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

Authors :: Rajab Ali Borzooei
Young Bae Jun
Seok-Zun Song
M. Mohseni Takallo
Source :: AIMS Mathematics, Vol 6, Iss 10, Pp 11029-11045 (2021)
Publication Year :: 2021
Publisher :: American Institute of Mathematical Sciences (AIMS), 2021.
Abstract: 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.

Tools