Fuzzy partial (pseudo-)metric spaces

This paper attempts to generalize partial (pseudo-) metric and fuzzy (pseudo-) metric to a more general framework (in this paper, we call it fuzzy (pseudo-) partial metric). Firstly, the concept of fuzzy partial (pseudo-) metric is given. Then the relationships between partial (pseudo-) metric, fuzzy (pseudo-) metric and fuzzy partial (pseudo-) metric are investigated. Finally, fuzzy partial pseudo-metric can be endowed with many-valued topological structures.