Non-additive measures are set functions where the additivity condition is replaced by monotonicity with respect to set inclusion. Outer measures are one of the examples of this type of measures. Non-additive measures are also known as capacities, fuzzy measures, and monotonic games. They are useful to represent interactions between elements and there are applications in mathematical economy, social choice and computer science.
Our research group (led by Prof. Vicenç Torra) has a long experience in the field, working on measures for both discrete and continuous domains. Our current research includes theoretical results on non-additive measures and integrals, numerical integration using non-additive measures, Radon-Nikodym-like derivatives and distances for these measures, probability distributions based on these measures. We have developed applications for modeling decisions and for data privacy.
The group collaborates with several national and international research groups on these topics (Japan, USA), and has active links with the private and public sectors. For more information see:
Research will be done in the area of non-additive measures and integrals. We are interested in developing probability distributions based on these measures, the interplay of these measures and probability distributions, and on defining distances for these measures. A successful candidate will have the opportunity to take part in developing the project.