In the present paper we reflect and focus on the ideas of utility streams and welfare criterions from a point of view of social choice and sustainability, thinking out on the suitability of the corresponding mathematical definitions used in the literature in order to formalize these concepts. These terms were mathematically characterized on a discrete manner. However, a continuous approach is presented, such that it allows to apply some new tech-niques (related to mathematical and software tools) to the study of some social choice problems, in particular, for nding desired preferences satisfying some axioms such as Pareto, non-dictatorship or fairness on the set of continuous utility streams. As a consequence, we present and construct a fair sustainable preference.