A new type of hesitant fuzzy subalgebras and ideals in BCK/BCI-algebras

Article type: Research Article

Authors: Song, Seok-Zun^{a; *} | Bordbar, Hashem^b | Jun, Young Bae^c

Affiliations: [a] Department of Mathematics, Jeju National University, Jeju, Republic of Korea | [b] Faculty of Mathematics, Statistics and Computer Science Shahid Bahonar University, Kerman, Iran | [c] Department of Mathematics Education, Gyeongsang National University, Jinju, Republic of Korea

Correspondence: [*] Corresponding author. Seok-Zun Song, Department of Mathematics, Jeju National University, Jeju 63243, Republic of Korea. Tel.: +82 64 754 3562; Fax: +82 64 725 2573; E-mail: szsong@jejunu.ac.kr.

Abstract: The concept of hesitant union (⋓) is introduced. Using this, the notions of ⋓-hesitant fuzzy subalgebras and ⋓-hesitant fuzzy ideals are introduced and several properties are investigated. Relations between ∪-hesitant fuzzy subalgebras (resp. ideals) and ⋓-hesitant fuzzy subalgebras (resp. ideals) are considered. Relations between a ⋓-hesitant fuzzy subalgebra/ideal and its lower level set are investigated. Characterizations of ∪-hesitant fuzzy subalgebras/ideals are discussed. Given a subalgebra (resp., ideal) A of a BCK/BCI-algebra X, a ⋓-hesitant fuzzy subalgebra (resp., ideal) is established.

Keywords: Hesitant union, ∪-hesitant fuzzy subalgebra, ∪-hesitant fuzzy ideal, ⋓-hesitant fuzzy subalgebra, ⋓-hesitant fuzzy ideal, lower hesitant level set

DOI: 10.3233/JIFS-161601

Journal: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 2009-2016, 2017