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The concept of universal integral, recently proposed and axiomatized, encompasses several integrals, including the Choquet, Shilkret and Sugeno integrals. In this paper we present two new axiomatizations of universal integrals on the scale [0,1]. In the first characterization, we look at universal integrals on the scale [0,1] as families of aggregation functions F satisfying some desired properties. The second characterization is given in the framing in which the original definition of universal integral was provided.

The aim of this paper is to introduce prospect theory in a game theoretic framework. We address the complexity of the weighting function by restricting the object of our analysis to a 2-player 2-strategy game, in order to derive some core results. We find that dominant and indifferent strategies are preserved under prospect theory. However, in absence of dominant strategies, equilibrium may not exist depending on parameters. We also discuss a different approach presented by Metzger and Rieger (2009) and give some interesting interpretations of the two approaches.

The proposal and the axiomatization of new fuzzy integrals has a central role in modern Multiple Criteria Decision Analysis. In this thesis we propose some generalizations of well known fuzzy integrals (Choquet, Shilkret and Sugeno). We propose and characterize bipolar fuzzy integrals, which are generalization of the most famous fuzzy integrals to the case of bipolar scale, i.e. those symmetric scale where it is possible for each value to find the opposite. We also deal with the generalization of the concept of universal integral (recently proposed to generalize several fuzzy integrals) to the case of bipolar scales. We also provide the characterization of the bipolar universal integral with respect to a level dependent bi-capacity. Finally, we consider the problem to adapt classical definitions of fuzzy integrals to the case of imprecise interval evaluations. More precisely, standard fuzzy integrals used in MCDA request that the starting evaluations of a choice on various criteria must be expressed in terms of exact-evaluations. We present the robust Choquet, Shilkret and Sugeno integrals, computed with respect to an interval capacity. These are quite natural generalizations of the Choquet, Shilkret and Sugeno integrals, useful to aggregate interval-evaluations of choice alternatives into a single overall evaluation.

We present the bipolar Cumulative Prospect Theory, a generalization of Cumulative Prospect Theory of Kahneman and Tversky. Moreover we get a characterization of the Choquet Integral with respect to a bi-capacity in a discrete setting. With our model we are able to explain some recent paradoxes regarding the separate valuation of gains and losses within a mixed gamble. We present the bipolar Cumulative Prospect Theory, a generalization of Cumulative Prospect Theory of Kahneman and Tversky. Moreover we get a characterization of the Choquet Integral with respect to a bi-capacity in a discrete setting. With our model we are able to explain some recent paradoxes regarding the separate valuation of gains and losses within a mixed gamble.