Extension of TOPSIS to determine weight of decision maker for group decision making problems with uncertain information

In traditional TOPSIS method, the ideal solutions for alternatives are expressed in vectors. An important step in the process of group decision making is to determine the relative importance of each decision maker. In this paper, the weights of decision makers derived from individual decision are determined by using an extended TOPSIS method with interval numbers. The ideal decisions for all individual decisions are expressed in matrices. The positive ideal decision is the intersection of all individual decisions; the negative ideal decision is the union of all individual decisions. Comparisons with other methods are also made. A numerical example is examined to show the potential applications of the proposed method.

► A group decision making model with uncertain information is established.
► Positive ideal decision is defined as the intersection of all individual decisions.
► Negative ideal decision is defined as the union of all individual decisions.
► The ideal decision is expressed as a matrix.
► The weights of decision makers are determined by the extended TOPSIS method.