Implicative ideals of BCK-algebras based on MBJ-neutrosophic sets

• Main Authors: M. Mohseni Takallo, Rajab Ali Borzooei, Seok-Zun Song, Young Bae Jun
• Format: Article
• Language: English
• Published: AIMS Press 2021-07-01
• Series: AIMS Mathematics
• Subjects: mbj-neutrosophic set; mbj-neutrosophic ideal; commutative mbj-neutrosophic ideal; implicative mbj-neutrosophic ideal; positive implicative mbj-neutrosophic ideal; mbj-neutrosophic subalgebra
• Online Access: https://www.aimspress.com/article/doi/10.3934/math.2021640?viewType=HTML
• ISSN: 2473-6988

The MBJ-neutrosophic set is applied to the implicative ideal of BCK-algebra to introduce the concept of implicative MBJ-neutrosophic ideal. Several properties are investigated. The relationship between implicative MBJ-neutrosophic ideal and each MBJ-neutrosophic subalgebra, (positive implicative, commutative) MBJ-neutrosophic ideal is established. Conditions for MBJ-neutrosophic subalgebra (resp., MBJ-neutrosophic ideal, positive implicative MBJ-neutrosophic ideal and commutative MBJ-neutrosophic ideal) to be implicative MBJ-neutrosophic ideal are provided. Characterizations of implicative MBJ-neutrosophic ideal are discussed.