3 research outputs found
Properties of several metric spaces of fuzzy sets
This paper discusses the properties the spaces of fuzzy sets in a metric
space equipped with the endograph metric and the sendograph metric,
respectively. We first give some relations among the endograph metric, the
sendograph metric and the -convergence, and then investigate the level
characterizations of the endograph metric and the -convergence. By
using the above results, we give some relations among the endograph metric, the
sendograph metric, the supremum metric and the metric, . On
the basis of the above results, we present the characterizations of total
boundedness, relative compactness and compactness in the space of fuzzy sets
whose -cuts are compact when equipped with the endograph
metric, and in the space of compact support fuzzy sets equipped with the
sendograph metric, respectively. Furthermore, we give completions of these
metric spaces, respectively