Affiliations: [a]
Department of Mathematics, University of Tabuk, Tabuk, Saudi Arabia
| [b]
Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul, Korea
| [c]
Department of Mathematics, Jeju National University, Jeju, Korea
| [d]
Department of Mathematics Education, Gyeongsang National University, Jinju, Korea
Correspondence:
[*]
Corresponding author. Hee Sik Kim, Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Korea. Tel.: +82 2 2290 0897; Fax: +82 2 2281 0019; E-mail: heekim@hanyang.ac.kr.
Abstract: The notions of hesitant fuzzy translations and hesitant fuzzy extensions of a hesitant fuzzy set on BCK/BCI-algebras are introduced, and related properties are investigated. We prove that every hesitant fuzzy translation of a hesitant fuzzy subalgebra (ideal) is a hesitant fuzzy subalgebra (ideal). Conditions for a hesitant fuzzy set to be a hesitant fuzzy subalgebra (ideal) are provided. We show that if a hesitant fuzzy set is a hesitant fuzzy subalgebra (ideal), then its support is a subalgebra (ideal), and also prove that if the support of a hesitant fuzzy set is a subalgebra (ideal), then its hesitant fuzzy translation is a hesitant fuzzy subalgebra (ideal).
