In this paper, an order induced by uninorms on bounded lattices is given and discussed. By defining such an order, the T-partial order is extended to a more general form. The relationship between the order induced by the underlying t-norm and t-conorm and the order induced by a uninorm is studied. Finally, the order is extended to the order induced by n-uninorms on chains. (C) 2015 Elsevier Inc. All rights reserved.