Interval complex neutrosophic soft sets (I-CNSSs) are interval neutrosophic soft sets (I-NSSs) described by three two-dimensional independent membership functions which are uncertainty interval, indeterminacy interval, and falsity interval respectively. Relation is a tool that helps in describing consistency and agreement between objects. Throughout this paper, we insert and discuss the interval complex neutrosophic soft relation (simply denoted by I-CNSR) that is a novel soft computing technique used to examine the degree of interaction between two corresponding models called I-CNSSs. We present the definition of the Cartesian product of I-CNSSs followed by the definition of I-CNSR. Further, the definitions and some theorems and properties related to the composition, inverse, and complement of I-CNSR are provided. The notions of symmetric, reflexive, transitive, and equivalent of I-CNSRs are proposed and the algebraic properties of these concepts are verified. Additionally, we point the contribution of our concept to real life problems by presenting a proposed algorithm to solve a real-life decision-making problem. Finally, a comparison between the proposed model and the existing relations is conducted to clarify the importance of this model.

## Why is it important?

Interval complex neutrosophic soft sets (I-CNSSs) are interval neutrosophic soft sets (I-NSSs) described by three two-dimensional independent membership functions which are uncertainty interval, indeterminacy interval, and falsity interval respectively. Relation is a tool that helps in describing consistency and agreement between objects. Throughout this paper, we insert and discuss the interval complex neutrosophic soft relation (simply denoted by I-CNSR) that is a novel soft computing technique used to examine the degree of interaction between two corresponding models called I-CNSSs. We present the definition of the Cartesian product of I-CNSSs followed by the definition of I-CNSR. Further, the definitions and some theorems and properties related to the composition, inverse, and complement of I-CNSR are provided. The notions of symmetric, reflexive, transitive, and equivalent of I-CNSRs are proposed and the algebraic properties of these concepts are verified. Additionally, we point the contribution of our concept to real life problems by presenting a proposed algorithm to solve a real-life decision-making problem. Finally, a comparison between the proposed model and the existing relations is conducted to clarify the importance of this model.