摘要
重叠函数是一类特殊的非结合的二元聚类函数.利用重叠函数可以诱导出不同形式的模糊蕴涵.文[7]介绍了由重叠函数O和模糊否定N诱导出的模糊蕴涵—(O,N)-蕴涵,并对(O,N)-蕴涵的基本性质进行了研究,但尚存一些重要性质尚未得到研究.主要基于自同构φ和模糊否定N的相关性质对(O,N)-蕴涵进行深入研究,给出(O,N)-蕴涵一些新的重要性质.
Overlap functions is one particular cases of bivariate continuous aggregation functions.The different forms of fuzzy implications can be generated by overlap functions.(O,N)-implications,which were generated by overlap function O and fuzzy negation N,were introduced in [7].The basic properties of(O,N)-implications were studied.But there are some important properties of(O,N)-implications which have not been discussed yet.In this paper,some new important properties of(O,N)-implications are given by use of the properties of automorphism and fuzzy negation N.
作者
谢海
XIE Hai(School of Science,Guilin University of Technology,Guilin 541004,China;Center for Data analysis and Algorithm Technology,Guilin University of Technology,Guilin 541004,China)
出处
《数学的实践与认识》
2021年第6期170-176,共7页
Mathematics in Practice and Theory
基金
国家自然科学基金(61763008,11661028,11661030)
广西自然科学基金(2017GXNSFAA198223)
桂林理工大学博士科研启动基金(002401003452)。
关键词
(O
N)-蕴涵
重叠函数
分组函数
模糊蕴涵
模糊否定
(O
N)-implications
overlap functions
grouping functions
fuzzy implications
fuzzy negation
