On the closure of families of fuzzy measures under eventwise aggregations

The paper contains some results on eventwise aggregation of fuzzy measures from the various families of lower probabilities. This investigation includes coherent lower probabilities, k-monotone measures', belief measures, etc. We study sufficient and necessary conditions on aggregation operators satisfying the closure property: it is necessary to guarantee that the aggregation belongs to the same family, as generating measures. We also propose an efficient way for constructing aggregation operators, using the found unique properties of multilinear extension. This representation method for fuzzy measures generalizes to the n-dimensional case the well-known one giving distorted probabilities.