Commutative Ideals of BCI-Algebras Using MBJ-Neutrosophic Structures

Seok-Zun Song, Mehmet Ali Öztürk and Young-Bae Jun
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Seok-Zun Song: Department of Mathematics, Jeju National University, Jeju 63243, Korea
Mehmet Ali Öztürk: Department of Mathematics, Faculty of Arts and Sciences, Adıyaman University, Adıyaman 02040, Turkey
Young-Bae Jun: Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea

Mathematics, 2021, vol. 9, issue 17, 1-13

Abstract: As a generalization of a neutrosophic set, the notion of MBJ-neutrosophic sets is introduced by Mohseni Takallo, Borzooei and Jun, and it is applied to BCK/BCI-algebras. In this article, MBJ-neutrosophic set is used to study commutative ideal in BCI-algebras. The concept of closed MBJ-neutrosophic ideal and commutative MBJ-neutrosophic ideal is introduced and their properties and relationships are studied. The conditions for an MBJ-neutrosophic ideal to be a commutative MBJ-neutrosophic ideal are given. The conditions for an MBJ-neutrosophic ideal to be a closed MBJ-neutrosophic ideal are provided. Characterization of a commutative MBJ-neutrosophic ideal is established. Finally, the extension property for a commutative MBJ-neutrosophic ideal is founded.

Keywords: MBJ-neutrosophic set; MBJ-neutrosophic subalgebra; MBJ-neutrosophic ideal; commutative MBJ-neutrosophic ideal (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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