A BASIC SET OF CANCELLATION VIOLATING SEQUENCES FOR FINITE TWO-DIMENSIONAL NON-ADDITIVE MEASUREMENT

被引：0

作者：

Ng, Che Tat ^{[1
]}

机构：

[1] Univ Waterloo, Dept Pure Math, Waterloo, ON N2L3G1, Canada

来源：

ANNALES MATHEMATICAE SILESIANAE | 2024年 / 38卷 / 01期

关键词：

Preference order; Cartesian product structure; additive measurement; cancellation conditions;

D O I：

10.2478/amsil-2023-0023

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Cancellation conditions play a central role in the representation theory of measurement for a weak order on a finite two-dimensional Cartesian product set X. A weak order has an additive representation if and only if it violates no cancellation conditions. Given X, a longstanding open problem is to determine the simplest set of cancellation conditions that is violated by every linear order that is not additively representable. Here, we report that the simplest set of cancellation conditions on a 5 by 5 product X is obtained.

引用

页码：64 / 77

页数：14

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