Multivariate capacity functionals vs. capacity functionals on product spaces

Schmelzer Bernhard

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Multivariate capacity functionals vs. capacity functionals on product spaces

机译：产品空间上的多元容量功能与容量功能

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The aim of this paper is to study the relation between multivariate capacity functionals and capacity functionals on product spaces (also called joint capacity functionals). Multivariate capacity functionals characterize the joint distribution of finitely many random sets whereas joint capacity functionals characterize the distribution of a random set in a product space and as such provide an upper bound on a set of (joint) probability measures. It is demonstrated how to define a multivariate capacity functional from a given joint capacity functional, and how to extend a multivariate capacity functional to a joint capacity functional. In addition, it is shown how to construct a joint capacity functional from marginal maxitive capacity functionals when a copula is used for modelling stochastic dependence. (C) 2018 Elsevier B.V. All rights reserved.

机译：本文的目的是研究产品空间上的多元容量功能和容量功能之间的关系（也称为联合容量功能）。多元容量功能描述了有限个随机集的联合分布，而联合容量功能描述了产品空间中随机集的分布，因此提供了一组（联合）概率测度的上限。演示了如何从给定的联合能力函数定义多元能力函数，以及如何将多元能力函数扩展为联合能力函数。此外，还显示了当使用copula建模随机依赖关系时，如何从边际最大容量函数构造联合容量函数。（C）2018 Elsevier B.V.保留所有权利。

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来源
《Fuzzy sets and systems》 |2019年第1期|1-35|共35页
作者
Schmelzer Bernhard;
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作者单位

Winklweg 6, A-6300 Woergl, Austria;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Capacity functional; Belief function; Random set; Copula; Possibility measure;

机译：能力功能;信念功能;随机集;Copula;可能性测度;

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Multivariate capacity functionals vs. capacity functionals on product spaces

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