Abstract: As a generalization of the notion of an (∈,∈∨q)-fuzzy implicative ideal of BCK-algebras, this paper intro-duces the concept of (∈,∈∨q_k)-fuzzy implicative ideals, and investigates related properties. Then, this paper points out that the fuzzy implicative ideals and (∈,∈∨q)-fuzzy implicative ideals are both (∈,∈∨q_k)-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 (∈,∈∨q_k)-fuzzy implicative ideals are all (∈,∈∨q_k)-fuzzy ideals, and gives an example to show that this converse proposition is not true. Finally, this paper gives some equivalent characterizations of an (∈,∈∨q_k)-fuzzy implicative ideal, and discusses the implication-based fuzzy implicative ideals of BCK-algebras.

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

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(∈,∈∨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[(∈,∈∨qk)]-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。

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