New type of soft positive implicative ideals of weak-BCI-algebras

doi:10.3778/j.issn.1002-8331.1804-0312

Computer Engineering and Applications ›› 2018, Vol. 54 ›› Issue (21): 31-36.DOI: 10.3778/j.issn.1002-8331.1804-0312

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New type of soft positive implicative ideals of weak-BCI-algebras

HUANG Yu1, LIAO Zuhua2, LI Lun3

1.School of Basic Education, Taihu University of Wuxi, Wuxi, Jiangsu 214064, China
2.School of Science, Jiangnan University, Wuxi, Jiangsu 214122, China
3.Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

Online:2018-11-01 Published:2018-10-30

亚BCI-代数的新型软正关联理想

黄昱1，廖祖华2，李论3

1.无锡太湖学院基础教育学院，江苏无锡 214064
2.江南大学理学院，江苏无锡 214122
3.中国科学院数学与系统科学研究院，北京 100190

Abstract

Abstract: The notion of positive implicative ideals of weak-BCI-algebras is introduced, and the relationship between positive implicative ideals and ideals is discussed. By endowing a parameter set as a weak-BCI-algebra, the definition of a new type of soft positive implicative ideals of weak-BCI-algebras is proposed. Examples are given to show that it is different from common soft positive implicative ideals. Relationship between a new type of soft positive implicative ideals and soft ideals is discussed. By using operations of two soft sets, some properties of a new type of soft positive implicative ideals of Weak-BCI-algebras are obtained. Finally, by applying the dual soft sets and level set of soft set, the equivalent characterizations of a new type of soft ideals of weak-BCI-algebras are given.

Key words: weak-BCI-algebra, soft set, new type of soft positive implicative ideal, dual soft set, level set

摘要： 给出了亚BCI-代数正关联理想的概念，讨论了亚BCI-代数正关联理想与理想的关系。将软集的参数集赋予亚BCI-代数，提出了亚BCI-代数新型软正关联理想的概念，举例说明了它与通常的软正关联理想不同。研究了亚BCI-代数新型软正关联理想与新型软理想之间的关系，讨论了亚BCI-代数新型软正关联理想在软集运算下的运算性质，最后分别利用对偶软集和软集的水平集，给出了亚BCI-代数新型软正关联理想与正关联理想之间的等价刻画。

关键词: 亚BCI-代数, 软集, 新型软正关联理想, 对偶软集, 水平集

HUANG Yu1, LIAO Zuhua2, LI Lun3. New type of soft positive implicative ideals of weak-BCI-algebras[J]. Computer Engineering and Applications, 2018, 54(21): 31-36.

黄昱1，廖祖华2，李论3. 亚BCI-代数的新型软正关联理想[J]. 计算机工程与应用, 2018, 54(21): 31-36.

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New type of soft positive implicative ideals of weak-BCI-algebras

亚BCI-代数的新型软正关联理想

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