Fuzzy partial metric spaces

In this paper we provide a concept of fuzzy partial metric space 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 , a topology on X deduced from P is constructed, and it is showed that is a -space.