The Relationship Between Fuzzy Soft and Soft Topologies

This paper attempts to forward both soft topology and fuzzy soft topology with a pioneering analysis of their mutual relationships. With each soft topology we associate a parameterized family of fuzzy soft topologies called its t-pushes. And each fuzzy soft topology defines a parameterized family of soft topologies called its t-throwbacks. Different soft topologies produce different t-pushes. But we prove by example that not all fuzzy soft topologies are characterized by their t-throwbacks. The import of these constructions is that some properties stated in one setting can be investigated in the other setting. Our conclusions should fuel future research on both fuzzy soft topology and soft topology.

Automated summary

This paper aims to develop both soft topology and fuzzy soft topology by analyzing their mutual relationships. The construction and conclusions introduced in this paper provide new approaches for studying and applying these concepts in different settings.