Fuzzy metrics have demonstrated to be useful in engineering problems. They show a better performance comparing with their classical counterparts. So, to obtain new examples of fuzzy metrics or methods to construct them is a topic of interest. Recently in [10] two new methods to construct fuzzy pseudo-metrics from pseudo-metrics have been established. The aim of this paper is to determine the relationship between the topology induced by the fuzzy pseudo-metric constructed using these two methods and the topology induced by the pseudo-metric from which is it constructed. In this direction, we show that for one of these two methods both topologies coincide whereas for the other one, two additional conditions on the one of the functions used in the method must be required to get such a conclusion. In addition, examples which justify and illustrate our study are provided in the paper.