LAMSADE- CNRS,

The paper presents some preliminary results concerning the comparison of intervals using a continuous evaluation of positive and negative reasons. More precisely we present a valued exten-sion of the recently introduced concept of PQI interval order. The main idea is that, while comparing objects rep-resented by intervals of values, there is a zone of hesitation between strict difference and strict similarity which could be modelled through valued rela-tions. The paper presents suitable def-initions of such valued relations fulfill-ing a number of interesting properties. The use of such a tool in data analysis and rough sets theory is discussed in the paper