计算机科学与探索 ›› 2018, Vol. 12 ›› Issue (4): 662-670.DOI: 10.3778/j.issn.1673-9418.1612018

• 理论与算法 • 上一篇    下一篇

BCK-代数的广义(∈,∈∨q)-模糊蕴涵理想

彭家寅+   

  1. 内江师范学院 数学与信息科学学院,四川 内江 641199
  • 出版日期:2018-04-01 发布日期:2018-04-04

Generalized (∈,∈∨q)-Fuzzy Implicative Ideals of BCK-Algebra

PENG Jiayin+   

  1. College of Mathematics and Information Sciences, Neijiang Normal University, Neijiang, Sichuan 641199, China
  • Online:2018-04-01 Published:2018-04-04

摘要: 为推广BCK-代数的(∈,∈∨q)-模糊蕴涵理想,引入了[(∈,∈∨qk)]-模糊蕴涵理想的概念,研究了相关性质;指出了模糊蕴涵理想和(∈,∈∨q)-模糊蕴涵理想都是(∈,∈∨qk)-模糊蕴涵理想,反之不然;给出了BCK-代数的模糊子集成为[(∈,∈∨qk)]-模糊蕴涵理想的条件;证明了(∈,∈∨qk)-模糊蕴涵理想都是(∈,∈∨qk)-模糊理想,用实例说明其逆命题不真;给出了(∈,∈∨qk)-模糊蕴涵理想的若干等价刻画,讨论了BCK-代数的基于蕴涵的模糊蕴涵理想。

关键词: BCK-代数;模糊蕴涵理想;(&isin, ,&isin, &or, qk)-模糊理想;(&isin, ,&isin, &or, qk)-模糊蕴涵理想;不分明化蕴涵理想;t-蕴涵的模糊蕴涵理想

Abstract: As a generalization of the notion of an (∈,∈∨q)-fuzzy implicative ideal of BCK-algebras, this paper intro-duces the concept of (∈,∈∨qk)-fuzzy implicative ideals, and investigates related properties. Then, this paper points out that the fuzzy implicative ideals and (∈,∈∨q)-fuzzy implicative ideals are both (∈,∈∨qk)-fuzzy implication ideals but?not?vice?versa. Furthermore, this paper gives the condition for the fuzzy subset of BCK-algebras to be [(∈,∈∨qk)]-fuzzy implicative ideals, proves that (∈,∈∨qk)-fuzzy implicative ideals are all (∈,∈∨qk)-fuzzy ideals, and gives an example to show that this converse proposition is not true. Finally, this paper gives some equivalent characterizations of an (∈,∈∨qk)-fuzzy implicative ideal, and discusses the implication-based fuzzy implicative ideals of BCK-algebras.

Key words: BCK-algebra, fuzzy implicative ideal; (∈,∈∨qk)-fuzzy ideal; (∈,∈∨qk)-fuzzy implicative ideal, fuzzifying implicative ideal; t-implication-based fuzzy implicative ideal