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Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 68))

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Abstract

Choquet integral models are useful comprehensive evaluation models including interaction effects among evaluation items. Introducing a constant, Choquet integral model enables to change evaluation attitudes at the constant. In this paper, monotonicity and normality are defined for the model. We propose a global fuzzy measure identification method from upper and lower ordinal fuzzy measures and a constant. Lastly, we compare the models with the ordinal Choquet integral, the Choquet-integral-based evaluations by fuzzy rules, the cumulative prospect theory and the bi-capacities model.

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References

  1. Choquet, M.: Theory of Capacities. Annales de l’Institut Fourier 5, 131–295 (1954)

    MathSciNet  Google Scholar 

  2. Murofushi, T., Sugeno, M.: A theory of fuzzy measures: representations, the Choquet integral, and null sets. J. Math. Anal. Appl. 159(2), 532–549 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  3. Grabisch, M., Labreuche, C.: Bi-capacities — Part I: definition, Möbius transform and interaction. Fuzzy Sets and Systems 151, 211–236 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  4. Grabisch, M., Labreuche, C.: Bi-capacities — Part II: the Choquet integral. Fuzzy Sets and Systems 151, 237–259 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  5. Takahagi, E.: Choquet-integral-based Evaluations by Fuzzy Rules. In: Proceedings of the Joint 2009 International Fuzzy Systems Association World Congress and 2009 European Society of Fuzzy Logic and Technology Conference, Lisbon, pp. 843–848 (2009)

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  6. Tversky, A., Kahneman, D.: Advances in Prospect Theory: Cumulative Representation of Uncertainty. J. of Risk and Uncertainty 5, 297–323 (1992)

    Article  MATH  Google Scholar 

  7. Å ipoÅ¡, J.: Integral with respect to a pre-measure. Math. Slovaca 29, 141–155 (1979)

    MATH  MathSciNet  Google Scholar 

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Takahagi, E. (2010). Choquet Integral Models with a Constant. In: Huynh, VN., Nakamori, Y., Lawry, J., Inuiguchi, M. (eds) Integrated Uncertainty Management and Applications. Advances in Intelligent and Soft Computing, vol 68. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11960-6_23

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  • DOI: https://doi.org/10.1007/978-3-642-11960-6_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11959-0

  • Online ISBN: 978-3-642-11960-6

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