Abstract
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.
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Acknowledgements
Both authors were supported by the Slovak Research and Development Agency under the contracts no. APVV-17-0066 and no. APVV-18-0052. Also the support of the grant VEGA 1/0006/19 is kindly announced.
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Mesiar, R., Šeliga, A. (2021). Collection and Decomposition Integrals in Multicriteria-Decision Support. In: Pap, E. (eds) Artificial Intelligence: Theory and Applications. Studies in Computational Intelligence, vol 973. Springer, Cham. https://doi.org/10.1007/978-3-030-72711-6_2
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DOI: https://doi.org/10.1007/978-3-030-72711-6_2
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