MBJ-neutrosophic structures and its applications in BCK/BCI-algebras

Smarandache (F. Smarandache. Neutrosophy, neutrosophic probability, set, and logic, ProQuest Information & Learning, Ann Arbor, Michigan, USA, 105 p., 1998) initiated neutrosophic sets which can be used as a mathematical tool for dealing with indeterminates and inconsistent information. As a gen...

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Published inNeutrosophic sets and systems Vol. 23; pp. 72 - 84
Main Authors Takallo, M. Mohseni, Borzooei, R.A, Jun, Young Bae
Format Journal Article
LanguageEnglish
Published Neutrosophic Sets and Systems 01.12.2018
University of New Mexico
Subjects
Algebra
Mathematical research
MBJ-neutrosophic set
MBJ-neutrosophic subalgebra
Online information services
Set theory
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Summary:Smarandache (F. Smarandache. Neutrosophy, neutrosophic probability, set, and logic, ProQuest Information & Learning, Ann Arbor, Michigan, USA, 105 p., 1998) initiated neutrosophic sets which can be used as a mathematical tool for dealing with indeterminates and inconsistent information. As a generalization of a neutrosophic set, the notion of MBJ-neutrosophic sets is introduced, and it is applied to BCK/BCI-algebras. The concept of MBJ-neutrosophic subalgebras in BCK/BCI-algebras is introduced, and related properties are investigated. A characterization of MBJ-neutrosophic subalgebra is provided. Using an MBJ-neutrosophic subalgebra of a BCI-algebra, a new MBJ-neutrosophic subalgebra is established. Homomorphic inverse image of MBJ-neutrosophic subalgebra is considered. Translation of MBJ-neutrosophic subalgebra is discussed. Conditions for an MBJ-neutrosophic set to be an MBJ-neutrosophic subalgebra are provided. Keywords: MBJ-neutrosophic set; MBJ-neutrosophic subalgebra; MBJ-neutrosophic S-extension.
ISSN:2331-6055
2331-608X
DOI:10.5281/zenodo.2155211