计算机工程与应用 ›› 2017, Vol. 53 ›› Issue (5): 31-35.DOI: 10.3778/j.issn.1002-8331.1507-0102

• 理论与研发 • 上一篇    下一篇

基于强正则蕴涵算子的加权模糊度量空间

李  骏,付  超   

  1. 兰州理工大学 理学院,兰州 730050
  • 出版日期:2017-03-01 发布日期:2017-03-03

Weighted fuzzy metric spaces based on strong regular implication operators

LI Jun, FU Chao   

  1. School of Science, Lanzhou University of Technology, Lanzhou 730050, China
  • Online:2017-03-01 Published:2017-03-03

摘要: 在强正则蕴涵算子的统一框架下给出了加权正则度量的定义,建立了基于强正则蕴涵算子的加权正则模糊度量空间,并且研究了该模糊度量空间的性质,分析了常用的逻辑连接词所对应的映射关于加权正则度量的连续性,最后证明了基于Lukasiewicz蕴涵的加权正则模糊度量空间是最适宜于展开模糊推理的模糊度量空间。

关键词: 模糊度量空间, 模糊推理, 强正则蕴涵算子, 加权正则度量

Abstract: The concept of weighted regular metric is proposed in the unified framework of strong regular implication operators. The weighted fuzzy metric space is established based on strong regular implication operators and its properties are studied. Continuity of mappings corresponding to commonly used logic connectives is analyzed. Finally, it is proved that the weighted regular fuzzy metric space based on Lukasiewicz implication is most suitable for developing fuzzy reasoning.

Key words: fuzzy metric space, fuzzy reasoning, strong regular implication operator, weighted regular metric