On ordered weighted averaging aggregation operators in multicriteria decisionmaking
IEEE Transactions on Systems, Man and Cybernetics
Fuzzy integral in multicriteria decision making
Fuzzy Sets and Systems - Special issue on fuzzy information processing
A Theoretical Study on Six Classifier Fusion Strategies
IEEE Transactions on Pattern Analysis and Machine Intelligence
An axiomatic approach of the discrete Choquet integral as a tool to aggregate interacting criteria
IEEE Transactions on Fuzzy Systems
"Fuzzy" versus "nonfuzzy" in combining classifiers designed by Boosting
IEEE Transactions on Fuzzy Systems
Series approximations for moments of order statistics using MAPLE
Computational Statistics & Data Analysis
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We study the moments and the distribution of the discrete Choquet integral when regarded as a real function of a random sample drawn from a continuous distribution. Since the discrete Choquet integral includes weighted arithmetic means, ordered weighted averaging functions, and lattice polynomial functions as particular cases, our results encompass the corresponding results for these aggregation functions. After detailing the results obtained in [J.-L. Marichal, I. Kojadinovic, Distribution functions of linear combinations of lattice polynomials from the uniform distribution, Statistics & Probability Letters 78 (2008) 985-991] in the uniform case, we present results for the standard exponential case, show how approximations of the moments can be obtained for other continuous distributions such as the standard normal, and elaborate on the asymptotic distribution of the Choquet integral. The results presented in this work can be used to improve the interpretation of discrete Choquet integrals when employed as aggregation functions.