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《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (11): 58-65.doi: 10.6040/j.issn.1671-9352.4.2020.241

• • 上一篇    

毕达哥拉斯模糊三支概念格

姬儒雅1,2,魏玲1,2*,任睿思1,2,赵思雨1,2,3   

  1. 1.西北大学数学学院, 陕西 西安 710127;2.西北大学概念、认知与智能研究中心, 陕西 西安 710127;3.咸阳师范学院数学与信息科学学院, 陕西 咸阳 712000
  • 发布日期:2020-11-17
  • 作者简介:姬儒雅(1995— ), 女, 硕士研究生, 研究方向为形式概念分析、粗糙集、粒计算等. E-mail:124988147@qq.com*通信作者简介:魏玲(1972— ), 女, 博士, 教授, 研究方向为形式概念分析、粗糙集、粒计算等. E-mail:wl@nwu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(61772021);陕西省教育厅科研计划资助项目(19JK0929)

Pythagorean fuzzy three-way concept lattice

JI Ru-ya1,2, WEI Ling1,2*, REN Rui-si1,2, ZHAO Si-yu1,2,3   

  1. 1. School of Mathematics, Northwest University, Xian 710127, Shaanxi, China;
    2. Institute of Concepts, Cognition and Intelligence, Northwest University, Xian 710127, Shaanxi, China;
    3. College of Mathematics and Information Science, Xianyang Normal University, Xianyang 712000, Shaanxi, China
  • Published:2020-11-17

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摘要： 将毕达哥拉斯模糊集理论引入模糊三支概念格中, 在毕达哥拉斯模糊形式背景下研究毕达哥拉斯模糊三支概念格的构造。首先, 结合毕达哥拉斯模糊集理论将对象与属性的关系同时用隶属度和非隶属度表示, 给出毕达哥拉斯模糊形式背景的定义;其次, 基于给定的阈值α和β以及三支决策思想, 将对象集(属性集)划分为正域、负域, 边界域3个部分;在此基础上, 给出2种毕达哥拉斯模糊三支概念(对象导出毕达哥拉斯模糊三支概念与属性导出毕达哥拉斯模糊三支概念)的定义和相关定理, 构建相应的概念格;最后, 结合实例阐释毕达哥拉斯模糊三支概念格在实际问题中的应用。

关键词: 三支决策, 模糊三支概念格, 毕达哥拉斯模糊形式背景, 毕达哥拉斯模糊三支概念格

Abstract: Pythagorean fuzzy set theory is introduced into fuzzy three-way concept lattice. The construction of Pythagorean fuzzy three-way concept lattice is studied under the Pythagorean fuzzy formal context. First, the relationships between objects and attributes are expressed by the membership degree and non-membership degree combined with the Pythagorean fuzzy set theory. On this foundation, the definition of the Pythagorean fuzzy formal context is given. Next, based on threshold α, β and the idea of three-way decision, the object sets(the attribute sets)are divided into three parts: positive region, negative region and boundary region. On this basis, the definitions and relevant theorems of two kinds of Pythagorean fuzzy three-way concepts(the object induced Pythagorean fuzzy three-way concept and the attribute induced Pythagorean fuzzy three-way concept)are given, and the corresponding Pythagorean fuzzy three-way concept lattices are constructed. Finally, the applications of Pythagorean fuzzy three-way concept lattice in real problems are explained in detail with examples.

Key words: three-way decision, fuzzy three-way concept lattice, Pythagorean fuzzy formal context, Pythagorean fuzzy three-way concept lattice

中图分类号: 

  • O29
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