Mathematics (Aug 2021)

Commutative Ideals of BCI-Algebras Using MBJ-Neutrosophic Structures

  • Seok-Zun Song,
  • Mehmet Ali Öztürk,
  • Young-Bae Jun

DOI
https://doi.org/10.3390/math9172047
Journal volume & issue
Vol. 9, no. 17
p. 2047

Abstract

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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.

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