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JACIII Vol.11 No.8 pp. 891-896
doi: 10.20965/jaciii.2007.p0891
(2007)

Paper:

# A Joint-Receipt Conjoint Structure and its Additive Representation

## Yutaka Matsushita

Department of Psychological Informatics, Kanazawa Institute of Technology, 7-1 Ohgigaoka, Nonoichi, Ishikawa 921-8501, Japan

April 5, 2007
Accepted:
July 23, 2007
Published:
October 20, 2007
Keywords:
additive representation, joint receipt, conjoint structure, independence
Abstract

This paper introduces a componentwise joint receipt operation ⊕ on an n -component product set Πni=1 gi, and develops an axiom system to justify an additive representation for a binary relation ≿ on Πni=1 gi. Basically, our axiom system is similar to the n -component (n ≥ 3), additive conjoint structure. However, the introduction of the operation ⊕ yields two new axioms – additive solvability and invariance under multiplication – and hence we can weaken the independence axiom of the conjoint structure. The weakened independence axiom requires the independence of the order for each single factor from fixed levels of the other factors, while the conjoint structure involves the independence of the order for two or more factors. Finally, it is shown by a brief experimental test that the weakened independence axiom is sustained.

Yutaka Matsushita, “A Joint-Receipt Conjoint Structure and its Additive Representation,” J. Adv. Comput. Intell. Intell. Inform., Vol.11, No.8, pp. 891-896, 2007.
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References
1. [1] J. Aczél, R. D. Luce, and T. C. Ng, “Functional equations arising in a theory of rank dependence and homogeneous joint receipts,” Journal of Mathematical Psychology, Vol.47, pp. 171-183, 2003.
2. [2] L. Fuchs, “Partially ordered algebraic systems,” Reading, Massachusetts: Addison-Wesley, 1963.
3. [3] D. H. Krantz, R. D. Luce, P. Suppes, and A. Tversky, “Foundations of measurement,” Vol.1. New York: Academic Press, 1971.
4. [4] R. D. Luce, “Utility of gains and losses: Measurement-theoretical and experimental approaches,” Mahwah, NJ: Erlbaum, 2000.
5. [5] R. D. Luce and P. C. Fishburn, “Rank- and sign-dependent linear utility models for finite first-order gambles,” Journal of Risk and Uncertainty, Vol.4, pp. 29-59, 1991.
6. [6] T. Marchant and R. D. Luce, “Technical note on the joint receipt of quantities of a single good,” Journal of Mathematical Psychology, Vol.47, pp. 66-74, 2003.
7. [7] F. S. Roberts and R. D. Luce, “Axiomatic thermodynamics and extensive measurement,” Synthese, Vol.18, pp. 311-326, 1968.
8. [8] A. Tversky and D. Kahneman, “Advances in prospect theory: Cumulative representation of uncertainty,” Journal of Risk and Uncertainty, Vol.5, pp. 297-323, 1992.
9. [9] P. P. Wakker, “Additive representations of preferences: A new foundation of decision analysis,” Dordrecht: Kluwer Academic Publishers, 1989.

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