Abstract: It applies the concept of interval valued fuzzy sets which is introduced by Zadeh to BCK algebras, introduces the notion of interval valued (∈,∈∨q) fuzzy sub-algebras of BCK algebras and discusses their properties. The sufficient and necessary condition for interval valued fuzzy set to an interval valued (∈,∈∨q) fuzzy sub-algebras is given. The relations between interval valued (∈,∈∨q) fuzzy sub-algebras and sub-algebras, (∈,∈∨q) fuzzy sub-algebras of BCK algebras are discussed. The images and inverse images of interval valued fuzzy sets are defined, and the conditions for the images and inverse images of interval valued (∈,∈∨q) fuzzy sub-algebras to be interval valued (∈,∈∨q) fuzzy sub-algebras are obtained.

Key words: BCK-algebras, sub-algebras, interval valued fuzzy sets, interval valued (∈, ∈∨q) fuzzy sub-algebras

摘要： 将Zadeh提出的区间值模糊集的概念应用于BCK代数，提出BCK代数的区间值(∈,∈∨q)模糊子代数的概念并研究其性质。给出了区间值模糊集成为区间值(∈,∈∨q)模糊子代数的充要条件；讨论了区间值(∈,∈∨q)模糊子代数与子代数以及(∈,∈∨q)模糊子代数间的关系；定义了区间值模糊集的象与原象，获得了区间值(∈,∈∨q)模糊子代数的象与原象成为区间值(∈,∈∨q)模糊子代数的条件。

关键词: BCK代数, 子代数, 区间值模糊集, 区间值(∈, ∈∨q)-模糊子代数