This paper takes place in the computing with words framework where a unified model of several linguistic representation models is proposed. We consider (i) the 2-tuple fuzzy linguistic representation model, (ii) the proportional 2-tuple fuzzy linguistic representation model, (iii) the linguistic degrees and their associated generalized symbolic modifiers. Our approach is based on a vectorial representation. Using vectors and scalar multiplications, we translate and then unify these three models into a single one. In this paper, the scope of our research is limited to the definitions of a linguistic value, the attached aggregation operators remaining the next logical step.