Bhatia-Davis 下部和上部前值及协方差不等式

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

Fuzzy Sets and Systems Pub Date : 2024-10-18 DOI:10.1016/j.fss.2024.109145

Renato Pelessoni, Paolo Vicig

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引用次数: 0

摘要

我们探讨了经典的巴蒂亚-戴维斯（Bhatia-Davis）不等式如何通过不同一致性程度的不精确（下限或上限）预设，扩展到赌局（有界随机数）的不确定性评估。首先，利用 2 一致性不精确预设找到了一些扩展。随后，研究了一致的下部和上部预设的边界，以及下部和上部方差和 p 方框的应用边界。最后，我们得到了协方差以及下协方差和上协方差的边界。与经典情况一样，不精确的巴蒂亚-戴维斯不等式需要更少的不确定性信息才能应用。当可用信息更少时，我们证明可以得到各种版本的波波维奇不等式。

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Bhatia-Davis inequalities for lower and upper previsions and covariances

We explore how the classical Bhatia-Davis inequality bounding variances can be extended to uncertainty evaluations of gambles (bounded random numbers) by means of imprecise (lower or upper) previsions with different degrees of consistency. Firstly, a number of extensions are found with 2-coherent imprecise previsions. Subsequently, bounds with coherent lower and upper previsions are investigated, together with applications bounding lower and upper variances as well as p-boxes. Finally, bounds for covariances and for lower and upper covariances are obtained. Like the classical situation, imprecise Bhatia-Davis inequalities require a reduced amount of uncertainty information to be applied. When even less information is available, we show that various versions of Popoviciu's inequality obtain.

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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.