模糊赋范Riesz空间上模糊Riesz-Fischer性的基本性质
The Basic Property of Fuzzy Riesz-Fischer Property on Fuzzy Normed Riesz Spaces
郑富丽 1程娜 1刘艳丽1
作者信息
- 1. 西华大学理学院,四川成都 610039
- 折叠
摘要
模糊赋范Riesz空间是一个结合了模糊数学理论和经典Riesz空间理论的数学结构,其中的范数是一个模糊数,而非实数.模糊Riesz-Fischer性则定义在这样的空间中,强调了模糊度在序列收敛过程中的作用.通过对Riesz-Fischer性的研究,给出了模糊赋范Riesz空间上模糊Riesz-Fischer性的定义,继而讨论了模糊Riesz-Fischer性的基本性质,并用Riesz-Fischer性刻画了模糊赋范Riesz空间的完备性,丰富和推广了已有结论.
Abstract
Fuzzy Normed Riesz space is a mathematical structure that combines fuzzy mathematical theory and classical Riesz space theory,where the norm is a fuzzy number rather than a real number.The fuzzy Riesz-Fischer property is defined in such a space,emphasizing the role of ambiguity in the sequence convergence process.Through the study of the Riesz-Fischer property,the definition of fuzzy Riesz-Fischer property in fuzzy normed Riesz space is given,and then the basic properties of fuzzy Riesz-Fischer property are discussed,and the completeness of fuzzy normed Riesz space is described by Riesz-Fischer property,which enriches and generalizes the existing conclusions.
关键词
模糊赋范Riesz空间/模糊Riesz-Fischer性/模糊弱Riesz-Fischer性Key words
fuzzy normed Riesz space/fuzzy Riesz-Fischer property/fuzzy weak Riesz-Fischer property引用本文复制引用
出版年
2024
NETL
NSTL
万方数据