Ordered subalgebras of ordered BCI-algebras based on the MBJ-neutrosophic structure

Abstract

The neutrosophic set consists of three fuzzy sets called true membership function, false membership function and indeterminate membership function. MBJ-neutrosophic structure is a structure constructed using interval-valued fuzzy set instead of indeterminate membership function in the neutrosophic set. In general, the indeterminate part appears in a wide range. So instead of treating the indeterminate part as a single value, it is treated as an interval value, allowing a much more comprehensive processing. In an attempt to apply the MBJ-neutrosophic structure to ordered BCI-algebras, the notion of MBJ-neutrosophic (ordered) subalgebras is introduced and their properties are studied. The relationship between MBJ-neutrosophic subalgebra and MBJ-neutrosophic ordered subalgebra is established, and MBJ-neutrosophic ordered subalgebra is formed using (intuitionistic) fuzzy ordered subalgebra. Given an MBJ-neutrosophic set, its (q,˜c, p)-translative MBJ-neutrosophic set is introduced and its characterization is considered. An MBJ-neutrosophic ordered subalgebra is created using (q,˜c, p)-translative MBJ-neutrosophic set.