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The algebra of measurement. (English) Zbl 0359.06028


MSC:

06F05 Ordered semigroups and monoids
06F25 Ordered rings, algebras, modules
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References:

[1] Aczél, J., Lectures on functional equations and their applications (1966), Academic Press: Academic Press New York · Zbl 0139.09301
[2] Hölder, O., Die Axiome der Quantität und die Lehre vom Mass, Ber. Verh. Kgl. Sächsis, Ges. Wiss, Leipzig, Math.-Phys. Classe, 53, 1-64 (1901) · JFM 32.0079.01
[3] Holman, E. W., A note on conjoint measurement with restricted solvability, J. Math. Psychol., 8, 489-494 (1971) · Zbl 0228.92007
[4] Krantz, D. H.; Luce, R. D.; Suppes, P.; Tversky, A., Foundations of measurement, Vol. I (1971), Academic Press: Academic Press New York · Zbl 0232.02040
[5] Luce, R. D., A “fundamental” axiomatization of multiplicative power relations among three variables, Phil. Sci., 32, 301-309 (1965)
[6] Luce, R. D., Two extensions of conjoint measurement, J. Math. Psychol., 3, 348-370 (1966) · Zbl 0151.25601
[7] Luce, R. D.; Marley, A. A.J., Extensive measurement when concatenation is restricted and maximal elements may exist, (Morgenbesser, S.; Suppes, P.; White, M. G., Philosophy, science, and method: essays in honor of Ernest Nagel (1969), St. Martin’s Press: St. Martin’s Press New York), 235-249
[8] Luce, R. D.; Narens, L., A qualitative equivalent to the relativistic addition law for velocities (1974), submitted to Synthese
[9] Luce, R. D.; Tukey, J. W., Simultaneous conjoint measurement: a new type of fundamental measurement, J. Math. Psychol., 1, 1-27 (1964) · Zbl 0166.42201
[10] Narens, L., Utility-uncertainty trade-off structures, J. Math. Psychol. (1974), submitted to · Zbl 0351.92029
[11] Narens, L., Measurement without Archimedean axioms, Phil. Sci., 41, 374-393 (1974)
[12] Narens, L., Minimal conditions for additive conjoint measurement and qualitative probability, J. Math. Psychol., 11, 404-430 (1974) · Zbl 0307.02038
[13] Pfanzagl, J., Theory of measurement (1968), Wiley: Wiley New York · Zbl 0186.53602
[14] Ramsey, J. O., Review of Krantz, Foundations of Measurement, Psychometrika, 40, 257-262 (1975), Vol. I
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