Properties of several fuzzy set spaces

Subjects: Mathematics >> Mathematics （General） submitted time 2022-06-30

Huan Huang

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.

Peer Review Status:Awaiting Review

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