A Simple Method of Calculating the Choquet Integral using T-formula

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  • Choquet積分のT-formulaによる簡単計算

Abstract

As for the other expressions of the Choquet integral with respect to non-additive measures, there are the ones using the Inclusion-exclusion integral or Möbius transform. In this paper another expression called T-formula is shown, which was proposed in 2013 by the author. In order to calculate the Choquet integral with respect to capacities, permutation is required in advance. Using this formula, such a permutation is not necessary. The purposes of this paper are to show that the Choquet integral is derived from the T-formula and to propose an easy method of calculating the Choquet integral using the T-formula with an example, where it suffices to use only the database function in Excel 2007 to obtain the solution.

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