On Strong Fuzzy Partial Metric Spaces

In 2019, Gregori et al. (Int. J. Gen. Syst. 48(3):260–279, 2019), initiated the structure of fuzzy partial metric space (FPMS) based on the residuum operators. Since it is not easy to show different examples when one works with residuum operators, in recent papers, we face to lack of examples of FPMs. Motivated by this fact, in this work, we aim to generate different FPMs from partial metrics (PMs) and vice versa. For this aim, we first give the concept of strong FPMSs by investigating some properties of them and providing some examples by considering different t-norms. In continuation, we give some techniques to construct strong FPMs from existing PMs by means of the pseudo-inverse (p-inverse) of the additive generator (a-generator) of continuous Archimedean t-norms. We also show that FPMs can induce PMs via a-generators. Moreover, we study whether the topologies induced by the presented techniques coincide or not.