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《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

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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

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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}
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