摘要
模糊数列统计收敛问题是模糊分析学的重要组成内容,模糊数列统计收敛方面的理论,前人已经行深入研究,然而,收敛条件较强.在扩大了模糊数列收敛范围,引入了Orlicz函数和权重的概念,利用权重的意义给出了模糊数列基于Orlicz函数加权统计收敛和加权强收敛的概念.讨论了新定义的两类收敛空间的一些性质.同时,证明了加权强收敛模糊数列空间、加权统计收敛模糊数列空间以及统计收敛模糊数列之间的相互关系,结果表明关于Orlicz函数加权强收敛的模糊数列一定加权统计收敛;当模糊数列有界时,反之成立.
The problem of statistical convergence of fuzzy sequence is an important part of fuzzy analysis.The theory of statistical convergence of fuzzy sequence has been studied by predecessors.However,the convergence conditions are strong.In order to expand the convergence range of fuzzy sequence,the concepts of Orlicz function and weight have been introduced.The concepts of weighted statistical convergence and weighted strong convergence based on Orlicz function are given by using the meaning of weight.Some properties of the newly defined two kinds of convergence spaces were discussed.At the same time,the relationship between weighted strongly convergent fuzzy sequence space,weighted statistically convergent fuzzy sequence space and statistically convergent fuzzy sequence was proved.The results showed that the weighted strongly convergent fuzzy sequence of Orlicz function had certain weighted statistical convergence.
作者
冯雪
FENG Xue(College of Mathematics and Statics,Qinghai Nationalities University,Xining 810007,China)
出处
《哈尔滨商业大学学报（自然科学版）》
CAS
2021年第3期351-355,384,共6页
Journal of Harbin University of Commerce：Natural Sciences Edition
基金
国家自然科学基金(11761056,11665019)
青海省自然科学基金(2020-ZJ-920)
青海民族大学校级规划项目(2021XJGH24)。
关键词
模糊数列
ORLICZ函数
权重
统计收敛
加权统计收敛
加权强收敛
fuzzy numbers
Orlicz functions
weight
statistical convergence
weighted statistical convergence
weighted strong convergence
