Abstract
Complex decisions in human decision-making may arise when the Emotional Intelligence and Rational Reasoning produce different preference ordering between alternatives. From a mathematical point of view, complex decisions can be defined as decisions where a preference ordering between random variables cannot be represented by a linear functional. The Asymmetric and the Symmetric Choquet integrals with respect to non additive-measures have been defined as aggregation operators of data sets and as a tool to assess an ordering between random variables. They could be considered to represent preference orderings of the conscious and unconscious mind when a human being make decision. Sufficient conditions are given such that the two integral representations of a coherent upper conditional prevision by the Asymmetric Choquet integral and the Symmetric Choquet integral with respect to Hausdorff outer measures coincide and linearity holds.
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Doria, S. (2018). Integral Representations of a Coherent Upper Conditional Prevision by the Symmetric Choquet Integral and the Asymmetric Choquet Integral with Respect to Hausdorff Outer Measures. In: Ciucci, D., Pasi, G., Vantaggi, B. (eds) Scalable Uncertainty Management. SUM 2018. Lecture Notes in Computer Science(), vol 11142. Springer, Cham. https://doi.org/10.1007/978-3-030-00461-3_8
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