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Properties of several fuzzy set spaces

Submit Time: 2021-11-27
Author: Huan Huang 1 ;
Institute: 1.Jimei University;


This paper discusses the properties the spaces of fuzzy sets in a metric s- pace equipped with the endograph metric and the sendograph metric, re- spectively. We fist discuss the level characterizations of the Γ-convergence and the endograph metric, and point out the elementary relationships among Γ-convergence, endograph metric and the sendograph metric. On the basis of these results, we present the characterizations of total boundedness, rel- ative compactness and compactness in the space of compact positive α-cuts fuzzy sets equipped with the endograph metric, and in the space of com- pact support fuzzy sets equipped with the sendograph metric, respectively. Furthermore, we give completions of these two kinds of spaces, respectively.
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From: Huan Huang
Recommended references: Huan Huang.(2021).Properties of several fuzzy set spaces.[ChinaXiv:202107.00011] (Click&Copy)
Version History
[V5] 2021-11-27 23:25:48 chinaXiv:202107.00011V5 Download
[V4] 2021-11-01 22:40:35 chinaXiv:202107.00011v4(View This Version) Download
[V3] 2021-08-01 19:20:48 chinaXiv:202107.00011v3(View This Version) Download
[V2] 2021-07-22 22:58:13 chinaXiv:202107.00011v2(View This Version) Download
[V1] 2021-07-10 12:03:03 chinaXiv:202107.00011v1(View This Version) Download
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