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《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (11): 81-89.doi: 10.6040/j.issn.1671-9352.0.2018.674

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基于MV-代数的度量型模糊粗糙集

熊兴国1,路玲霞2*   

  1. 1.河北地质大学社会科学部, 河北 石家庄 050031;2.南京信息工程大学数学与统计学院, 江苏 南京 210044
  • 发布日期:2019-11-06
  • 作者简介:熊兴国(1977— ),女,硕士,讲师,研究方向为辩证逻辑. E-mail:xxgxiongxingguo@126.com*通信作者简介:路玲霞(1978— ),女,博士,副教授,研究方向为粗糙集和拟阵理论. E-mail:lu_lingxia@163.com
  • 基金资助:
    国家自然科学基金资助项目(11871189)

MV-algebra valued metric-based fuzzy rough sets

XIONG Xing-guo1, LU Ling-xia2*   

  1. 1. School of Social Science, Hebei GEO University, Shijiazhuang 050018, Hebei, China;
    2. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, Jiangsu, China
  • Published:2019-11-06

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摘要： 研究基于多值逻辑MV-代数的度量型模糊粗糙集模型,给出-半度量和通常的实数值半度量的关系,证明-半度量和 -相似关系的等价性,研究-半度量诱导的模糊粗糙近似算子的性质及其可定义集的性质。

关键词: MV-代数, -半度量, -相似关系, 模糊粗糙近似算子, 可定义集

Abstract: MV-algebra valued metric-based fuzzy rough set model is defined. The interrelations between -hemimetrics and the standard real valued hemimetrics are investigated. It is shown that -hemimetrics and -similarities are equivalent to each other. The properties of fuzzy rough approximation operators and the related definable sets are studied.

Key words: MV-algebra, -hemimetric, -similarity, fuzzy rough approximation operator, definable set

中图分类号: 

  • O159
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