New results on interval comparison

In this paper we propose a general framework for the interval comparison which finds different classes of preference structures having an interval representation. First of all we propose an axiomatisation for an interval representation and then we present some results which generalise the characterisation of some classical properties such as transitivity, Ferrers relation, etc. We make use of these results to find all the preference structures which satisfy our axioms and which may be represented with classical intervals (interval defined with two extreme points) and with 3-points intervals (intervals with an intermediate point).