Introduction to Soft Metric Preserving Functions

In this study, we aim to present the notion of soft metric preserving functions (SMPFs) which allows us to transform a soft metric into another one. We study some properties of SMPFs and investigate some characterizations to decide whether a soft function is soft metric preserving or not. Then, we show that the soft topology induced by soft metric was not preserved under SMPFs, present the stronger concept for these functions and also research the relationships of this concept with continuity.