几个模糊集空间的性质
Properties of several fuzzy set spaces
摘要: 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 Γ-convergence, and then investigate the level characterizations?of the endograph metric and the Γ-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 α-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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[V13] |
2022-06-30 23:01:49 |
ChinaXiv:202107.00011V13
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[V1] |
2021-07-10 12:03:03 |
ChinaXiv:202107.00011v1
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