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Weighted Quasi-Arithmetic Means: Utility Functions and Weighting Functions

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Modeling Decisions for Artificial Intelligence (MDAI 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8234))

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Abstract

This paper discusses weighted quasi-arithmetic means from viewpoint of a combined index of utility functions and weighting functions, which represent stochastic risk in economics. The combined index characterizes decision maker’s attitude and background risks in stochastic environments by conditional expectation representations of weighted quasi-arithmetic means. The first-order stochastic dominance and risk premium are demonstrated using weighted quasi-arithmetic means and aggregated mean ratios, and they are characterized by the combined index. Finally, examples of weighted quasi-arithmetic mean and aggregated mean ratio for various typical utility functions are given.

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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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Editors and Affiliations

  1. IIIA-CSIC, Campüus UAB s/n, 08193, Bellaterra, Catalonia, Spain

    Vicenç Torra

  2. Toho Gakuen, 3-1-10, Naka, 186-0004, Kunitachi, Tokyo, Japan

    Yasuo Narukawa

  3. Departament d’Enginyeria de la Informació i de les Comunicacions, Universitat Autonoma de Barcelona, 08193, Bellaterra, Catalonia, Spain

    Guillermo Navarro-Arribas

  4. Internet Interdisciplinary Institute (IN3); Estudis d’Informàtica, Multimèdia i Telecomunicació, Universitat Oberta de Catalunya, Rambla del Poblenou, 156, 08018, Barcelona, Catalonia, Spain

    David Megías

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Yoshida, Y. (2013). Weighted Quasi-Arithmetic Means: Utility Functions and Weighting Functions. In: Torra, V., Narukawa, Y., Navarro-Arribas, G., Megías, D. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2013. Lecture Notes in Computer Science(), vol 8234. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41550-0_3

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  • DOI: https://doi.org/10.1007/978-3-642-41550-0_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-41549-4

  • Online ISBN: 978-3-642-41550-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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