Properties of fuzzy set spaces with L_p metrics

2022/09/23 by Huang, Huan
#FOS: Mathematics #General Mathematics (math.GM)

paper · doi:10.48550/arxiv.2209.12978

Abstract

This paper discusses the properties of the spaces of fuzzy sets in a metric space with L_p-type d_p metrics, p≥ 1. The d_p metrics are well-defined if and only if the corresponding Haudorff distance functions are measurable. In this paper, we give some fundamental conclusions on the measurability of these Haudorff distance functions. Then we give the characterizations of compactness in fuzzy set space with d_p metrics. At last we present the completions of fuzzy set spaces with d_p metrics.

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