JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (12): 118-126.doi: 10.6040/j.issn.1671-9352.4.2022.6483

•   • Previous Articles     Next Articles

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)

337

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

CLC Number: 

  • C934

Table 1

Hesitation triangle fuzzy evaluation matrix 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)}

Table 2

New hesitation triangle fuzzy evaluation matrix $\tilde{{\boldsymbol{T}}}$"

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)}

Table 3

Comparative analysis table"

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] ZHANG Yu-qian, ZHANG Tai-lei. An SEAIR model with relapse effect and its application in COVID-19 transmission [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(1): 56-68.
[2] GAO Yue-yue, LI Xin-ying, LI Ning. Firing bifurcation characteristics and synchronization of Chay neuron under electromagnetic induction [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(1): 43-51.
[3] DONG Xiang-zhong, GUAN Jie. Linear properties of the round function of SIMON family of block ciphers [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(09): 49-54.
[4] WANG Ling-yin1, LIU Ju2. Time-frequency block interleaving schemes for PAPR reduction in OFDM systems [J]. J4, 2012, 47(11): 83-87.
[5] DU Ning,GUO Wei-hua,WU Da-qian,WANG Qi and WANG Ren-qing . Inter-specific relations of shrub and herbage species under a typical forest on Kunyu Mountain [J]. J4, 2007, 42(3): 71-77 .
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] YANG Jun. Characterization and structural control of metalbased nanomaterials[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2013, 48(1): 1 -22 .
[2] HE Hai-lun， CHEN Xiu-lan* . Circular dichroism detection of the effects of denaturants and buffers on the conformation of cold-adapted protease MCP-01 and  mesophilic protease BP01[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2013, 48(1): 23 -29 .
[3] ZHAO Jun1, ZHAO Jing2, FAN Ting-jun1*, YUAN Wen-peng1,3, ZHANG Zheng1, CONG Ri-shan1. Purification and anti-tumor activity examination of water-soluble asterosaponin from Asterias rollestoni Bell[J]. J4, 2013, 48(1): 30 -35 .
[4] SUN Xiao-ting1, JIN Lan2*. Application of DOSY in oligosaccharide mixture analysis[J]. J4, 2013, 48(1): 43 -45 .
[5] LUO Si-te, LU Li-qian, CUI Ruo-fei, ZHOU Wei-wei, LI Zeng-yong*. Monte-Carlo simulation of photons transmission at alcohol wavelength in  skin tissue and design of fiber optic probe[J]. J4, 2013, 48(1): 46 -50 .
[6] YANG Lun, XU Zheng-gang, WANG Hui*, CHEN Qi-mei, CHEN Wei, HU Yan-xia, SHI Yuan, ZHU Hong-lei, ZENG Yong-qing*. Silence of PID1 gene expression using RNA interference in C2C12 cell line[J]. J4, 2013, 48(1): 36 -42 .
[7] MAO Ai-qin1,2, YANG Ming-jun2, 3, YU Hai-yun2, ZHANG Pin1, PAN Ren-ming1*. Study on thermal decomposition mechanism of  pentafluoroethane fire extinguishing agent[J]. J4, 2013, 48(1): 51 -55 .
[8] YANG Ying, JIANG Long*, SUO Xin-li. Choquet integral representation of premium functional and related properties on capacity space[J]. J4, 2013, 48(1): 78 -82 .
[9] LI Yong-ming1, DING Li-wang2. The r-th moment consistency of estimators for a semi-parametric regression model for positively associated errors[J]. J4, 2013, 48(1): 83 -88 .
[10] DONG Wei-wei. A new method of DEA efficiency ranking for decision making units with independent subsystems[J]. J4, 2013, 48(1): 89 -92 .
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd