Fuzzifying pseudo-quasi-metric topologies on the fuzzy real line

Abstract

In this paper, three natural fuzzifying topologies are presented on the fuzzy real line. Then the notion of fuzzifying pseudo-quasi-metrics is introduced. It is proved that the three fuzzifying topologies can be induced respectively by three fuzzifying pseudo-quasi-metrics. Our definition of fuzzifying pseudo-metric is slightly different from that of KM-fuzzy metric. A fuzzifying pseudo-metrics can be regarded as a weak form of a KM fuzzy metric.

Keywords

• fuzzy real line
• fuzzifying topology
• fuzzifying pseudo-quasi-metric
• fuzzy pseudo-metric

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