On the coincidence of lower and upper generalized Sugeno integrals

Abstract

We provide the necessary and sufficient conditions for a pair of nondecreasing binary operators on , for some , such that the generalized upper Sugeno integral with respect to Δ coincides with the generalized lower Sugeno integral with respect to ∇. This result gives a solution to the problem posed by Boczek and Kaluszka for a class of all pairs of nondecreasing binary operators.