The probabilistic linguistic term set (PLTS) extends the notion of the linguistic variable (LV). The existing operations of PLTSs are mainly based on the subscripts of linguistic terms and their probabilities while the membership functions of linguistic terms are ignored. Consequently, these operations may cause a loss of information. The extension principle is useful in doing the calculations between LVs and it considers membership functions simultaneously. Inspired by this idea, in this study, we introduce the extension principle for PLTSs and then define the operations of PLTSs. A novel representation of the PLTS is given. Then, the union of PLTSs is presented. Afterwards, we define the extension principle for PLTSs and give the algebraic operations of PLTSs. These algebraic operations based on the extension principle contain both the probabilities and membership functions of linguistic terms, and thus can enhance the precision of final results.