Abstract
In this paper, we deal with the transformation theorem for the generalized upper Sugeno integral I∘. We formulate the sufficient and necessary conditions under which the transformation holds, thus providing a complete solution to this problem. We also provide some representations of the I∘ integral via left-continuous (right-continuous) modifications of level measures. We characterize the class of binary operations for which the I∘ integral can be represented via the quantile function. As a consequence, we get complete solutions to these problems for the smallest semicopula-based universal integral. We thus solve several open problems related to this class of integrals in the literature.
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