A Representation Theorem for L-fuzzy Pseudo-metrics

Abstract Through this article, the definitions of an L -fuzzy pseudo-metric and a family of pseudo-metric that satisfies the property of lower-semicontinuity (or named nests of pseudo-metrics) are introduced. After that, we indicated that an L -fuzzy pseudo-metric can be constructed from nests of pseudo-metrics and nests of pseudo-metrics can be constructed from an L -fuzzy pseudo-metric. Therefore, we establish a each to each association between L - fuzzy pseudo-metrics and nests of pseudo-metrics.