS, 2012, 159-163
    [96] Natarajan R, Subramanian J, Papageorgiou E I. Hybrid learning of fuzzy cognitive maps for sugarcane yield classification. Computers and Electronics in Agriculture, 2016, 127: 147-157 doi: 10.1016/j.compag.2016.05.016
    [97] Madeiro S S, Zuben F J V. Gradient-based algorithms for the automatic construction of fuzzy cognitive maps. In: Proceedings of the 2012 11th International Conference on Machine Learning and Applications, Boca Raton, FL, USA: IEEE, 2012. 1: 344−349.
    [98] 李慧, 陈红倩, 马丽仪, 梁磊, 孙旸.模糊认知图的算法改进与应用综述.南京大学学报(自然科学), 2016, 52(04): 746-761

    Li Hui, Chen Hong-Qian, Ma Li-Yi, Liang Lei, Sun Yang. A review of algorithm improvement and application of fuzzy cognitive map. Journal of Nanjing University(Natural Science), 2016, 52(04): 746-761
    [99] Wu K, Liu J. Learning large-scale fuzzy cognitive maps under limited resources. Engineering Applications of Artificial Intelligence, 2022, 116: Article No. 105376 doi: 10.1016/j.engappai.2022.105376
    [100] Haritha K, Judy M V, Papageorgiou K, Papageorgiou E. Distributed genetic algorithm for community detection in large graphs with a parallel fuzzy cognitive map for focal node identification. Applied Sciences, 2023, 13(15):8735 doi: 10.3390/app13158735
    [101] Hatwágner M F, Kóczy L T. Parameterization and concept optimization of fcm models. In: Proceedings of the 2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), Istanbul, Turkey: IEEE, 2015. 1−8
    [102] Hatwágner M F, Yesil E, Dodurka M F, Papageorgiou E, Urbas L, Kóczy L T. Two-stage learning based fuzzy cognitive maps reduction approach. IEEE Transactions on Fuzzy Systems, 2018, 26(5): 2938-2952 doi: 10.1109/TFUZZ.2018.2793904
    [103] Zou X, Liu J. A mutual information-based two-phase memetic algorithm for large-scale fuzzy cognitive map learning. IEEE Transactions on Fuzzy Systems, 2017, 26(4): 2120-2134
    [104] Liu J, Chi Y, Zhu C, Jin Y. A time series driven decomposed evolutionary optimization approach for reconstructing large-scale gene regulatory networks based on fuzzy cognitive maps. BMC Bioinformatics, 2017, 18(1): 1-14 doi: 10.1186/s12859-016-1414-x
    [105] Yang Z, Liu J. Learning of fuzzy cognitive maps using a niching-based multi-modal multi-agent genetic algorithm. Applied Soft Computing, 2019, 74: 356-367 doi: 10.1016/j.asoc.2018.10.038
    [106] Douali N, Papageorgiou E I, De Roo J, Cools H, Jaulent M C. Clinical decision support system based on fuzzy cognitive maps. Journal of Computer Science & Systems Biology, 2015, 8(2): 112
    [107] Zhai D S, Chang Y N, Zhang J. An application of fuzzy cognitive map based on active hebbian learning algorithm in credit risk evaluation of listed companies. In: Proceedings of the 2009 International Conference on Artificial Intelligence and Computational Intelligence, Shanghai, China: IEEE, 2009. 4: 89−93
    [108] Kannappan A, Tamilarasi A, Papageorgiou E I. Analyzing the performance of fuzzy cognitive maps with non-linear Hebbian learning algorithm in predicting autistic disorder. Expert Systems with Applications, 2011, 38(3): 1282-1292 doi: 10.1016/j.eswa.2010.06.069
    [109] Beena P, Ganguli R. Structural damage detection using fuzzy cognitive maps and hebbian learning. Applied Soft Computing, 2011, 11(1): 1014-1020 doi: 10.1016/j.asoc.2010.01.023
    [110] Anninou A P, Groumpos P P. Modeling of parkinson's disease using fuzzy cognitive maps and non-linear hebbian learning. International Journal on Artificial Intelligence Tools, 2014, 23(05): Article No. 1450010 doi: 10.1142/S0218213014500109
    [111] Antigoni A P, Peter G P. Nonlinear hebbian learning techniques and fuzzy cognitive maps in modeling the parkinson's disease. In: Proceedings of the 21st Mediterranean Conference on Control and Automation, Platanias, Greece: IEEE, 2013. 709−715
    [112] Sivabalaselvamani D, Harishankher A S, Rahunathan L, Tamilarasi A. Accident identification using fuzzy cognitive maps with adaptive non-linear hebbian learning algorithm. In: Proceedings of the International Conference on Intelligent Computing Systems (ICICS 2017–Dec 15th-16th 2017) organized by Sona College of Technology, Salem, Tamilnadu, India: 2017. 1−10
    [113] Senniappan V, Subramanian J, Papageorgiou E I, Mohan S. Application of fuzzy cognitive maps for crack categorization in columns of reinforced concrete structures. Neural Computing and Applications, 2017, 28(1): 107-117
    [114] Subramanian J, Karmegam A, Papageorgiou E, Papandrianos N, Vasukie A. An integrated breast cancer risk assessment and management model based on fuzzy cognitive maps. Computer Methods and Programs in Biomedicine, 2015, 118(3): 280-297 doi: 10.1016/j.cmpb.2015.01.001
    [115] Chen J, Gao X, Rong J, Gao X. A situation awareness assessment method based on fuzzy cognitive maps. Journal of Systems Engineering and Electronics, 2022, 33(5): 1108-1122 doi: 10.23919/JSEE.2022.000108
    [116] Orang O, de Lima e Silva P C, Guimarães F G. Time series forecasting using fuzzy cognitive maps: a survey. Artificial Intelligence Review, 2023, 56(8): 7733-7794 doi: 10.1007/s10462-022-10319-w
    [117] Froelich W, Papageorgiou E I. Extended evolutionary learning of fuzzy cognitive maps for the prediction of multivariate time-series. In: Proceeding of Fuzzy Cognitive Maps for Applied Sciences and Engineering. Berlin, Heidelberg: Springer, 2014. 121−131
    [118] Luo C, Zhang N, Wang X. Time series prediction based on intuitionistic fuzzy cognitive map. Soft Computing, 2020, 24(9): 6835-6850 doi: 10.1007/s00500-019-04321-8
    [119] Liu X, Zhang Y, Wang J, Huang H, Yin H. Multi-source and multivariate ozone prediction based on fuzzy cognitive maps and evidential reasoning theory. Applied Soft Computing, 2022, 119: Article No. 108600 doi: 10.1016/j.asoc.2022.108600
    [120] Qin D, Peng Z, Wu L. Deep attention fuzzy cognitive maps for interpretable multivariate time series prediction. Knowledge-Based Systems, 2023, 275: Article No. 110700 doi: 10.1016/j.knosys.2023.110700
    [121] Homenda W, Jastrzebska A, Pedrycz W. Joining concept's based fuzzy cognitive map model with moving window technique for time series modeling. In: Proceedings of the IFIP International Conference on Computer Information Systems and Industrial Management. Berlin, Heidelberg: Springer, 2014. 397−408
    [122] Yuan K, Liu J, Yang S, Shen F. Time series forecasting based on kernel mapping and high-order fuzzy cognitive maps. Knowledge-Based Systems, 2020, 206: Article No. 106359 doi: 10.1016/j.knosys.2020.106359
    [123] Feng G, Zhang L, Yang J, Lu W. Long-term prediction of time series using fuzzy cognitive maps. Engineering Applications of Artificial Intelligence, 2021, 102: Article No. 104274 doi: 10.1016/j.engappai.2021.104274
    [124] Wu K, Liu J, Liu P, Yang S. Time series prediction using sparse autoencoder and high-order fuzzy cognitive maps. IEEE Transactions on Fuzzy Systems, 2019, 28(12): 3110-3121
    [125] Feng G, Lu W, Yang J. Time series modeling with fuzzy cognitive maps based on partitioning strategies. In: Proceedings of the 2021 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), Luxembourg, Luxembourg: IEEE, 2021. 1−6
    [126] Feng G, Lu W, Yang J. The modeling of time series based on least square fuzzy cognitive map. Algorithms, 2021, 14(3): 69 doi: 10.3390/a14030069
    [127] Wang Y, Yu F, Homenda W, Pedrycz W, Jastrzebska A, Wang X. Training novel adaptive fuzzy cognitive map by knowledge-guidance learning mechanism for large-scale time-series forecasting. IEEE Transactions on Cybernetics, 2021, Article No. 3132704
    [128] Xia Y, Wang J, Zhang Z, Wei D, Yin L. Short-term pv power forecasting based on time series expansion and high-order fuzzy cognitive maps. Applied Soft Computing, 2023, 135, Article No. 110037 doi: 10.1016/j.asoc.2023.110037
    [129] Mohammadi H A, Ghofrani S, Nikseresht A. Using empirical wavelet transform and high-order fuzzy cognitive maps for time series forecasting. Applied Soft Computing, 2023, 135, Article No. 109990 doi: 10.1016/j.asoc.2023.109990
    [130] Qiao B, Liu J, Wu P, Teng Y. Wind power forecasting based on variational mode decomposition and high-order fuzzy cognitive maps. Applied Soft Computing, 2022, 129, Article No. 109586 doi: 10.1016/j.asoc.2022.109586
    [131] Li Y, Liu J, Teng Y. A decomposition-based memetic neural architecture search algorithm for univariate time series forecasting. Applied Soft Computing, 2022, 130, Article No. 109714 doi: 10.1016/j.asoc.2022.109714
    [132] Salmeron J L, Froelich W. Dynamic optimization of fuzzy cognitive maps for time series forecasting. Knowledge-Based Systems, 2016, 105: 29-37 doi: 10.1016/j.knosys.2016.04.023
    [133] Homenda W, Jastrzebska A. Clustering techniques for fuzzy cognitive map design for time series modeling. Neurocomputing, 2017, 232: 3-15 doi: 10.1016/j.neucom.2016.08.119
    [134] Szwed P. Classification and feature transformation with fuzzy cognitive maps. Applied Soft Computing, 2021, 105: Article No. 107271 doi: 10.1016/j.asoc.2021.107271
    [135] Wu K, Yuan K, Teng Y, Liu J, Jiao L. Broad fuzzy cognitive map systems for time series classification. Applied Soft Computing, 2022, 128: Article No. 109458 doi: 10.1016/j.asoc.2022.109458
    [136] Jastrzebska A, Nápoles G, Homenda W, Vanhoof K. Fuzzy cognitive map-driven comprehensive time-series classification. IEEE Transactions on Cybernetics, 2021, 1-12
    [137] Zhou X, Zhang H. An algorithm of text categorization based on similar rough set and fuzzy cognitive map. In: Proceedings of the 2008 Fifth International Conference on Fuzzy Systems and Knowledge Discovery, Jinan, China: IEEE, 2008. 127−131
    [138] Kannappan A, Papageorgiou E I. A new classification scheme using artificial immune systems learning for fuzzy cognitive mapping. In: Proceedings of the 2013 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), Hyderabad, India: IEEE, 2013. 1−8
    [139] Froelich W, Wakulicz-Deja A. Mining temporal medical data using adaptive fuzzy cognitive maps. In: Proceedings of the 2009 2nd Conference on Human System Interactions, Catania, Italy: IEEE, 2009. 16−23
    [140] Froelich W, Papageorgiou E I, Samarinas M, Skriapas K. Application of evolutionary fuzzy cognitive maps to the long-term prediction of prostate cancer. Applied Soft Computing, 2012, 12(12): 3810-3817 doi: 10.1016/j.asoc.2012.02.005
    [141] Papageorgiou E I, Poczeta K, Laspidou C. Application of fuzzy cognitive maps to water demand prediction. In: Proceedings of the 2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), Istanbul, Turkey: IEEE, 2015. 1−8
    [142] Poczeta K, Papageorgiou E I, Gerogiannis V C. Fuzzy cognitive maps optimization for decision making and prediction. Mathematics, 2020, 8(11): 2059 doi: 10.3390/math8112059
    [143] Trappey A J C, Trappey C V, Wu C R. Genetic algorithm dynamic performance evaluation for rfid reverse logistic management. Expert Systems with Applications, 2010, 37(11): 7329-7335 doi: 10.1016/j.eswa.2010.04.026
    [144] Georgopoulos V C, Stylios C D. Diagnosis support using fuzzy cognitive maps combined with genetic algorithms. In: Proceedings of the 2009 Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Minneapolis, MN, USA: IEEE, 2009. 6226−6229
    [145] Mohr S. Software design for a fuzzy cognitive map modeling tool. Tensselaer Polytechnic Institute, 1997
    [146] The website of fcmappers.net [Online], available: http://www.fcmappers.net/joomla/, June 19, 2023
    [147] León M, Napoles G, Rodriguez C, García M M, Bello R, Vanhoof K. A fuzzy cognitive maps modeling, learning and simulation framework for studying complex system. In: Proceedings of the International Work-Conference on the Interplay Between Natural and Artificial Computation. Berlin, Heidelberg: Springer, 2011. 243−256
    [148] Jose A, Contreras J. The fcm designer tool. Fuzzy cognitive maps. Berlin, Heidelberg: 2010. 71−87
    [149] Aguilar J. Multilayer cognitive maps in the resolution of problems using the fcm designer tool. Applied Artificial Intelligence, 2016, 30: 720-43 doi: 10.1080/08839514.2016.1214422
    [150] Gray S A, Gray S, Cox L J, Henly-Shepard S. Mental modeler: a fuzzy-logic cognitive mapping modeling tool for adaptive environmental management. In: Proceedings of the 2013 46th Hawaii International Conference on System Sciences, Wailea, HI, USA: IEEE, 2013. 965−973
    [151] Franciscis D D. Jfcm: a java library for fuzzy cognitive maps. Fuzzy Cognitive Maps for Applied Sciences and Engineering, 2014, 54: 199-220
    [152] Poczeta K, Yastrebov A, Papageorgiou E I. Learning fuzzy cognitive maps using structure optimization genetic algorithm. In: Proceedings of the 2015 Federated Conference on Computer Science and Information Systems (FedCSIS), Lodz, Poland: IEEE, 2015. 547−554
    [153] Papageorgiou E I, Poczeta K, Laspidou C. Hybrid model for water demand prediction based on fuzzy cognitive maps and artificial neural networks. In: Proceedings of the 2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), Vancouver, BC, Canada: IEEE, 2016. 1523−1530
    [154] Hagan M T, Menhaj M B. Training feedforward networks with the marquardt algorithm. IEEE Transactions on Neural Networks, 1994, 5(6): 989-993 doi: 10.1109/72.329697
    [155] Nápoles G, Leon M, Grau I, Vanhoof K. Fuzzy cognitive maps tool for scenario analysis and pattern classification. In: Proceedings of the 2017 IEEE 29th International Conference on Tools with Artificial Intelligence (ICTAI), Boston, MA, USA: IEEE, 2017. 644−651
    [156] Nápoles G, Grau I, Bello R, Grau R. Two-steps learning of fuzzy cognitive maps for prediction and knowledge discovery on the hiv-1 drug resistance. Expert Systems with Applications, 2014, 41(3): 821-830 doi: 10.1016/j.eswa.2013.08.012
    [157] Nápoles G, Bello R, Vanhoof K. How to improve the convergence on sigmoid fuzzy cognitive maps?. Intelligent Data Analysis, 2014, 18(6S): S77-S88 doi: 10.3233/IDA-140710
    [158] Nápoles G, Papageorgiou E, Bello R, Vanhoof K. On the convergence of sigmoid fuzzy cognitive maps. Information Sciences, 2016, 349: 154-171
    [159] Mkhitaryan S, Giabbanelli P, Wozniak M K, Napoles G, De Vries N, Crutzen R. Fcmpy: a python module for constructing and analyzing fuzzy cognitive maps. Peer J Computer Science, 2022, 8: e1078 doi: 10.7717/peerj-cs.1078
  • 加载中
计量
  • 文章访问数:  88
  • HTML全文浏览量:  52
  • 被引次数: 0
出版历程
  • 收稿日期:  2023-03-09
  • 录用日期:  2023-09-08
  • 网络出版日期:  2024-01-25

目录

    /

    返回文章
    返回