Several types of sets, such as hesitant fuzzy sets, permit to express hesitation, doubt, or perplexity during, e.g., a decision-making process. In this paper, we start giving thought to the hesitant operators in certain models such as the 2-tuple models or the symbolic model. On the basis of the definition of uncertainty, hesitation, doubt, etc. in linguistics, we suggest to shed new light on their meaning and on the way they can be linked in the considered frameworks. Five types of hesitant expressions are discussed, and a parallel between the expressions and the mathematical operators in the considered models is drawn. Two new operators in the 2-tuple semantic model and one new operator in the symbolic model are proposed with a classification of all the discussed operators.