Fuzzy partial metric spaces

In this paper we provide a concept of fuzzy partial metric space (X,P,∗) as an extension to fuzzy setting in the sense of Kramosil and Michalek, of the concept of partial metric due to Matthews. This extension has been defined using the residuum operator →∗ associated to a continuous t-norm ∗ and without any extra condition on ∗. Similarly, it is defined the stronger concept of GV -fuzzy partial metric (fuzzy partial metric in the sense of George and Veeramani). After defining a concept of open ball in (X,P,∗), a topology TP on X deduced from P is constructed, and it is showed that (X,TP) is a T0-space.