An axiomatization of the ratio/difference representation
dc.contributor.author | Miyamoto, John M. | en_US |
dc.date.accessioned | 2006-04-07T18:36:29Z | |
dc.date.available | 2006-04-07T18:36:29Z | |
dc.date.issued | 1983-12 | en_US |
dc.identifier.citation | Miyamoto, John M. (1983/12)."An axiomatization of the ratio/difference representation." Journal of Mathematical Psychology 27(4): 439-455. <http://hdl.handle.net/2027.42/25051> | en_US |
dc.identifier.uri | http://www.sciencedirect.com/science/article/B6WK3-4D7JNND-93/2/23841a6083dc75470ccc11ea209f738c | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/25051 | |
dc.description.abstract | If >=r and >=d are two quaternary relations on an arbitrary set A, a ratio/difference representation for >=r and >=d is defined to be a function f that represents >=r as an ordering of numerical ratios and >=d as an ordering of numerical differences. Krantz, Luce, Suppes and Tversky (1971, Foundations of Measurement. New York, Academic Press) proposed an axiomatization of the ratio/difference representation, but their axiomatization contains an error. After describing a counterexample to their axiomatization, Theorem 1 of the present article shows that it actually implies a weaker result: if >=r and >=d are two quaternary retations satisfying the axiomatization proposed by Krantz et al. (1971), and if >=r' and >=d' are the relations that are inverse to >=r and >=d, respectively, then either there exists a ratio/difference representation for >=r and >=d, or there exists a ratio/difference representation for >=r' and >=d', but not both. Theorem 2 identifies a new condition which, when added to the axioms of Krantz et al. (1971), yields the existence of a ratio/difference representation for relations >=r and >=d. | en_US |
dc.format.extent | 1163702 bytes | |
dc.format.extent | 3118 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Elsevier | en_US |
dc.title | An axiomatization of the ratio/difference representation | en_US |
dc.type | Article | en_US |
dc.rights.robots | IndexNoFollow | en_US |
dc.subject.hlbsecondlevel | Psychology | en_US |
dc.subject.hlbtoplevel | Social Sciences | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | University of Michigan, USA | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/25051/1/0000479.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1016/0022-2496(83)90036-6 | en_US |
dc.identifier.source | Journal of Mathematical Psychology | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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