Comparison of Risk Aversity for Two Utility Functions on ℝ<sup>2</sup>

Yuji Yoshida

doi:10.20965/jaciii.2019.p0555

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JACIII Vol.23 No.3 pp. 555-560

doi: 10.20965/jaciii.2019.p0555

(2019)

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Comparison of Risk Aversity for Two Utility Functions on ℝ²

Yuji Yoshida

Faculty of Economics and Business Administration, University of Kitakyushu
4-2-1 Kitagata, Kokuraminami, Kitakyushu 802-8577, Japan

Received:

November 21, 2017

Accepted:

January 16, 2019

Published:

May 20, 2019

Keywords:

weighted quasi-arithmetic means, risk averse decision-making, comparison of utility functions

Abstract

Utility functions on two-dimensional regions are demonstrated for decision makers’ risk averse behavior by weighted quasi-arithmetic means. For two utility functions on two-dimensional regions, a concept is introduced that decision making with one utility is more risk averse than decision making with the other utility. A necessary condition and sufficient conditions for the concept are demonstrated by their utility functions.

<i>M<sup>f</sup><sub>w</sub></i>(<i>R</i>) and <i>M<sup>g</sup><sub>w</sub></i>(<i>R</i>) in Example 1

M^f_w(R) and M^g_w(R) in Example 1

Cite this article as:

Y. Yoshida, “Comparison of Risk Aversity for Two Utility Functions on ℝ²,” J. Adv. Comput. Intell. Intell. Inform., Vol.23 No.3, pp. 555-560, 2019.

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References

[1] J. Aczél, “On weighted mean values,” Bulletin of the American Math. Society, Vol.54, pp. 392-400, 1948.
[2] A. N. Kolmogoroff, “Sur la notion de la moyenne,” Acad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez., Vol.12, pp. 388-391, 1930.
[3] K. Nagumo, “Über eine Klasse der Mittelwerte,” Japanese J. of Mathematics, Vol.6, pp. 71-79, 1930.
[4] P. C. Fishburn, “Utility Theory for Decision Making,” John Wiley and Sons, New York, 1970.
[5] Y. Yoshida, “Aggregated mean ratios of an interval induced from aggregation operations,” Int. Conf. on Modeling Decisions for Artificial Intelligence (MDAI2008), Vol.5285, pp. 26-37, 2008.
[6] Y. Yoshida, “Weighted quasi-arithmetic means and a risk index for stochastic environments,” Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems, Vol.16, suppl., pp. 1-16, 2011.
[7] H. Bustince, T. Calvo, B. De Baets, J. Fodor, R. Mesiar, J. Montero, D. Paternain, and A. Pradera, “A class of aggregation functions encompassing two-dimensional OWA operators,” Information Sciences, Vol.180, pp. 1977-1989, 2010.
[8] C. Labreuche and M. Grabisch, “The Choquet integral for the aggregation of interval scales in multicriteria decision making,” Fuzzy Sets and Systems, Vol.137, pp. 11-26, 2003.
[9] V. Torra and L. Godo, “On defuzzification with continuous WOWA operators,” Aggregation Operators, pp. 159-176, 2002.
[10] Y. Yoshida, “Weighted quasi-arithmetic means on two-dimensional regions and their applications,” Int. Conf. on Modeling Decisions for Artificial Intelligence (MDAI2015) LNAI, Vol.9321, pp. 42-53, 2015.
[11] Y. Yoshida, “Comparison of risk averse utility functions on two-dimensional regions,” Int. Conf. on Modeling Decisions for Artificial Intelligence (MDAI2017), Vol.10571, pp. 15-25, 2017.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] J. Aczél, “On weighted mean values,” Bulletin of the American Math. Society, Vol.54, pp. 392-400, 1948.

[2] [2] A. N. Kolmogoroff, “Sur la notion de la moyenne,” Acad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez., Vol.12, pp. 388-391, 1930.

[3] [3] K. Nagumo, “Über eine Klasse der Mittelwerte,” Japanese J. of Mathematics, Vol.6, pp. 71-79, 1930.

[4] [4] P. C. Fishburn, “Utility Theory for Decision Making,” John Wiley and Sons, New York, 1970.

[5] [5] Y. Yoshida, “Aggregated mean ratios of an interval induced from aggregation operations,” Int. Conf. on Modeling Decisions for Artificial Intelligence (MDAI2008), Vol.5285, pp. 26-37, 2008.

[6] [6] Y. Yoshida, “Weighted quasi-arithmetic means and a risk index for stochastic environments,” Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems, Vol.16, suppl., pp. 1-16, 2011.

[7] [7] H. Bustince, T. Calvo, B. De Baets, J. Fodor, R. Mesiar, J. Montero, D. Paternain, and A. Pradera, “A class of aggregation functions encompassing two-dimensional OWA operators,” Information Sciences, Vol.180, pp. 1977-1989, 2010.

[8] [8] C. Labreuche and M. Grabisch, “The Choquet integral for the aggregation of interval scales in multicriteria decision making,” Fuzzy Sets and Systems, Vol.137, pp. 11-26, 2003.

[9] [9] V. Torra and L. Godo, “On defuzzification with continuous WOWA operators,” Aggregation Operators, pp. 159-176, 2002.

[10] [10] Y. Yoshida, “Weighted quasi-arithmetic means on two-dimensional regions and their applications,” Int. Conf. on Modeling Decisions for Artificial Intelligence (MDAI2015) LNAI, Vol.9321, pp. 42-53, 2015.

[11] [11] Y. Yoshida, “Comparison of risk averse utility functions on two-dimensional regions,” Int. Conf. on Modeling Decisions for Artificial Intelligence (MDAI2017), Vol.10571, pp. 15-25, 2017.

Comparison of Risk Aversity for Two Utility Functions on ℝ2

Yuji Yoshida

Comparison of Risk Aversity for Two Utility Functions on ℝ²