The upper integral is a type of non-linear integral with respect to non-additive measures, which represents the maximum potential of efficiency for a group of features with interaction. The value of upper integrals can be evaluated through solving a linear programming problem. Considering the upper integral as a classifier, this paper first investigates its implementation and performance. Fusin...

In this paper we discuss the Choquet integral model in the realm of Preference Learning, and point out advantages of learning simultaneously partial utility functions and capacities rather than sequentially, i.e., first utility functions and then capacities or vice-versa. Moreover, we present possible interpretations of the Choquet integral model in Preference Learning based on Shapley values a...

We introduce bi-capacities as a natural generalization of capacities (or fuzzy measures) through the identity of Choquet integral of binary alternatives with fuzzy measures. We examine the underlying structure and derive the Möbius transform of bi-capacities. Next, the Choquet and Sugeno integrals w.r.t bicapacities are introduced. It is shown that symmetric and asymmetric integrals are recover...

The unitarity equations for the boson interaction amplitudes in the superstring theory are used to calculate the interaction amplitudes including the Ramond states, which are 10-fermion and Ramond bosons. The n-loop, 4-point amplitude with two massless Neveu-Schwarz bosons and two massless Ramond states is obtained explicitly. It is shown that, in addition, the unitarity equations require some ...

We report on the development and validation of a new numerical wave tank (NWT) solving fully nonlinear potential flow (FNPF) equations, as more efficient variation Grilli et al.'s NWT [Grilli al., A model for three-dimensional overturning waves over arbitrary bottom. Int J Numer Methods Fluids. 2001; 35:829-867], which was successful at modeling many phenomena, including landslide-generated tsu...