A Basic Set of Cancellation Violating Sequences for Finite Two-Dimensional Non-Additive Measurement

Che Tat Ng

doi:10.2478/amsil-2023-0023

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A Basic Set of Cancellation Violating Sequences for Finite Two-Dimensional Non-Additive Measurement

Annales Mathematicae Silesianae

Volume 38 (2024): Issue 1 (March 2024)

By: Che Tat Ng

Open Access

|Dec 2023

Abstract

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.

References

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Articles in this issue

DOI: https://doi.org/10.2478/amsil-2023-0023 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

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Language: English

Page range: 64 - 77

Submitted on: Sep 18, 2023

Accepted on: Nov 17, 2023

Published on: Dec 13, 2023

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

Preference order,

Cartesian product structure,

additive measurement,

cancellation conditions

Related subjects:

Mathematics,

General mathematics

© 2023 Che Tat Ng, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 38 (2024): Issue 1 (March 2024)