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.
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Yue et al. (2014) studied this question.
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