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

Abstract

Smarandache (F. Smarandache. Neutrosophy, neutrosophic probability, set, and logic, ProQuest Infor-mation & Learning, Ann Arbor,Michigan, USA, 105 p., 1998) initiated neutrosophic sets which can be used as amathematical tool for dealing with indeterminates and inconsistent information. As a generalization of a neutrosophicset, the notion of MBJ-neutrosophic sets is introduced, and it is applied toBCK/BCI-algebras. The concept ofMBJ-neutrosophic subalgebras inBCK/BCI-algebras is introduced, and related properties are investigated. A char-acterization of MBJ-neutrosophic subalgebra is provided. Using an MBJ-neutrosophic subalgebra of aBCI-algebra,a new MBJ-neutrosophic subalgebra is established. Homomorphic inverse image of MBJ-neutrosophic subalgebra isconsidered. Translation of MBJ-neutrosophic subalgebra is discussed. Conditions for an MBJ-neutrosophic set to bean MBJ-neutrosophic subalgebra are provided.