On stratified single-valued soft topogenous structures

Area of Science:

• Mathematics
• Topology
• Neutrosophic Set Theory

Background:

• Existing topological spaces lack the flexibility to handle uncertainty and imprecision inherent in real-world data.
• Neutrosophic set theory offers a framework for managing vague and indeterminate information, but its integration with topological structures requires further development.

Purpose of the Study:

• To introduce and define novel concepts: stratified single-valued neutrosophic soft topogenous, stratified single-valued neutrosophic soft filter, stratified single-valued neutrosophic soft quasi uniformity, and stratified single-valued neutrosophic soft quasi proximity.
• To investigate the properties of single-valued neutrosophic soft topogenous structures formed by integrating stratified svns-topogenous and stratified svns-filter.
• To explore the relationships between these newly defined single-valued neutrosophic soft topological structures and their corresponding stratifications.

Main Methods:

• Development of theoretical frameworks for stratified single-valued neutrosophic soft structures.
• Integration of stratified single-valued neutrosophic soft topogenous and filter concepts to form new topological structures.
• Analytical investigation of the properties and interrelationships of these novel structures.

Main Results:

• Formal definitions and properties of stratified single-valued neutrosophic soft topogenous, filter, quasi uniformity, and quasi proximity spaces.
• Characterization of single-valued neutrosophic soft topogenous structures through the combination of stratified svns-topogenous and svns-filter.
• Established connections between the defined single-valued neutrosophic soft topological structures and their stratified counterparts.

Conclusions:

• The study successfully introduces and defines novel stratified single-valued neutrosophic soft topological structures.
• The research provides a theoretical foundation for understanding these advanced neutrosophic soft topological concepts and their stratifications.
• This work contributes to the growing field of neutrosophic topology, offering potential applications in areas requiring robust handling of uncertainty.