1 research outputs found
Some properties of Skorokhod metric on fuzzy sets
In this paper, we have our discussions on normal and upper semi-continuous
fuzzy sets on metric spaces. The Skorokhod-type metric is stronger than the
Skorokhod metric. It is found that the Skorokhod metric and the Skorokhod-type
metric are equivalent on compact fuzzy sets. However, the Skorokhod metric and
the Skorokhod-type metric need not be equivalent on -integrable fuzzy
sets. Based on this, we investigate relations between these two metrics and the
-type metric. It is found that the relations can be divided into
three cases. On compact fuzzy sets, the Skorokhod metric is stronger than the
metric. On -integrable fuzzy sets, which take compact fuzzy sets as
special cases, the Skorokhod metric is not necessarily stronger than the
metric, but the Skorokhod-type metric is still stronger than the metric.
On general fuzzy sets, even the Skorokhod-type metric is not necessarily
stronger than the metric. We also show that the Skorokhod metric is
stronger than the sendograph metric