This paper describes two kinds of decentralized economic dispatch framework for the coordinated operation of multi-microgrids in a distribution network. Considering the high uncertainties of renewable energy sources and load demands, robust optimization-based distributed framework exhibits a prospective application on networked multi-microgrids in the future. By integrating analytical target cascading and robust model which can be solved using a column-and-constraint generation method, the robust economic dispatch problem can be applied in different entities, respectively, distribution network operator and microgrid operator in a decentralized way. Second way, column-and-constraint generation algorithm can be naturally realized in a decentralized and coordinated manner, specifically, the sub-problems and master-problem can be separately executed in microgrid operators and distribution network operator. Decentralized framework can respect the independence and privacy of different operators, and be beneficial to solve technical and economic challenges brought by centralized optimization. Numerical results of a modified IEEE 33-bus test distribution system with three microgrids validate the effectiveness of the proposed methods, and compare the characteristics of two kinds of decentralized implementations, and it is found that the first methodology shows better information privacy and lower communication burden, while the second way can obtain quicker convergence speed. In addition, cost comparison between cooperative case and three kinds of uncooperative cases is analyzed to explain economic benefits of cooperative operation. Furthermore, sensitivity analysis of lateral uncertainty and longitudinal uncertainty are given to show that robustness is enhanced at the expense of adding costs.