Subjects: Mathematics >> Mathematics （General） submitted time 2022-06-30
Abstract：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 fist 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 dp* metric. On the basis of the above results,?we present the characterizations of total boundedness, relative compactness?and compactness in the space of compact positive -cuts fuzzy sets 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.
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Subjects: Mathematics >> Mathematics （General） submitted time 2022-06-20
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Peer Review Status:Awaiting Review
Subjects: Mathematics >> Mathematics （General） submitted time 2022-04-30
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Peer Review Status:Awaiting Review
Subjects: Mathematics >> Mathematics （General） submitted time 2021-08-10
Abstract： "
Peer Review Status:Awaiting Review
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