The Hausdorff fuzzy quasi-metric
Removing the condition of symmetry in the notion of a fuzzy (pseudo-)metric in Kramosil and Michalek's sense, one has the notion of a fuzzy quasi-(pseudo-)metric. Then for each fuzzy quasi-pseudo-metric on a set \(X\), a fuzzy quasi-pseudo-metric is constructed on the collection of all nonempty subsets of \(X\), called the Hausdorff fuzzy quasi-pseudo-metric. Some properties of this structure are investigated. In fact, a KM fuzzy metric is exactly a \((2, I)\)-fuzzy metric which can be found in the reviewer's paper \textit{F.-G. Shi} [Indian J. Math. 52, No.~2, 231--250 (2010; Zbl 1204.54007)].
scientific article; zbMATH DE number 5706283
scientific article