A nonlinear integral defined on partition and its application to decision trees (Q882797)

The paper tries to contribute to the theory of nonlinear integrals introducing a functional \(I\) based on a fixed partition and on two set functions. The name ``integral'' is not appropriate here -- for example, \(I(cf)= I(f)\) for any positive constant \(c\). Also several typos have damaged the otherwise interesting idea of the authors. An example of possible application of the introduced functional \(I\) related to Shannon entropy is also included, however, the proofs in this part contain some analytical errors by differentiation and even undefined notions.