IJPAM: Volume 64, No. 2 (2010)

POSITIVE ADDITIVE REPRESENTATIONS

Susan H. Gensemer
Department of Economics
Syracuse University
Syracuse, NY 13244-1020, USA
e-mail: [email protected]


Abstract.Axioms are presented which guarantee the positive additive numerical representability of an algebraic structure. Uniqueness of the representation up to a positive scalar multiple is shown as well. With insights derived from the literature on partial groupoids, an effort is made to limit restrictions on the domain of the concatenation operation, thus increasing the potential applicability of the system. The structure is compared to other similar measurement structures. An economic illustration in utility theory is presented.

Received: July 20, 2010

AMS Subject Classification: 91C05, 08A55, 91B16

Key Words and Phrases: measurement theory, partial groupoids, utility theory

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 64
Issue: 2