Measurement representations of ordered, relational structures with archimedean ordered translations
Mathématiques et Sciences humaines, Volume 101  (1988), p. 35-47
@article{MSH_1988__101__35_0,
author = {Luce, R. Duncan},
title = {Measurement representations of ordered, relational structures with archimedean ordered translations},
journal = {Math\'ematiques et Sciences humaines},
publisher = {Ecole des hautes-\'etudes en sciences sociales},
volume = {101},
year = {1988},
pages = {35-47},
zbl = {0658.92025},
mrnumber = {954943},
language = {en},
url = {http://www.numdam.org/item/MSH_1988__101__35_0}
}

Luce, R. D. Measurement representations of ordered, relational structures with archimedean ordered translations. Mathématiques et Sciences humaines, Volume 101 (1988) , pp. 35-47. http://www.numdam.org/item/MSH_1988__101__35_0/

Alper, T.M., "A note on real measurement structures of scale type (m,m+1)", Journal of Mathematical Psychology, 29 (1985), 73-81. | MR 793867 | Zbl 0602.92022

Alper, T.M., "A classification of all order-preserving homeomorphism groups of the reals that satisfy finite uniqueness", Journal of Mathematical Psychology, 31 (1987) , 135-154. | MR 900065 | Zbl 0626.06018

Cameron, P.J., Groups of order-automorphisms of the rationals with prescribed scale type. Unpublished manuscript (1987).

Cohen, M. & Narens, L., "Fundamental unit structures : a theory of ratio scalability", Journal of Mathematical Psychology, 20 (1979), 193-232. | MR 558151 | Zbl 0422.92029

Falmagne, J.-C., Elements of Psychophysical Theory, New York, Oxford University Press, 1985. | MR 802072

Falmagne, J.-C. & Narens, L., "Scales and meaningfulness of quantitative laws", Synthese, 55 (1983), 287-325. | MR 716481 | Zbl 0521.92027

Fuchs, L., Partially Ordered Algebraic Systems, Reading, MA, Addison-Wesley and Oxford, Pergamon Press, 1963. | MR 171864 | Zbl 0137.02001

Glass, A.M.W., Ordered Permutation Groups, London Mathematical Society Lecture Notes Series, 55, Cambridge, Cambridge University Press, 1981. | MR 645351 | Zbl 0473.06010

Hölder, O., "Die Axioms der Quantität und die Lehre vom Mass", Ber. Verh. Kgl. Sächsis. Ges. Wiss. Leipzig, Math. -Phys. Classe, 53 (1901), 1-64. | JFM 32.0079.01

Krantz, D.H., Luce, R.D., Suppes, P. & Tversky A., Foundations of Measurement, Vol. I, New York, Academic Press, 1971. | MR 459067 | Zbl 0232.02040

Luce, R.D., "Dimensionally invariant numerical laws correspond to meaningful qualitative relations", Philosophy of Science, 45 (1978), 1-16. | MR 489405

Luce, R.D., "Uniqueness and homogeneity of ordered relational structures", Journal o f Mathematical Psychology, 30 (1986) , 391-415. | MR 868772 | Zbl 0603.06010

Luce, R.D., Measurement structures with Archimedean ordered translation groups, Order, 4 (1987) , 165-189. | MR 916493 | Zbl 0629.08001

Luce, R.D., Krantz, D.H., Suppes, P. & Tversky, A., Foundations of Measurement, Vol. III, in press. | MR 459067 | Zbl 0749.03001

Luce, R.D. & Narens, L., "Classification of concatenation measurement structures according to scale type", Journal of Mathematical Psychology, 29 (1985), 1-72. | MR 793866 | Zbl 0578.92028

Luce, R.D. & Narens, L., "Measurement scales on the continuum", Science, 236 (1987) , 1527-1532. | MR 893168

Luce, R.D. & Narens, L., "Intrinsic Archimedeaness and the continuum", in C.W. Savage & P. Ehrlich (eds.), The Nature and Purpose of Measurement, in press.

Narens, L., "Utility-uncertainty tradeoff structures", Journal of Mathematical Psychology, 13 (1976), 296-322. | MR 418941 | Zbl 0351.92029

Narens, L., "A general theory of ratio scalability with remarks about the measurement-theoretic concept of meaningfulness", Theory and Decision, 13 (1981a), 1-70. | MR 612005 | Zbl 0497.00021

Narens, L., "On the scales of measurement", Journal of Mathematical Psychology, 24 (1981b), 249-275. | MR 653091 | Zbl 0496.92020

Narens, L., Abstract Measurement Theory, Cambridge, MA, MIT Press, 1985. | MR 776041 | Zbl 0607.00021

Narens L. & Luce, R.D., "The algebra of measurement", Journal of Pure and Applied Algebra, 8 (1976), 197-233. | MR 465299 | Zbl 0359.06028

Narens, L. & Luce, R.D., "Measurement : The theory of numerical assignments", Psychological Bulletin, 99 (1986) , 166-180.

Roberts, F.S., Measurement Theory, Vol. 7, Encyclopedia of Mathematics and its Applications, Reading, MA, Addison Wesley, 1979. | MR 551364 | Zbl 0432.92001

Stevens, S.S., "On the theory of scales of measurement", Science, 103 (1946), 677-680.

Stevens, S.S., "Mathematics, measurement and psychophysics", in S.S. Stevens (ed.) Handbook of Experimental Psychology, New York, Wiley, 1951, pp. 1-49.