arXivDaily arXiv每日学术速递 周一至周五更新
北美退伍军人节(Veterans Day),12 日无更新
arXiv cs/0310044cs.AI
收藏

效用推理的代数

The Algebra of Utility Inference

Ali E. Abbas

摘要:

理查德·考克斯[1]建立了概率推理和命题代数的公理基础。他表明,这些公理的一致性需要某些规则来更新信念。在本文中,我们使用[2]中引入的概率和效用之间的类比,为效用推理和偏好代数提供了一个公理化基础。我们表明,这些公理的一致性需要一定的规则更新偏好。我们讨论了一类效用函数,源于公理的效用推理,并表明这一类是任何一般的多属性效用函数的基本组成部分。我们使用这类效用函数与偏好代数一起构造由属性上的逻辑运算表示的效用函数。

英文摘要:

Richard Cox [1] set the axiomatic foundations of probable inference and the algebra of propositions. He showed that consistency within these axioms requires certain rules for updating belief. In this paper we use the analogy between probability and utility introduced in [2] to propose an axiomatic foundation for utility inference and the algebra of preferences. We show that consistency within these axioms requires certain rules for updating preference. We discuss a class of utility functions that stems from the axioms of utility inference and show that this class is the basic building block for any general multiattribute utility function. We use this class of utility functions together with the algebra of preferences to construct utility functions represented by logical operations on the attributes.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑