具有Lp度量的模糊集合空间的性质

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems Pub Date : 2024-12-31 DOI:10.1016/j.fss.2024.109256

Huan Huang

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引用次数: 0

摘要

讨论了p≥1的lp型dp度量空间中模糊集空间的性质。当且仅当相应的豪多夫距离函数是可测量的，dp度量是定义良好的。本文给出了关于这些豪多夫距离函数的可测性的几个基本结论。然后给出了模糊集合空间中具有dp度量的全有界性、相对紧性和紧性的一些刻画。最后给出了具有dp度量的模糊集空间的补全。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Properties of fuzzy set spaces with Lp metrics

This paper discusses the properties of the spaces of fuzzy sets in a metric space with

L_{p}

-type

d_{p}

metrics,

p \geq 1

. The

d_{p}

metrics are well-defined if and only if the corresponding Haudorff distance functions are measurable. In this paper, we give several fundamental conclusions on the measurability of these Haudorff distance functions. Then we give some characterizations of total boundedness, relative compactness and compactness in fuzzy set spaces with

d_{p}

metrics. At last we present the completions of fuzzy set spaces with

d_{p}

metrics.

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来源期刊

Fuzzy Sets and Systems 数学-计算机：理论方法

CiteScore

6.50

自引率

17.90%

发文量

321

审稿时长

6.1 months

期刊介绍： Since its launching in 1978, the journal Fuzzy Sets and Systems has been devoted to the international advancement of the theory and application of fuzzy sets and systems. The theory of fuzzy sets now encompasses a well organized corpus of basic notions including (and not restricted to) aggregation operations, a generalized theory of relations, specific measures of information content, a calculus of fuzzy numbers. Fuzzy sets are also the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling: fuzzy rule-based systems. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies. In mathematics fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. Fuzzy sets are also part of a recent trend in the study of generalized measures and integrals, and are combined with statistical methods. Furthermore, fuzzy sets have strong logical underpinnings in the tradition of many-valued logics.