An extended TOPSIS for determining weights of decision makers with interval numbers

In this paper, we develop a method for determining weights of decision makers under group decision environment, in which the each individual decision information is expressed by a matrix in interval numbers. We define the positive and negative ideal solutions of group decision, which are expressed by a matrix, respectively. The positive ideal solution is expressed by the average matrix of group decision and the negative ideal solution is maximum separation from positive ideal solution. The separation measures of each individual decision from the ideal solution and the relative closeness to the ideal solution are defined based on Euclidean distance. According to the relative closeness, we determine the weights of decision makers in accordance with the values of the relative closeness. Finally, we give an example for integrated assessment of air quality in Guangzhou during 16th Asian Olympic Games to illustrate in detail the calculation process of the developed approach.

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