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《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (9): 43-53.doi: 10.6040/j.issn.1671-9352.0.2019.038

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区间毕达哥拉斯模糊集的信息度量及其应用

孙倩倩,李小南*   

  1. 西安电子科技大学数学与统计学院, 陕西 西安 710071
  • 出版日期:2019-09-20 发布日期:2019-07-30
  • 作者简介:孙倩倩(1993— ),女,硕士研究生,研究方向为模糊集、粗糙集及三支决策. E-mail:18865735253@163.com*通信作者简介:李小南(1981— ),男,博士,副教授,研究方向为拟阵推广理论、粗糙集及三支决策. E-mail:lxn2007@163.com
  • 基金资助:
    国家自然科学基金资助项目(61772019)

Information measures of interval valued Pythagorean fuzzy sets and their applications

SUN Qian-qian, LI Xiao-nan*   

  1. School of Mathematics and Statistics, Xidian University, Xian 710071, Shaanxi, China
  • Online:2019-09-20 Published:2019-07-30

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摘要： 熵、距离和相似度是模糊集及其推广理论中重要的信息度量工具。基于区间毕达哥拉斯模糊集的信息度量研究大多涉及区间毕达哥拉斯模糊数的距离公式,很少涉及模糊性和相似性的度量方法。针对这种情况,首先提出区间毕达哥拉斯模糊集的熵、距离和相似度的公理化定义。然后研究熵、距离和相似度之间的关系。最后将提出区间毕达哥拉斯模糊集的熵和相似度应用到模式识别领域,对比分析表明所提出的度量方法具有灵活性和有效性的特点。

关键词: 区间毕达哥拉斯模糊集, 熵, 距离, 相似度, 模式识别

Abstract: Entropy, distance and similarity are important information measurement tools in fuzzy sets and their generalization theories. The information metrics research based on interval valued Pythagorean fuzzy sets mostly involves the distance formula of interval valued Pythagorean fuzzy numbers, and rarely involves metrics of ambiguity and similarity. In view of this situation, firstly, the axiomatization definition of entropy, distance and similarity of interval valued Pythagorean fuzzy sets is first proposed. Then study the relationship between entropy, distance and similarity. Finally, the entropy and similarity of the interval valued Pythagorean fuzzy set are applied to the field of pattern recognition. Comparative analysis shows the flexibility and effectiveness of the proposed measures.

Key words: interval valued Pythagorean fuzzy set, entropy, distance, similarity, pattern recognition

中图分类号: 

  • O159
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