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Mathematical Foundation of Artificial Intelligence

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Artificial Intelligence: Theory and Applications

Part of the book series: Studies in Computational Intelligence ((SCI,volume 973))

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Abstract

In this chapter we present some of the mathematical tools used in AI, mostly related to decision making. One of the main tools are general aggregation functions (operators) with some special important cases as triangular norms and copulas. We present briefly some of their important applications. Important extension of the classical field of real numbers is related to the so called pseudo-operations: pseudo-addition and pseudo-multiplication. Here we present some of the important cases. Then corresponding pseudo additive measures and corresponding integrals are introduced, which make the base for the so called pseudo-analysis. The usefulness of the pseudo-analysis, which is a approach to nonlinearity, uncertainty and optimization, is illustrated with a short overview of some important applications. Very important tools in modeling decision making with overlaped events are general fuzzy measures and corresponding integrals as Choquet integral. We present a fuzzy integral approach to Cumulative Prospect theory. Further, we present many different generalizations of the Choquet integral.

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Acknowledgements

This research was supported by Science Fund of the Republic of Serbia, \(\#\)Grant No. 6524105, AI-ATLAS.

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    Endre Pap

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Pap, E. (2021). Mathematical Foundation of Artificial Intelligence. 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_1

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