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An Ordered Weighted Average with a Truncation Weight on Intervals

  • Conference paper
Modeling Decisions for Artificial Intelligence (MDAI 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7647))

Abstract

This paper deals with ordered weighted averages on a closed interval, and their fundamental properties are investigated. In this paper we focus on ordered weighted average with a truncation weight, and the sub-additivity of a top-concentrated average is derived. Several examples are given to understand the idea. Further we deal with ordered weighted average from the bottom, and their relations are investigated. Finally, ordered weighted averages based on a probability are discussed and value-at-risks are explained as their example.

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References

  1. Artzner, P., Delbaen, F., Eber, J.-M., Heath, D.: Thinking coherently. Risk 10, 68–71 (1997)

    Google Scholar 

  2. Artzner, P., Delbaen, F., Eber, J.-M., Heath, D.: Coherent measures of risk. Mathematical Finance 9, 203–228 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  3. Beliakov, G., Pradera, A., Calvo, T.: Aggregation Functions: A Guide for Practioners. Springer (2007)

    Google Scholar 

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

    Google Scholar 

  5. Dellacherie, C.: Quelques commentarires sur les prolongements de capacités, Séminare de Probabilites 1969/1970, Strasbourg. LNAI, vol. 191, pp. 77–81. Springer(1971)

    Google Scholar 

  6. Meucci, A.: Risk and Asset Allocation. Springer, Heidelberg (2005)

    Book  MATH  Google Scholar 

  7. Narukawa, Y., Torra, V.: Continuous OWA Operator and its Calculation. In: (CD-ROM Proceedings, IFSA-EUSFLAT 2009), pp. 1132–1134 (2009)

    Google Scholar 

  8. Narukawa, Y., Torra, V., Sugeno, M.: Choquet integral of a function on the real line. In: Torra, V., Narukawa, Y., Daumas, M. (eds.) Modeling Decisions for Artificial Intelligence 2010, CD-ROM Proceedings, MDAI 2010, pp. 24–33 (2010)

    Google Scholar 

  9. Renneberg, D.: Non Additive Measure and Integral. Kluwer Academic Publ., Dordrecht (1994)

    Google Scholar 

  10. Torra, V.: The weighted OWA operator. Int. J. of Intel. Syst. 12, 153–166 (1997)

    Article  MATH  Google Scholar 

  11. Torra, V., Godo, L.: Continuous WOWA operators with application to defuzzification. In: Aggregation Operators: New Trends and Applications, pp. 159–176. Physica-Verlag, Springer (2002)

    Google Scholar 

  12. Torra, V., Narukawa, Y.: Modeling Decisions - Information Fusion and Aggregation Operators. Springer (2002)

    Google Scholar 

  13. Yager, R.R.: Ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Trans. on Systems, Man and Cybernetics. Int. J. of Intel. Syst. 18, 183–190 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  14. Yager, R.R.: Families of OWA operators. Fuzzy Sets and Systems 59, 125–148 (1993)

    Article  MathSciNet  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. Yager, R.R., Filev, D.P.: Parameterized and-like and or-like OWA opera-tors. Int. J. of General Systems 22, 297–316 (1994)

    Article  Google Scholar 

  17. Yager, R.R., Xu, Z.: The continuous order weighted geometric operator and its application to decision making. Fuzzy Sets and Systems 157, 1393–1402 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  18. Yoshida, Y.: A Perception-Based Portfolio Under Uncertainty: Minimization of Average Rates of Falling. In: Torra, V., Narukawa, Y., Inuiguchi, M. (eds.) MDAI 2009. LNCS (LNAI), vol. 5861, pp. 149–160. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  19. Yoshida, Y.: An average value-at-risk portfolio model under uncertainty: A perception-based approach by fuzzy random variables. Journal of Advanced Computational Intelligence and Intelligent Informatics 15, 56–62 (2011)

    Google Scholar 

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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

Authors
  1. Yuji Yoshida
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Editor information

Editors and Affiliations

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

    Vicenç Torra

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

    Yasuo Narukawa

  3. Universitat de Girona, Campus Montilivi, building EPS-4, 17071, Girona, Spain

    Beatriz López  & Mateu Villaret  & 

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Yoshida, Y. (2012). An Ordered Weighted Average with a Truncation Weight on Intervals. In: Torra, V., Narukawa, Y., López, B., Villaret, M. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2012. Lecture Notes in Computer Science(), vol 7647. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34620-0_6

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  • DOI: https://doi.org/10.1007/978-3-642-34620-0_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34619-4

  • Online ISBN: 978-3-642-34620-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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