On the Moments and the Distribution of the Choquet Integral

We investigate the distribution functions and the moments of the so-called Choquet integral, also known as the Lov´asz extension, when regarded as a real function of a random sample drawn from a continuous population. Since the Choquet integral includes weighted arithmetic means, ordered weighted averaging operators, and lattice polynomials as particular cases, our results encompass the corresponding results for these aggregation operators. After recalling the results obtained by the authors in the uniform case, we present approaches that can be used in the non-uniform case to obtain moment approximations.

• Type: Conference
• Year: 2007
• Where: EUSFLAT
• Authors: Ivan Kojadinovic, Jean-Luc Marichal
• Keywords: Choquet Integral, EUSFLAT 2007, Fuzzy Logic, So-called Choquet Integral, Weighted Averaging Operators