Method for uncertain linguistic group decision making based on projection and dominance degree

In order to solve multiple attribute group decision making problems with multi-granularity uncertain linguistic assessment information, where the information of attribute weights are incomplete, a group decision making method based on projection and dominance degree is proposed. Firstly, the uncertain linguistic evaluation matrices with multi-granularity are transformed to two-tuple decision matrices according to the continuous interval two-tuple ordered weighted harmonic (ITC-OWH) operator. By using projection method, a goal programming model is set up to determine the attribute weights vector of individual decision maker. Then, under every decision makers, integrative attribute dominance degree between pairwise comparisons of arbitrary alternatives are computed, a group integrative dominance degree matrix is obtained based on integrative dominance degree matrices and expert weight vector. The priority-time matrix is given to calculate the general priority time of alternatives, consequently, the rank result of alternatives can be determined. Finally, an example of submarine design scheme selection problem shows the effectiveness and feasibility of this method.