Collection and Decomposition Integrals in Multicriteria-Decision Support

Integrals generalizing the expected value of random variables play an essential role in multi-criteria decision problems, where they are considered as utility functions. In this chapter, we focus on the recently introduced collection and decomposition integrals, covering, among others, the Choquet, the Shilkret and the PAN integrals. We discuss some properties and give several examples of these integrals, in particular those extending the Lebesgue integral. Later, we discuss this type of integral for interval-valued functions. Finally, possible applications in multi-criteria-decision support and imprecise probability domains are shown.