Vector-Valued Choquet Integrals for Set Functions and Bi-capacities

  • Eiichiro Takahagi
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 300)


Logical vector-valued Choquet integral models are vector-valued functions calculated by m times Choquet integral calculations with respect to the m-th set functions to the interval [0,1]. By placing restrictions on the set functions, we can get some good properties, such as a normalized output. To introduce a symmetric difference expression, some set functions are transformed into monotone set functions, and they can be interpreted by using fuzzy measure tools such as Shapley values. Similarly, we introduce a vector-valued Choquet integral for bi-capacities and their symmetric difference expressions. Despite from the vector-valued Choquet integral for set functions, the output values match with original and symmetric difference expressions.


vector-valued Choquet integral bi-capacities symmetric difference classification 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Eiichiro Takahagi
    • 1
  1. 1.Senshu UniversityKawasakiJapan

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