An approach to determining the integrated weights of decision makers based on interval number group decision matrices

In this paper, we develop an approach to determining the integrated weights of decision makers (DMs) with interval numbers in multiple attribute group decision making (MAGDM) problems. We first map the interval numbers of each DM's decision matrix into two-dimensional coordinates. The interval number values correspond to the coordinate values one to one. By integrating up-front subjective weight assignment with the relative importance of the DMs simultaneously, we derive the adjusted subjective DM weights. Based on the adjusted subjective weights, a plant growth simulation algorithm (PGSA) is used to find the generalized Fermat–Torricelli point of every point set, i.e., the optimal rally points that reflect the preferences of the DM group as a whole. From the mapping relationship, the generalized Fermat–Torricelli points constitute the ideal interval number decision matrix. Using deviation distance between each DM's decision matrix and the DM group's ideal matrix, we then obtain the degree of similarity indexes of the DMs. Next, by normalizing the degree of similarity indexes, we calculate the objective DM weights. Finally, we derive the stable integrated DM weights by combining the adjusted subjective weights and the objective weights. In addition, a numerical example is provided to illustrate the efficiency and reasonableness of the proposed approach.