Abstract.

Using the concepts of soft set, bipolar fuzzy set, and interval-valued fuzzy set, hybrid structure, called ”Dokdo structure”, is introduced, and it applies to BCK/BCI-algebras. The concepts of (null, full) Dokdo structure, (positive, negative) internel Dokdo structure, (positive, negative) externel Dokdo structure are introduced, and appropriate examples are given. The notions of (closed) Dokdo subalgebra and Dokdo ideal are introduced, and their properties are investigated. Conditions for Dokdo subalgebra to be closed are considered, and conditions for Dokdo structure to be Dokdo subalgebra are provided. Relationship between Dokdo subalgebra and Dokdo ideal is discussed, and conditions for Dokdo structure to be Dokdo ideal in BCK-Dokdo universe are provided. The conditions under which Dokdo ideal can be Dokdo subalgebra in BCI-Dokdo universe are explored.

Keywords:

Dokdo structure, (positive, negative) internel Dokdo structure, (positive, negative) externel Dokdo structure, Dokdo subalgebra, Dokdo ideal.