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Multiple-Output Choquet Integral Models and Their Applications in Classification Methods

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Book cover Nonlinear Mathematics for Uncertainty and its Applications

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 100))

Abstract

Two types of the multiple-output Choquet integral models are defined. Vector-valued Choquet integral models are vector-valued functions calculated by m times Choquet integral calculations with respect to the m-th fuzzy measure of a fuzzy measure vector. Logical set-function-valued Choquet integral models are set-function-valued functions that can be used in classification. The set function shows singleton, overlap, and unclassifiable degrees. The sum value of the set function is equal to 1. A method for transformation from vector-valued Choquet integral models to logical set-function-valued Choquet integral models is proposed.

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References

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Authors and Affiliations

  1. School of Commerce, Senshu University, 2-1-1, Tamaku, Kawasaki, 214-8580, Japan

    Eiichiro Takahagi

Authors
  1. Eiichiro Takahagi
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Editor information

Editors and Affiliations

  1. College of Applied Sciences, Beijing University of Technology, 100 Pingleyuan, 100124, Chaoyang District, Beijing, P.R. China

    Shoumei Li , Xia Wang  & Li Guan ,  & 

  2. Department of Systems Design and Informatics, Kyushu Institute of Technology, 680-4, Kawazu, 820-8502, lizuka, Japan

    Yoshiaki Okazaki

  3. Department of Mathematics, Shinshu University, 4-17-1 Wakasato, 380-8553, Nagano, Japan

    Jun Kawabe

  4. Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, 4259-G3-47, Nagatsuta, Midori-ku, 226-8502, Yokohama, Japan

    Toshiaki Murofushi

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© 2011 Springer-Verlag Berlin Heidelberg

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Takahagi, E. (2011). Multiple-Output Choquet Integral Models and Their Applications in Classification Methods. In: Li, S., Wang, X., Okazaki, Y., Kawabe, J., Murofushi, T., Guan, L. (eds) Nonlinear Mathematics for Uncertainty and its Applications. Advances in Intelligent and Soft Computing, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22833-9_11

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  • DOI: https://doi.org/10.1007/978-3-642-22833-9_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22832-2

  • Online ISBN: 978-3-642-22833-9

  • eBook Packages: EngineeringEngineering (R0)

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