Herrera and Martinez initiated a 2-tuple fuzzy linguistic representation model for computing with words. Moreover, Wang and Hao further developed a new 2-tuple fuzzy linguistic representation model to deal with the linguistic term sets that are not uniformly and symmetrically distributed. This study proposes another linguistic computational model based on 2-tuples and intervals, which we call an interval version of the 2-tuple fuzzy linguistic representation model. The proposed model possesses three steps: 1) interval numerical scale; 2) computation based on interval numbers; and 3) a generalized inverse operation of the interval numerical scale. The first step transforms linguistic terms into interval numbers, based on which the second step is executed with output as an interval number. Finally, this number is then mapped into the interval of the linguistic 2-tuples by the generalized inverse operation. This study also generalizes the numerical scale approach, presented in the Wang and Hao model, to set the interval numerical scale, by considering the context where semantics of linguistic terms are defined by interval type-2 fuzzy sets (IT2 FSs). In order to compare the proposed model with the existing linguistic computational model based on IT2 FSs, we have conducted extensive simulations. The simulations demonstrate that the results obtained by our proposal are consistent with the results of the linguistic computational model based on IT2 FSs (in some sense) in a vast majority of cases.