- Vivi Padova
- Il Bo
Wednesday 3 November 2010 h. 14:30, room 2AB40
Maddalena Manzi (Univ. Padova, Dip. Mat.)
"The concept of supermodularity in aggregation functions and copulas"
In many domains we are faced with the problem of aggregating a collection of numerical readings to obtain a typical value, not only in mathematics or physics, but also in majority of engineering, economical, social and other sciences. So, aggregation functions are used to obtain a global score for each alternative taking into account the given criteria, even if the problems of aggregation are very broad and heterogeneous. For example, there is a lot of contributions about the aggregation of finite or infinite number of real inputs, topics treating of inputs from ordinal scales, or also the problem of aggregating complex inputs (such as probability distributions, fuzzy sets).
In this talk I will discuss the way to construct, in particular, supermodular aggregation functions, which can be analyzed under various aspects: algebraic, analytical, probabilistic. So, in the first part I will introduce the general concept of supermodularity, which comes from lattice theory, and we will see several basic examples. Then, we will be able to apply this theory to aggregation functions and, in particular, to a subclass of aggregation functions, i.e. the family of copulas. In the last part, we will see some results obtained with a particular intersection with fuzzy set theory. So, a basic background will be given also in this direction.
The talk will be based on some joint works with M. Cardin, M. Kalina, E. P. Klement and R. Mesiar.
Rif. int. C. Marastoni, T. Vargiolu