A note on upper and lower Sugeno integrals (Q2572275)

The Sugeno integral for functions measurable with respect to a paving \({\mathcal A}\) (system of subsets of a universe \(X\) containing the empty set) and fuzzy measures on \({\mathcal A}\) (monotone \({\mathcal A}\to [0,1]\) set functions vanishing at the empty set) is introduced and discussed, and extended for arbitrary \(X\to [0,1]\) functions in two ways: as an upper and a lower Sugeno integral (compared with the standard extensions to an upper and a lower measure in the classical measure theory). Some properties are discussed and illustrated by an example.