模糊数据的统计深度和支持中值

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

Fuzzy Sets and Systems Pub Date : 2025-01-03 DOI:10.1016/j.fss.2024.109257

Luis González-De La Fuente , Alicia Nieto-Reyes , Pedro Terán

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引用次数: 0

摘要

统计深度函数根据概率分布或数据集的中心性对空间元素排序。由于许多深度函数通过中位数在实线中最大化，因此它们为更一般类型的数据（在我们的例子中是模糊数据）提供了一种自然的方法来定义类似中位数的位置估计器。我们分析了基于深度的中位数、基于支持函数的中位数以及文献中模糊数据中位数的一些概念之间的关系。我们利用了我们在以前的论文中定义的模糊数据的特定深度函数：Tukey深度、简单深度、l1深度和投影深度的自适应。

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Statistical depth and support medians for fuzzy data

Statistical depth functions order the elements of a space with respect to their centrality in a probability distribution or dataset. Since many depth functions are maximized in the real line by the median, they provide a natural approach to defining median-like location estimators for more general types of data (in our case, fuzzy data). We analyze the relationships between depth-based medians, medians based on the support function, and some notions of a median for fuzzy data in the literature. We take advantage of specific depth functions for fuzzy data defined in our former papers: adaptations of Tukey depth, simplicial depth,

L^{1}

-depth and projection depth.

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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.