新型软粗糙集:软粗糙半群

doi:10.11896/j.issn.1002-137X.2019.02.035

摘要/Abstract

摘要： 为进一步简化处理不确定性问题的方法,在半群上研究了一种新型的软粗糙集(MSR-半群)。首先,基于软集、粗糙集和半群的一些基本理论,对它们之间的关系进行深入研究,并讨论了软粗糙集的运算和基本性质;接着,为了进一步了解软逼近空间,应用了下软粗糙逼近和上软粗糙逼近的概念;同时,在半群上提出了两种特殊软集即G-软集和GG-软集的概念,对其做相应的运算,并给出实例进行了证明;接着,对MSR-逼近空间的粗糙性进行讨论,提出了MSR-半群的概念,并且研究了上MSR-半群和下MSR-半群的基本特征;最后,通过实例进行比较分析,说明了软粗糙半群的研究价值。

关键词: MSR-半群, MSR-集, 粗糙集, 软粗糙集

Abstract: In order to further simplify the method of dealing with the problem of uncertainty,this paper studied a new type of soft rough set (MSR-semigroup)on semigroups.First of all,based on some basic theories of soft sets,rough sets and semigroups,the relationship among them were deeply studied,and the operation and basic properties of soft rough sets were discussed.Then,in order to further understand the soft approximation space,the concepts of the lower and upper soft rough approximation were applied.At the same time,two special soft sets G-soft sets and GG-soft sets were proposed on semigroups,corresponding operations were given and some examples were given.Then,the roughness of the soft approximation space was discussed,the concept of MSR-semigroups was proposed,and the basic characteristics of the upper and lower MSR-semigroups were studied.Finally,a comparative analysis of example shows the research value of the soft rough semigroup.

Key words: MSR-semigroups, MSR-sets, Rough set, Soft rough set

中图分类号:

O144.1

路怡瑶, 孔祥智. 新型软粗糙集:软粗糙半群[J]. 计算机科学, 2019, 46(2): 230-235. https://doi.org/10.11896/j.issn.1002-137X.2019.02.035

LU Yi-yao, KONG Xiang-zhi. Novel Soft Rough Set:Soft Rough Semigroups[J]. Computer Science, 2019, 46(2): 230-235. https://doi.org/10.11896/j.issn.1002-137X.2019.02.035

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