Aggregation functions defined on linguistic scales (i.e., finite chains) have been intensively investigated for about two decades. Among these functions, fuzzy connectives (such as uninorms) are binary operations that play in an important role in fuzzy logic. In this talk we focus on the characterization of the class of idempotent uninorms on finite chains. Indeed, we provide an axiomatic characterization of the idempotent uninorms in terms of three conditions only : quasitriviality, symmetry and non-decreasing monotonicity. Moreover, we provide a graphical characterization of these operations in terms of their contour plots. Finally, we present an algebraic translation of the previous graphical characterization in terms of single-peaked linear orderings.