In this paper, we present new fuzzy connectives that allow to specify an order to the considered operation. These operators are generalization of usual fuzzy connectives, i.e. triangular norms and triangular conorms. A potential use of the proposed operators consists in assessing to what extent several values are high or low in unconstrained fuzzy sets is given. We also present weighted k-order fuzzy connectives, where weights are associated to different subsets of criteria. Finally, we show that these fuzzy connectives can be used from a set-theoretic point of view, enabling to define new kinds of fuzzy intersection and union.