BCK-代数的广义(∈,∈∨q)-模糊蕴涵理想  

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

作　　者：彭家寅[1] PENG Jiayin(College of Mathematics and Information Sciences,Neijiang Normal University,Neijiang,Sichuan 641199,China)

机构地区：[1]内江师范学院数学与信息科学学院,四川内江641199

出　　处：《计算机科学与探索》2018年第4期662-670,共9页Journal of Frontiers of Computer Science and Technology

基　　金：国家自然科学基金No.11071178;教育部数学与应用数学专业综合改革项目 No.ZG0464~~

摘　　要：为推广BCK-代数的(∈,∈∨q)-模糊蕴涵理想,引入了(∈,∈∨q_k)-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(∈,∈∨q_k)-模糊蕴涵理想,反之不然;给出了BCK-代数的模糊子集成为(∈,∈∨q_k)-模糊蕴涵理想的条件;证明了(∈,∈∨q_k)-模糊蕴涵理想都是(∈,∈∨q_k)-模糊理想,用实例说明其逆命题不真;给出了(∈,∈∨q_k)-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。As a generalization of the notion of an(∈,∈∨q)-fuzzy implicative ideal of BCK-algebras,this paper introduces 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.

关 键 词：BCK-代数 模糊蕴涵理想 (∈ ∈∨qk)-模糊理想 (∈ ∈∨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 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程] O141[自动化与计算机技术—控制科学与工程]