A new approach to soft set through applications of cubic set

TL;DR

This paper introduces new concepts of cubic soft sets and explores their properties and operations, providing conditions under which these sets maintain their internal or external nature, advancing the mathematical framework of soft set theory.

Contribution

It presents novel definitions and properties of cubic soft sets, including union and intersection operations, and establishes conditions for their internal or external classifications.

Findings

P-union and P-intersection of internal cubic soft sets are also internal.

Conditions for external cubic soft sets to become internal or external after operations.

Analysis of when cubic soft set operations preserve their classification.

Abstract

The notions of (internal, external) cubic soft sets, P-(R-)order,P-(R-)union, P-(R-)intersection and P-OR, R-OR, P-AND and R-AND are introduced, and related properties are investigated. We show that the P-union and the P-intersection of internal cubic soft sets are also internal cubic soft sets. We provide conditions for the P-union (resp. P-intersection) of two external cubic soft sets to be an internal cubic soft set. We give conditions for the P-union (resp. R-union and R-intersection) of two external cubic soft sets to be an external cubic soft set. We consider conditions for the R-intersection (resp.P-intersection) of two cubic sof sets to be both an external cubic soft set and an internal cubic soft set.