模糊赋范线性空间的1-最佳逼近

1-Best Approximation of Fuzzy Normed Linear Space

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。

Abstract: 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.