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

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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

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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}
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