Novel survival functions based on conditional aggregation operators

In this paper we define a novel survival function motivated by real life problems, which generalizes the super level measure introduced by Do and Thiele (2015). This concept is based on conditional aggregation operators extending the definition of aggregation opera-tors introduced by Calvo et al. (2002) for all bounded measurable functions and not only for finite sequences. Some basic properties and several examples of conditional aggregation operators are presented. Using the novel survival function, the Choquet-Stieltjes functional is introduced and the conditions are indicated under which this functional can be called an integral. The new functional generalizes several known integrals including the Choquet-Stieltjes integral as well as Choquet integral with respect to level dependent capacity intro-duced by Greco et al. (2011). (c) 2020 Elsevier Inc. All rights reserved.