Secure and perfect maximality

IF 2.2 4区心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematical Psychology Pub Date : 2025-05-01 DOI:10.1016/j.jmp.2025.102922

Federico Quartieri

引用次数: 0

Abstract

The paper introduces a refinement of maximality, called secure maximality, and a refinement of secure maximality, called perfect maximality. The effectivity of these refinements and the connection with other relevant optimality notions are investigated. Furthermore, necessary and sufficient conditions are provided for the secure maximality of all maximals and for the perfect maximality of all maximals as well as for the perfect maximality of all secure maximals. Several sufficient conditions for (as well as two characterizations of) the existence of secure and perfect maximals are established. The precise structure of the entire sets of secure and perfect maximals is examined for some specific classes of relations like interval orders that admit a certain type of representability by means of two real-valued functions, relations induced by cones and relations that admit linear multi-utility representations.

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安全和完美的极大化

本文介绍了极大性的一种改进，称为安全极大性，以及安全极大性的一种改进，称为完美极大性。研究了这些改进的有效性以及与其他相关最优性概念的联系。进一步给出了所有极大值的安全极大值、所有极大值的完美极大值以及所有安全极大值的完美极大值的充分必要条件。建立了安全极大值和完美极大值存在的几个充分条件（以及两个刻画）。对于某些特定类型的关系，如通过两个实值函数承认某种类型的可表征性的区间阶、由锥诱导的关系和承认线性多效用表示的关系，研究了整个安全和完美极大值集的精确结构。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Mathematical Psychology 医学-数学跨学科应用

CiteScore

3.70

自引率

11.10%

发文量

审稿时长

20.2 weeks

期刊介绍： The Journal of Mathematical Psychology includes articles, monographs and reviews, notes and commentaries, and book reviews in all areas of mathematical psychology. Empirical and theoretical contributions are equally welcome. Areas of special interest include, but are not limited to, fundamental measurement and psychological process models, such as those based upon neural network or information processing concepts. A partial listing of substantive areas covered include sensation and perception, psychophysics, learning and memory, problem solving, judgment and decision-making, and motivation. The Journal of Mathematical Psychology is affiliated with the Society for Mathematical Psychology. Research Areas include: • Models for sensation and perception, learning, memory and thinking • Fundamental measurement and scaling • Decision making • Neural modeling and networks • Psychophysics and signal detection • Neuropsychological theories • Psycholinguistics • Motivational dynamics • Animal behavior • Psychometric theory