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A Probabilistic Theory of Extensive Measurement

Published online by Cambridge University Press:  01 April 2022

Jean-Claude Falmagne
Jean-Claude Falmagne*
Affiliation:
New York University
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Abstract

Algebraic theories for extensive measurement are traditionally framed in terms of a binary relation ≲ and a concatenation (x,y) → xy. For situations in which the data is “noisy,” it is proposed here to consider each expression y ≲ x as symbolizing an event in a probability space. Denoting P(x,y) the probability of such an event, two theories are discussed corresponding to the two representing relations: with

Axiomatic analyses are given, and representation theorems are proven in detail.

Type
Research Article
Information
Philosophy of Science , Volume 47 , Issue 2 , June 1980 , pp. 277 - 296
Copyright
Copyright © Philosophy of Science Association 1980

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Footnotes

†

This work is supported by Grant No. BNS 77-16984 to New York University from the National Science Foundation. The author is grateful to the Department of Psychology and Social Relations at Harvard University for its hospitality. I also wish to thank H. Colonius and Z. Domotor for their comments on a previous draft.

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