on partial fuzzy metric-preserving functions

The target of this paper is to present partial fuzzy metric-preserving functions and characterize the functions $f:[0,1]to[0,1]$ with this aspect. we give a characterization for partial fuzzy  metric-preserving functions considering the different t-norms. also, we show that the topology induced by partial fuzzy metric does not preserve under these functions with  an example. then we  give a characterization of those partial fuzzy metric-preserving functions which preserve completeness and contractivity under some conditions. finally, we discussed the relation between fuzzy  metric preserving and partial fuzzy preserving functions.