In information fusion, aggregations with various backgrounds require a vari
ety of integrals to handle. These integrals are generally nonlinear since t
he set functions used are nonadditive in many real problems. In this study,
the set functions considered are nonnegative and vanishing at the empty se
t. They are a class of set functions including fuzzy measures and even impr
ecise probabilities. A new type of nonlinear integrals with respect to such
a set function for nonnegative functions is introduced and its primary pro
perties are detailed. These type of integrals has a natural explanation and
, therefore, has wide applicability. We also show a comparison between the
newly introduced nonlinear integral and other nonlinear integrals, such as
the Choquet integral, the natural extension in the theory of imprecise prob
abilities, and the common pan-integral. With a flowchart, the algorithm for
calculating the integral is given in this paper when the universe of disco
urse (the set of all information sources) is finite. (C) 2000 Elsevier Scie
nce B.V. All rights reserved.