Modeling and updating uncertain evidence within belief function theory

IF 3.2 3区 计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
Pierre Pomeret-Coquot
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引用次数: 0

Abstract

We propose a framework that enhances the expressiveness of the evidential and credal interpretations of Belief Function Theory while remaining within its scope. It allows uncertain evidence to be represented “as is” by associating meaningful intervals of N or R to focal elements, providing an intrinsic justification for belief values. This improves the modeling and manipulation of knowledge. From a credal perspective, the framework enables the accurate representation of non-maximal credal sets, when their extrema are belief and plausibility functions.
We introduce three update operations that extend Dempster's, geometric, and Bayesian conditioning to uncertain evidence. These updates are expressed in terms of transfer of evidence, ensuring linear complexity relative to the number of focal elements. This approach provides clear evidential semantics to Bayesian conditioning, resolves several of its anomalies by making it tractable and commutative, and explains its apparent dilation effect. Most importantly, it accurately yields the updated credal set, rather than merely providing its bounds.
信念函数理论中不确定证据的建模与更新
我们提出了一个框架,增强了信念函数理论的证据和可信解释的表现力,同时保持在其范围内。它允许通过将N或R的有意义区间与焦点元素相关联来“按原样”表示不确定的证据,为信念值提供了内在的理由。这改进了知识的建模和操作。从可信度的角度来看,该框架能够准确地表示非极大可信度集,当它们的极值是信念和似然函数时。我们介绍了三种更新操作,将登普斯特条件反射、几何条件反射和贝叶斯条件反射扩展到不确定证据。这些更新以证据转移的方式表示,确保了相对于焦点元素数量的线性复杂性。该方法为贝叶斯条件反射提供了清晰的证据语义,解决了贝叶斯条件反射的一些异常现象,使其易于处理和交换,并解释了贝叶斯条件反射的明显扩张效应。最重要的是,它准确地生成更新的凭证集,而不仅仅是提供其边界。
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来源期刊
International Journal of Approximate Reasoning
International Journal of Approximate Reasoning 工程技术-计算机:人工智能
CiteScore
6.90
自引率
12.80%
发文量
170
审稿时长
67 days
期刊介绍: The International Journal of Approximate Reasoning is intended to serve as a forum for the treatment of imprecision and uncertainty in Artificial and Computational Intelligence, covering both the foundations of uncertainty theories, and the design of intelligent systems for scientific and engineering applications. It publishes high-quality research papers describing theoretical developments or innovative applications, as well as review articles on topics of general interest. Relevant topics include, but are not limited to, probabilistic reasoning and Bayesian networks, imprecise probabilities, random sets, belief functions (Dempster-Shafer theory), possibility theory, fuzzy sets, rough sets, decision theory, non-additive measures and integrals, qualitative reasoning about uncertainty, comparative probability orderings, game-theoretic probability, default reasoning, nonstandard logics, argumentation systems, inconsistency tolerant reasoning, elicitation techniques, philosophical foundations and psychological models of uncertain reasoning. Domains of application for uncertain reasoning systems include risk analysis and assessment, information retrieval and database design, information fusion, machine learning, data and web mining, computer vision, image and signal processing, intelligent data analysis, statistics, multi-agent systems, etc.
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