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

• Autorzy: Che Tat Ng
• Języki publikacji: EN

Abstrakty

EN

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.(original abstract)

Słowa kluczowe

EN

Mathematics; Algebra

PL

Matematyka; Algebra

• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2024
• Tom: 38 (1)
• Strony: 64--77

Twórcy

autor

Che Tat Ng

• University of Waterloo, Canada

Bibliografia

• Fishburn P.C., Failure of cancellation conditions for additive linear orders, J. Combin. Des. 5 (1997), no. 5, 353-365.
• Fishburn P.C., Cancellation conditions for finite two-dimensional additive measurement, J. Math. Psych. 45 (2001), no. 1, 2-26.
• Li L. and Ng C.T., A minimal set of cancellation violating sequences for finite twodimensional non-additive measurement, Publ. Math. Debrecen 89 (2016), no. 3, 389- 398.
• Ng C.T., On Fishburn's questions about finite two-dimensional additive measurement, J. Math. Psych. 75 (2016), 118-126. DOI: 10.1016/j.jmp.2016.04.002
• Ng C.T., On Fishburn's questions about finite two-dimensional additive measurement, II, J. Math. Psych. 82 (2018), 1-11. DOI: 10.1016/j.jmp.2017.10.003
• Ng C.T., Replication Data for: A basic set of cancellation violating sequences for finite two-dimensional non-additive measurement, Borealis 1 (2023). DOI: 10.5683/SP3/J3OMIR
• Slinko A., Additive representability of finite measurement structures, in: S.J. Brams et al. (eds.), The Mathematics of Preference, Choice and Order: Essays in Honor of Peter C. Fishburn, Stud. Choice Welf., Springer-Verlag, Berlin, 2009, pp. 113-133.

Identyfikatory

DOI

10.2478/amsil-2023-0023