# Miguel Couceiro

**Miguel Couceiro** Professor at Université de Lorraine

Title: **Lattice Polynomails and their use in qualitative Decision Making**

**Abstract**: Traditionally, aggregation functions are regarded as mappings A: In ! I, where I is a real interval (e.g., I = [0; 1]), which are nondecreasing and satisfy the boundary conditions A(∧In) = ∧I and A(∨In) = ∨I. Typical examples nclude the arithmeticand geometric means, and the Choquet integral. Such examples rely heavily on the rich arithmetic structure of the reals, and thus they are of little use over domains where no structure other than an order is ssumed, e.g., qualitative scales like very bad, bad, satisfactory, good, very good. In such situations, the most widely used aggregation function are the Sugeno integrals, which can be thought of as idempotent lattice polynomials. This observation will be the starting point of our talk, in which we shall present a study of these lattice functions rooted in aggregation theory and motivated by their application in qualitative decision making. We shall start by presenting characterizations of lattice polynomials in terms of necessary and sufficient conditions which have natural interpretations in aggregation theory. Then we shall consider certain extensions of lattice polynomials which play an important role in decision making, in particular, in preference modeling, and present their characterizations accordingly. As we shall see, these results pave the way towards an axiomatic treatment of qualitative decision making. Most of the results we shall discuss were obtained in collaboration with D. Dubois, J.-L. Marichal, H. Prade, and T. Waldhauser.

**Biography**: Miguel Couceiro received his degree of Doctor of Philosophy from the University of Tampere, Finland, in 2006, and his Habilitation degree in Computer Science from the University Paris-Dauphine, France, in 2013. He was a postdoctoral fellow at the University of Luxembourg (2007-2012) and an Associate Professor at University Paris-Dauphine (2012-2014). Currently he is a full Professor of Orpailleur Team at LORIA (CNRS – Inria Nancy Grand Est – University of Lorraine). His research interests can be found in discrete mathematics, theoretical computer science, multicriteria decision aid and artificial intelligence. His earlier work focused on function theory, including aggregation theory, clone theory, multiple-valued logic. His recent works are pertaining to multicriteria decision making, in particular, preference modelling, reasoning and learning (with particular emphasis on aggregation, decomposition and reconstruction techniques). He has more than 100 peer-reviewed papers in international journals and conference proceedings, he has co-organized several international conferences and colloquia, and he is a member of the editorial board of IJITS.