您的位置：山东大学 -> 科技期刊社 -> 《山东大学学报（理学版）》

《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (12): 118-126.doi: 10.6040/j.issn.1671-9352.4.2022.6483

•   • 上一篇    下一篇

基于犹豫三角模糊相关系数的聚类分析

马慧(),魏立力*()   

  1. 宁夏大学数学统计学院, 宁夏 银川 750021
  • 收稿日期:2022-08-17 出版日期:2023-12-20 发布日期:2023-12-19
  • 通讯作者: 魏立力 E-mail:liliwei@nxu.edu.cn
  • 作者简介:马慧(1992—)，女，硕士研究生，研究方向为应用统计与复杂数据分析. E-mail：liliwei@nxu.edu.cn
  • 基金资助:
    宁夏回族自治区自然科学基金资助项目(2021AAC03039)

Cluster analysis based on the hesitation triangle fuzzy correlation coefficient

Hui MA(),Lili WEI*()   

  1. School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, Ningxia, China
  • Received:2022-08-17 Online:2023-12-20 Published:2023-12-19
  • Contact: Lili WEI E-mail:liliwei@nxu.edu.cn

RichHTML

3

PDF (PC)

339

摘要：

针对评估值为犹豫三角模糊元的聚类问题，提出了基于犹豫三角模糊相关系数的聚类算法。首先给出犹豫三角模糊相关系数的定义和计算公式；其次考虑到犹豫三角模糊元权重的影响，将犹豫三角模糊相关系数推广为犹豫三角模糊加权相关系数；最后将提出的方法应用于犹豫模糊环境下的聚类问题，实例分析验证本文方法的可行性。

关键词: 犹豫三角模糊集, 相关系数, 层次聚类, 模糊数据

Abstract:

A clustering algorithm based on the hesitation triangle fuzzy correlation coefficient is proposed to solve the clustering problem of hesitating triangle fuzzy elements. Firstly, the definition and calculation formula of the hesitation triangle fuzzy correlation coefficient of are given. Secondly, considering the influence of the weight of the hesitancy triangle fuzzy element, the hesitation triangle fuzzy correlation coefficient is extended to the hesitation triangle fuzzy weighted correlation coefficient. Finally, the proposed method is applied to the clustering problem in a hesitant fuzzy environment, and the feasibility of the proposed method is demonstrated by an example.

Key words: hesitation triangle fuzzy set, correlation coefficient, hierarchical clustering, fuzzy data

中图分类号: 

  • C934

表1

犹豫三角模糊评价矩阵T"

聚类方案 x1 x2 x3 x4
A1 {(0.1, 0.2, 0.3),
(0.2, 0.3, 0.4)}		 {(0.1, 0.2, 0.4)} {(0.5, 0.6, 0.7),
(0.6, 0.7, 0.8)}		 {(0.2, 0.3, 0.4)}
A2 {(0.1, 0.2, 0.4),
(0.3, 0.4, 0.5),
(0.4, 0.5, 0.6)}		 {(0.2, 0.3, 0.4),
(0.5, 0.6, 0.7)}		 {(0.1, 0.3, 0.5)} {(0.5, 0.6, 0.7)}
A3 {(0.4, 0.5, 0.6)} {(0.1, 0.2, 0.3),
(0.3, 0.4, 0.5)}		 {(0.6, 0.7, 0.8),
(0.7, 0.8, 0.9)}		 {(0.4, 0.5, 0.6)}
A4 {(0.2, 0.3, 0.4),
(0.5, 0.6, 0.7)}		 {(0.1, 0.2, 0.3)} {(0.5, 0.6, 0.7),
(0.6, 0.7, 0.8)}		 {(0.6, 0.7, 0.8)}
A5 {(0.1, 0.2, 0.3)} {(0.3, 0.4, 0.5)} {(0.1, 0.2, 0.3),
(0.4, 0.5, 0.6)}		 {(0.7, 0.8, 0.9)}

表2

新的犹豫三角模糊评价矩阵$\tilde{{\boldsymbol{T}}}$"

聚类方案 x1 x2 x3 x4
A1 {(0.1, 0.2, 0.3),
(0.2, 0.3, 0.4),
(0.2, 0.3, 0.4)}		 {(0.1, 0.2, 0.4),
(0.1, 0.2, 0.4)}		 {(0.5, 0.6, 0.7),
(0.6, 0.7, 0.8)}		 {(0.2, 0.3, 0.4)}
A2 {(0.1, 0.2, 0.4),
(0.3, 0.4, 0.5),
(0.4, 0.5, 0.6)}		 {(0.2, 0.3, 0.4),
(0.5, 0.6, 0.7)}		 {(0.1, 0.3, 0.5),
(0.1, 0.3, 0.5)}		 {(0.5, 0.6, 0.7)}
A3 {(0.4, 0.5, 0.6),
(0.4, 0.5, 0.6),
(0.4, 0.5, 0.6)}		 {(0.1, 0.2, 0.3),
(0.3, 0.4, 0.5)}		 {(0.6, 0.7, 0.8),
(0.7, 0.8, 0.9)}		 {(0.4, 0.5, 0.6)}
A4 {(0.2, 0.3, 0.4),
(0.5, 0.6, 0.7),
(0.5, 0.6, 0.7)}		 {(0.1, 0.2, 0.3),
(0.1, 0.2, 0.3)}		 {(0.5, 0.6, 0.7),
(0.6, 0.7, 0.8)}		 {(0.6, 0.7, 0.8)}
A5 {(0.1, 0.2, 0.3),
(0.1, 0.2, 0.3),
(0.1, 0.2, 0.3)}		 {(0.3, 0.4, 0.5),
(0.3, 0.4, 0.5)}		 {(0.1, 0.2, 0.3),
(0.4, 0.5, 0.6)}		 {(0.7, 0.8, 0.9)}

表3

对比分析表"

方法 分4类 分3类 分2类
相关系数 {A1, A4}、{A2}、{A3}、{A5} {A1, A4}、{A2, A3}、{A5} {A1, A4, A5}、{A2, A3}
加权相关系数 {A1, A4}、{A2}、{A3}、{A5} {A1, A4}、{A2, A3}、{A5} {A1, A4, A5}、{A2, A3}
1 TORRA V . Hesitant fuzzy sets[J]. International Journal of Intelligent Systems, 2010, 25, 529- 539.
2 TORRA V, NARUKAWA Y. On hesitant fuzzy sets and decision[C]//Proceedings of the 18th IEEE International Conference on Fuzzy Systems. Jein Island: IEEE, 2009: 1378-1382.
3 YU Dejian . Triangular hesitant fuzzy set and its application to teaching quality evaluation[J]. Journal of Information and Computational Science, 2013, 10, 1925- 1934.
doi: 10.12733/jics20102025
4 马慧, 魏立力. 加权犹豫三角模糊距离度量及其在群决策中的应用[J]. 计算机工程与科学, 2020, 42 (8): 1430- 1439.
doi: 10.3969/j.issn.1007-130X.2020.08.013
MA Hui , WEI Lili . Weighted hesitant triangular fuzzy distance measurement and its application in group decision making[J]. Computer Engineeringand Science, 2020, 42 (8): 1430- 1439.
doi: 10.3969/j.issn.1007-130X.2020.08.013
5 GERSTENKORN T , MANKO J . Correlation of intuitionistic fuzzy sets[J]. Fuzzy Set Systems, 1991, 44, 39- 43.
doi: 10.1016/0165-0114(91)90031-K
6 CHEN Na , XU Zeshui , XIA Meimei . Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis[J]. Applied Mathematical Modelling, 2013, 37, 2197- 2211.
doi: 10.1016/j.apm.2012.04.031
7 徐俊艳, 孙贵东, 赵静. 新的犹豫模糊集相关系数及多属性决策应用[J]. 电子学报, 2018, (6): 1327- 1335.
XU Junyan , SUN Guidong , ZHAO Jing . Novel correlation coefficients between hesitant fuzzy sets and their applications in multi-attribute decision making[J]. Acta Electronica Sinica, 2018, (6): 1327- 1335.
8 MENG Fanyong , CHEN Xiaohong . Correlation coefficients of hesitant fuzzy sets and their application based on fuzzy measures[J]. Cognitive Computation, 2015, 7, 445- 463.
doi: 10.1007/s12559-014-9313-9
9 MENG Fanyong , WANG Chen , CHEN Xiaohong , et al. Correlation coefficients of interval-valued hesitant fuzzy sets and their application based on the Shapley function[J]. International Journal of Intelligent Systems, 2016, 31, 17- 43.
doi: 10.1002/int.21741
10 彭友, 刘晓鹤, 孙健博. 区间直觉模糊数环境下基于犹豫度和相关系数的多属性群决策模型研究[J]. 中国管理科学, 2021, 29 (8): 229- 240.
PENG You , LIU Xiaohe , SUN Jianbo . Interval-valued intuitionistic fuzzy multi-attribute group decision making approach based on the hesitancy degrees and correlation coefficient[J]. Chinese Journal of Management Science, 2021, 29 (8): 229- 240.
11 XU Zeshui , XIA Meimei . Distance and similarity measures for hesitant fuzzy sets[J]. Information Sciences, 2011, 181, 2128- 2138.
doi: 10.1016/j.ins.2011.01.028
12 谭旭, 吴俊江, 毛太田, 等. 基于三角模糊数犹豫直觉模糊集的多属性智能决策[J]. 系统工程与电子技术, 2017, 39 (4): 829- 836.
TAN Xu , WU Junjiang , MAO Taitian , et al. Multi-attribute intelligent decision-making method based on triangular fuzzy number hesitant intuitionistic fuzzy sets[J]. System Engineering and Electronics, 2017, 39 (4): 829- 836.
13 牟能冶. 基于广义犹豫三角模糊幂均算子的MADM方法[J]. 控制与决策, 2018, 33 (2): 282- 292.
MU Nengye . An approach to multiple attribute decision making on the basis of hesitant triangular fuzzy power average operator[J]. Control and Decision, 2018, 33 (2): 282- 292.
14 徐泽水, 赵华. 犹豫模糊集理论及应用[M]. 北京: 科学出版社, 2018.
XU Zeshui , ZHAO Hua . Theory and application of hesitant fuzzy sets[M]. Beijing: Science Press, 2018.
15 徐泽水. 三角模糊数互补判断矩阵的一种排序方法[J]. 模糊系统与数学, 2002, 16 (1): 47- 50.
XU Zeshui . A method for priorities of triangular fuzzy number complementary judgement matrices[J]. Fuzzy Systems and Mathematics, 2002, 16 (1): 47- 50.
16 葛涛, 万昆, 徐莉. 基于犹豫模糊三角函数的水利项目评价[J]. 技术经济, 2014, 33 (9): 125- 130.
GE Tao , WAN Kun , XU Li . Evaluation on hydraulic project based on hesitant triangular fuzzy function[J]. Technology Economics, 2014, 33 (9): 125- 130.
[1] 张钰倩,张太雷. 具有复发效应的SEAIR模型及在新冠肺炎传染病中的应用[J]. 《山东大学学报(理学版)》, 2022, 57(1): 56-68.
[2] 高月月,李新颖,李宁. 电磁感应下Chay神经元的放电分岔特性与同步[J]. 《山东大学学报(理学版)》, 2021, 56(1): 43-51.
[3] 董向忠, 关杰. SIMON类算法轮函数的线性性质[J]. 山东大学学报（理学版）, 2015, 50(09): 49-54.
[4] 李述山. 基于尾部样本数据的尾部相关性分析[J]. 山东大学学报（理学版）, 2014, 49(12): 49-54.
[5] 王灵垠1,刘琚2. 降低OFDM系统峰均功率比的时频联合块交织方法[J]. J4, 2012, 47(11): 83-87.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] 杨军. 金属基纳米材料表征和纳米结构调控[J]. 山东大学学报（理学版）, 2013, 48(1): 1 -22 .
[2] 何海伦， 陈秀兰*. 变性剂和缓冲系统对适冷蛋白酶MCP-01和中温蛋白酶BP-01构象影响的圆二色光谱分析何海伦， 陈秀兰*[J]. 山东大学学报（理学版）, 2013, 48(1): 23 -29 .
[3] 赵君1,赵晶2,樊廷俊1*,袁文鹏1,3,张铮1,丛日山1. 水溶性海星皂苷的分离纯化及其抗肿瘤活性研究[J]. J4, 2013, 48(1): 30 -35 .
[4] 孙小婷1,靳岚2*. DOSY在寡糖混合物分析中的应用[J]. J4, 2013, 48(1): 43 -45 .
[5] 罗斯特,卢丽倩,崔若飞,周伟伟,李增勇*. Monte-Carlo仿真酒精特征波长光子在皮肤中的传输规律及光纤探头设计[J]. J4, 2013, 48(1): 46 -50 .
[6] 杨伦，徐正刚，王慧*，陈其美，陈伟，胡艳霞，石元，祝洪磊，曾勇庆*. RNA干扰沉默PID1基因在C2C12细胞中表达的研究[J]. J4, 2013, 48(1): 36 -42 .
[7] 冒爱琴1, 2, 杨明君2, 3, 俞海云2, 张品1, 潘仁明1*. 五氟乙烷灭火剂高温热解机理研究[J]. J4, 2013, 48(1): 51 -55 .
[8] 杨莹,江龙*,索新丽. 容度空间上保费泛函的Choquet积分表示及相关性质[J]. J4, 2013, 48(1): 78 -82 .
[9] 李永明1, 丁立旺2. PA误差下半参数回归模型估计的r-阶矩相合[J]. J4, 2013, 48(1): 83 -88 .
[10] 董伟伟. 一种具有独立子系统的决策单元DEA排序新方法[J]. J4, 2013, 48(1): 89 -92 .
版权所有 © 2018 《山东大学学报(理学版)》编辑部　
地址: 山东省济南市山大南路27号山东大学中心校区（250100）　电话: +86-0531-88366917　E-mail: xblxb@sdu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发