The generalized dependent unbalanced linguistic ordered weighted average(GDULOWA) operator and the weighted generalized dependent unbalanced linguistic ordered weighted average(WGDULOWA) operator are proposed based on multiple attribute decision making, in which attribute values take the form of unbalanced linguistic variables. The associated weights depend on the decision maker and the aggregated unbalanced linguistic variable, which can relieve the influence of unfair linguistic variables by assigning low weights to the biased ones, and make the decision results more reasonable. The concrete expressions of these operators are obtained by derivation, and some properties of these operators are investigated. These operators are applied to multi-attribute decision making. At the same time, the influence of different parameters $\lambda$ on decision making is analyzed. The comparative analysis shows the effectiveness of the proposed generalized operators.