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Weighted Quasi-Arithmetic Mean on Two-Dimensional Regions and Their Applications

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Modeling Decisions for Artificial Intelligence (MDAI 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9321))

Abstract

This paper discusses a decision maker’s attitude regarding risks, for example risk neutral, risk averse and risk loving in micro-economics by the convexity and concavity of utility functions. Weighted quasi-arithmetic means on two-dimensional regions are introduced, and some conditions on utility functions are discussed to characterize the decision maker’s attitude. Risk premiums on two-dimensional regions are given and demonstrated. Some approaches to construct two-dimensional utilities from one-dimensional ones are given, and a lot of examples of weighted quasi-arithmetic means are shown.

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Author information

Authors and Affiliations

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

    Yuji Yoshida

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  1. Yuji Yoshida
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Correspondence to Yuji Yoshida .

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Editors and Affiliations

  1. University of Skövde, Skövde, Sweden

    Vicenc Torra

  2. Toho Gakuen, Tokyo, Japan

    Torra Narukawa

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Yoshida, Y. (2015). Weighted Quasi-Arithmetic Mean on Two-Dimensional Regions and Their Applications. In: Torra, V., Narukawa, T. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2015. Lecture Notes in Computer Science(), vol 9321. Springer, Cham. https://doi.org/10.1007/978-3-319-23240-9_4

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  • DOI: https://doi.org/10.1007/978-3-319-23240-9_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23239-3

  • Online ISBN: 978-3-319-23240-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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