Fujipress Home | Search | About FINDER

Paper:
Language: English:

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


Received: April 5, 2007

Accepted: July 23, 2007


Keywords: additive representation, joint receipt, conjoint structure, independence

Journal ref: Journal of Advanced Computational Intelligence and Intelligent Informatics, Vol.11, No.8 pp. 891-896, 2007

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.
preview Preview (PDF)  full text Full Text (PDF 114KB)

Reference

[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] L. Fuchs, “Partially ordered algebraic systems,” Reading, Massachusetts: Addison-Wesley, 1963.

[3] D. H. Krantz, R. D. Luce, P. Suppes, and A. Tversky, “Foundations of measurement,” Vol.1. New York: Academic Press, 1971.

[4] R. D. Luce, “Utility of gains and losses: Measurement-theoretical and experimental approaches,” Mahwah, NJ: Erlbaum, 2000.

[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] 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] F. S. Roberts and R. D. Luce, “Axiomatic thermodynamics and extensive measurement,” Synthese, Vol.18, pp. 311-326, 1968.

[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] P. P. Wakker, “Additive representations of preferences: A new foundation of decision analysis,” Dordrecht: Kluwer Academic Publishers, 1989.

[Notice]
* "Preview" is the first 2 pages of the article. You don't need the registration.
* To read the PDF file you will then need to download and install the Adobe Reader.
Adobe Reader is free and available for download here:

adobe reader

Terms and Conditions | Privacy Policy | Recruit | Advertising Information | Contact Us