A special fuzzy star-shaped number space with the sendograph metric

IF 3.2 1区 数学 Q2 COMPUTER SCIENCE, THEORY & METHODS Fuzzy Sets and Systems Pub Date : 2024-03-24 DOI:10.1016/j.fss.2024.108950
Wenjuan Liu , Dongming Liu
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引用次数: 0

Abstract

As a natural generalization of fuzzy numbers, fuzzy star-shaped numbers play a crucial role in fuzzy mathematics. Let Y be a non-degenerate compact convex subset of the n-dimensional Euclidean space, and let FSz0(Y) be the family consisting of all fuzzy star-shaped numbers with respect to z0 whose supports contained in Y. Using methods from infinite-dimensional topology, we mainly show that the space FSz0(Y) with the topology induced by the sendograph metric is homeomorphic to the separable Hilbert space 2.

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具有发送图度量的特殊模糊星形数空间
作为模糊数的自然概化,模糊星形数在模糊数学中起着至关重要的作用。让 Y 是 n 维欧几里得空间的非退化紧凑凸子集,让 FSz0(Y) 是所有支点包含在 Y 中的关于 z0 的模糊星形数所组成的族。利用无穷维拓扑学的方法,我们主要证明了具有发送图度量所诱导的拓扑的空间 FSz0(Y) 与可分离的希尔伯特空间 ℓ2 是同构的。
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来源期刊
Fuzzy Sets and Systems
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.
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