Scheme selection is a Multiple Attribute Decision Making (MADM) problem. The Uncertain Linguistic MADM (ULMADM) method is generally studied and widely used. The key point for this kind of decision making is the aggregation algorithm. It is necessary to compare and rank uncertain linguistic variables in the process of decision making. To overcome the error occuring in the existed ranking model, a new model that can accurately calculate the possibility degree is presented, which guarantees that the subscript value of an uncertain linguistic variable is subject to uniform distribution. During the aggregation algorithms, the uncertain linguistic hybrid geometric mean (ULHGM) operator is of good applicability. This operator deals with the weight of a datum itself ahead of the position weight, so it might allocate counterproductive position weights to experts' original opinions. To avoid this, its aggregation process is improved, and it directly allocates position weights to experts' original opinions. The ULHGM operator needs twice exponential weight operations to complete aggregation, but the improved ULHGM (IULHGM) operator only needs once, so the improved algorithm is more convenient. Then the scheme selection method based on ULWGM operator and IULHGM operator is formulated. Finally, taking the selection of the maintainability design scheme of a certain shipborne gun as an example, the experts' evaluation data are aggregated by IULHGM operator and ULHGM operator, respectively, which lead to different scheme ranking results, and the cause is analyzed. The case shows that the aggregation algorithm of IULHGM operator is more accurate and reasonable than that of ULHGM operator.