反复期望和不精确概率的法则

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.2024.109258

Enrique Miranda , Arthur Van Camp

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引用次数: 0

摘要

迭代期望定律告诉我们，当我们的不确定性是通过概率度量来建模时，如何组合层次信息。并通过Walley的相干下预见的边际推广定理，将其推广到不精确情况。在本文中，我们研究了在何种程度上可以为其他不精确的概率模型建立类似的结果，这些模型要么更一般（选择函数），要么更特殊（可能性测度，信念函数），而不是连贯的低预测。通过这样做，我们还在杰弗里规则的不精确版本的背景下，与文献中建立的其他结果建立了联系。

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The law of iterated expectation and imprecise probabilities

The law of iterated expectation tells us how to combine hierarchical pieces of information when our uncertainty is modelled by means of probability measures. It has been extended to the imprecise case through Walley's marginal extension theorem for coherent lower previsions. In this paper, we investigate the extent to which a similar result can be established for other imprecise probability models that are either more general (choice functions) or more particular (possibility measures, belief functions) than coherent lower previsions. By doing this, we also establish links with other results established in the literature in the context of imprecise versions of Jeffrey's rule.

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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.