A basic set of cancellation violating sequences for finite two-dimensional non-additive measurement

Che Tat Ng

Published: 2023-12-13

Vol. 38 No. 1 (2024)

A basic set of cancellation violating sequences for finite two-dimensional non-additive measurement

Che Tat Ng

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.

Keywords:

preference order , Cartesian product structure , additive measurement , cancellation conditions

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Ng, C. T. (2023). A basic set of cancellation violating sequences for finite two-dimensional non-additive measurement. Annales Mathematicae Silesianae, 38(1), 64–77. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/16498

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Vol. 38 No. 1 (2024)
Published: 2024-03-27

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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