Rough numerical series and their convergence properties

doi:10.3778/j.issn.1002-8331.1610-0386

Computer Engineering and Applications ›› 2017, Vol. 53 ›› Issue (8): 15-18.DOI: 10.3778/j.issn.1002-8331.1610-0386

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Rough numerical series and their convergence properties

TANG Lingyu1，2, ZHANG Xianyong1，2, MO Zhiwen1，2

1.College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China
2.Institute of Intelligent Information and Quantum Information, Sichuan Normal University, Chengdu 610066, China

Online:2017-04-15 Published:2017-04-28

粗糙数项级数及其粗糙收敛性质

唐玲玉1，2，张贤勇1，2，莫智文1，2

1.四川师范大学数学与软件科学学院，成都 610066
2.四川师范大学智能信息与量子信息研究所，成都 610066

Abstract

Abstract: This paper utilizes rough Cauchy sequences to investigate rough numerical series and their properties. Rough numerical series are defined to demine their rough convergence and divergency, both measure-based uniqueness and real-valued nonuniqueness of rough sums are established, and transformation relationships and property differences between rough and precise convergence of numerical series are achieved. This relevant study promotes rough sequences to rough numerical series.

Key words: rough set, rough sequence, rough numerical series, rough convergence

摘要： 基于粗糙Cauchy数列，研究粗糙数项级数及其粗糙收敛性质。定义粗糙数项级数的粗糙敛散性，确立粗糙和的离散度量唯一性与连续实值不唯一性，得到数项级数的粗糙收敛与精确收敛的转化关系与性质差异。相关研究推进粗糙数列到粗糙数项级数。

关键词: 粗糙集, 粗糙数列, 粗糙数项级数, 粗糙收敛

TANG Lingyu1，2, ZHANG Xianyong1，2, MO Zhiwen1，2. Rough numerical series and their convergence properties[J]. Computer Engineering and Applications, 2017, 53(8): 15-18.

唐玲玉1，2，张贤勇1，2，莫智文1，2. 粗糙数项级数及其粗糙收敛性质[J]. 计算机工程与应用, 2017, 53(8): 15-18.

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Rough numerical series and their convergence properties

粗糙数项级数及其粗糙收敛性质

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