BCK-代数的广义(∈,∈∨q)-模糊蕴涵理想

摘要

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 implic-ation 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 ide-als,and gives an example to show that this converse proposition is not true.Finally,this paper gives some equiva-lent characterizations of an (∈,∈∨qk)-fuzzy implicative ideal, and discusses the implication-based fuzzy implic-ative ideals of BCK-algebras.%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.