模糊赋范线性空间的1-最佳逼近  

1-Best Approximation of Fuzzy Normed Linear Space

作　　者：张入化 蒋浩 

机构地区：[1]西华大学理学院,四川 成都

出　　处：《应用数学进展》2023年第6期2958-2964,共7页Advances in Applied Mathematics

摘　　要：T. Bag和S. K. Samanta于2003年建立了模糊赋范线性空间,并研究了模糊范数导出的α-范数a(∈(0,1))性质,以及点列按照α-范数收敛与按照模糊范数收敛的关系。本文给出了由模糊范数导出的1-范数的概念,研究了点列按1-范数收敛与按模糊范数收敛的关系。同时,研究了按1-范数引入的逼近问题,得到了按1-范数定义的存在性集与模糊闭集之间的关系。T. Bag and S. K. Samanta established the fuzzy norm linear space in 2003, studied the properties of α-norm derived by fuzzy norm, and discussed the relationship between sequence convergence in sense of α-norm and convergence in sense of fuzzy norm. In this paper, we give the concept of 1-norm derived from fuzzy norm and study the relationship between convergence of sequence in sense of 1-norm and convergence in sense of fuzzy norm. Meanwhile, the approximation problem introduced by 1-norm is discussed, and the relationship between the 1-existence set and the fuzzy closed set defined by 1-norm is obtained.

关 键 词：模糊赋范线性空间 1-范数 1-最佳逼近 1-存在性集 

分 类 号：O17[理学—数学]