Interpretation of Neutrosophic Soft cubic T-ideal in the Environment of PS-Algebra

Abstract

This study provides an innovative approach to neutrosophic algebraic structures by introducing a
new structure called Neutrosophic Soft Cubic T-ideal (NSCTID), which combines T-ideal (TID) and Neutrosophic Soft Cubic Sets (NSCSs) within the framework of PS-Algebra. Within the already-existing neutrosophic
cubic structures, the addition of soft sets with the characteristics of TID makes this structure more desirable.
The theoretical development of the proposed structure includes the application of fundamental ideas as union,
intersection, the Cartesian product, and homomorphism. We also introduce the notions of NSCTID-translation
and NSCTID-multiplication to further enhance the structure of NSCTID. By applying the idea of translation
and multiplication, we offer improved algorithm for neutrosophic cubic sets to deal with different parameters
that are satisying the TID’s distinctive characteristics. Through this thorough research, we offer an elementary
understanding of NSCTID and its capabilities, providing the way to new algebraic structures