摘要
本文引入了两种基于阿贝尔半群上的模糊蕴含。一种是由一个严格递减函数f生成的Mf-蕴含,其中函数f的值域属于一个阿钡尔半群。另一种是M-蕴含,它是由Mf-蕴含族所生成。紧接着,我们讨论了这两种模糊蕴含的基本性质,证明了这两种模糊蕴含的确是两类新的模糊蕴含,并表明不同于已知的(S,N)-蕴含,R-蕴含,Yager的f-蕴含和苏勇给出的序和蕴含。
In this paper, at first, two new families of fuzzy implications are introduced. One is called an Mf-implieation defined by a strictly decreasing function such that its range belongs to an Abel semigroup, the other is said to be an M-implication which is the ordinal sum of a family of Mf-implications. Then the newly proposed properties of Mf-implications and M-implications are studied. Finally, it is shown that Mf-implications and M-implications are really new class, in other words, they are indeed different from the known （S, N）-, R-, Yager ＇s f-implications, and ordinal sum implications given by Y. Su, respectively.
出处
《模糊系统与数学》
CSCD
北大核心
2016年第2期5-14,共10页
Fuzzy Systems and Mathematics
基金
国家自然科学基金资助项目(61165014
61563020)
江西省自然科学基金资助项目(20151BAB201019)
石家庄学院2016年科研项目
石家庄学院模糊数学应用研究团队项目
关键词
模糊连接词
模糊蕴含
阿贝尔半群
序和蕴含
Fuzzy Connectives
Fuzzy Implications
Abel Semigroups
Ordinal Sum Implications
