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Aggregated Mean Ratios of an Interval Induced from Aggregation Operations

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Modeling Decisions for Artificial Intelligence (MDAI 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5285))

Abstract

This paper deals with quasi-arithmetic means of an interval through utility functions in decision making. The mean values are discussed from the viewpoint of aggregation operators, and they are given as aggregated values of each point in the interval. We investigate the properties of the quasi-arithmetic mean and its translation invariance, and next we demonstrate the decision maker’s attitude based on his utility by the quasi-arithmetic mean and the aggregated mean ratio. The dual quasi-arithmetic means are also discussed with dual aggregation operators. Finally, examples of the quasi-arithmetic means and the aggregated mean ratio for various typical utility functions are given to understand the motivation.

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References

  1. Arrow, K.J.: Essays in the Theory of Risk-Bearing. Markham, Chicago (1971)

    MATH  Google Scholar 

  2. Calvo, T., Kolesárová, A., Komorníková, M., Mesiar, R.: Aggregation operators: Basic concepts, issues and properties. In: Calvo, T., et al. (eds.) Aggregation Operators: New Trends and Applications, pp. 3–104. Physica-Verlag, Springer (2002)

    Google Scholar 

  3. Calvo, T., Pradera, A.: Double weighted aggregation operators. Fuzzy Sets and Systems 142, 15–33 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  4. Dujmović, J.J.: Weighted Conjunctive and disjunctive means and their application in system evaluation. Univ. Beograd. Publ. Elektotech. Fak. Ser. Mat. Fiz. 483, 147–158 (1974)

    MathSciNet  MATH  Google Scholar 

  5. Dujmović, J.J., Larsen, H.L.: Generalized Conjunction/disjunction. International Journal of Approximate Reasoning 46, 423–446 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  6. Dujmović, J.J., Nagashima, H.: LSP method and its use for evaluation of Java IDEs. International Journal of Approximate Reasoning 41, 3–22 (2006)

    Article  MATH  Google Scholar 

  7. Fishburn, P.C.: Utility Theory for Decision Making. John Wiley and Sons, New York (1970)

    MATH  Google Scholar 

  8. Fodor, J., Roubens, M.: Fuzzy Preference Modelling and Multi-Criteria Decision Support. Kluwer Academic Publishers, Dordrecht (1994)

    Book  MATH  Google Scholar 

  9. Kolesárová, A.: Limit properties of quasi-arithmetic means. Fuzzy Sets and Systems 124, 65–71 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  10. Kolmogoroff, A.N.: Sur la notion de la moyenne. Acad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. 12, 388–391 (1930)

    MATH  Google Scholar 

  11. Mesiar, R., Rückschlossová, T.: Characterization of invariant aggregation operators. Fuzzy Sets and Systems 142, 63–73 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  12. Nagumo, K.: Über eine Klasse der Mittelwerte. Japanese Journal of Mathematics 6, 71–79 (1930)

    MATH  Google Scholar 

  13. Lázaro, J., Rückschlossová, T., Calvo, T.: Shift invariant binary aggregation operators. Fuzzy Sets and Systems 142, 51–62 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  14. Pratt, J.W.: Risk Aversion in the Small and the Large. Econometrica 32, 122–136 (1964)

    Article  MATH  Google Scholar 

  15. Yager, R.R.: OWA aggregation over a continuous interval argument with application to decision making. IEEE Trans. on Systems, Man, and Cybern. - Part B: Cybernetics 34, 1952–1963 (2004)

    Article  Google Scholar 

  16. Yoshida, Y.: The Valuation of European Options in Uncertain Environment. European J. Oper. Res. 145, 221–229 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  17. Yoshida, Y.: A discrete-time model of American put option in an uncertain environment. European J. Oper. Res. 151, 153–166 (2003)

    Article  MathSciNet  MATH  Google Scholar 

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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

Authors
  1. Yuji Yoshida
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Editors and Affiliations

  1. IIIA, Artificial Intelligence Research Institute CSIC, Spanish National Research Council,, Campus UAB s/n, 08193, Bellaterra, Catalonia, Spain

    Vicenç Torra

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

    Yasuo Narukawa

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Yoshida, Y. (2008). Aggregated Mean Ratios of an Interval Induced from Aggregation Operations. In: Torra, V., Narukawa, Y. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2008. Lecture Notes in Computer Science(), vol 5285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88269-5_4

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  • DOI: https://doi.org/10.1007/978-3-540-88269-5_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88268-8

  • Online ISBN: 978-3-540-88269-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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