Preference Representation for Multicriteria Decision Making Marta Cardin Dept. of Applied Mathematics University of Venice e-mail: mcardin@unive.it Abstract: In this note we consider a multicriteria decision problem where the decision maker know the the state of the world but the set of consequences is multidimensional. We suppose that a value function is specified over the attribute of the decision problem and we analyze some classes of non additive functions that can represent interaction between criteria. Keywords: Multicriteria decision making, value function, Choquet signed integral, Schur-decreasing functions. M.S.C. classification: 62C05, 91B08 . J.E.L. classification: C60. 1 Introduction In multicriteria decision making we aim at ordering multidimensional alter- natives. We suppose that a decision can be made using a value function which represents the preference structure of the decision maker. In this framework the critical point of solving multi-attribute decision problem is to determine the value function. A traditional approach is to use a function that is a simple weight sum where each weight represents the importance given by the decision maker to a particular attribute. It should be noticed that the additive model implies independence between attributes so despite its simplicity this approach suf- fer a major drawback of not being able to take into account ”inter-attribute” relations that are present in many situations. The problem of modelling such an interaction is a difficult question because there are different types of dependence quite different from each other such as correlation, complementarity and preferential dependence. In this note we study some particular classes of non additive value functions that are usually considered in the area of decision theory under uncertainty. So this note points out a similarity between decision under uncertainty and 1