{"title":"Decision with belief functions and generalized independence: Two impossibility theorems1","authors":"Helene Fargier , Romain Guillaume","doi":"10.1016/j.ijar.2024.109283","DOIUrl":null,"url":null,"abstract":"<div><p>Dempster-Shafer theory of evidence is a framework that is expressive enough to represent both ignorance and probabilistic information. However, decision models based on belief functions proposed in the literature face limitations in a sequential context: they either abandon the principle of dynamic consistency, restrict the combination of lotteries, or relax the requirement for transitive and complete comparisons. This work formally establishes that these requirements are indeed incompatible when any form of compensation is considered. It then demonstrates that these requirements can be satisfied in non-compensatory frameworks by introducting and characterizing a dynamically consistent rule based on first-order dominance.</p></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"175 ","pages":"Article 109283"},"PeriodicalIF":3.2000,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Approximate Reasoning","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0888613X24001701","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 0
Abstract
Dempster-Shafer theory of evidence is a framework that is expressive enough to represent both ignorance and probabilistic information. However, decision models based on belief functions proposed in the literature face limitations in a sequential context: they either abandon the principle of dynamic consistency, restrict the combination of lotteries, or relax the requirement for transitive and complete comparisons. This work formally establishes that these requirements are indeed incompatible when any form of compensation is considered. It then demonstrates that these requirements can be satisfied in non-compensatory frameworks by introducting and characterizing a dynamically consistent rule based on first-order dominance.
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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