Selection and negotiation of purchasing bids is a complex decision making process that requires consideration of a variety of vendor attributes such as price, delivery performance, and quality. Several decision models have been utilized for vendor evaluation and selection. Talluri [EUR. J. Operat. Res. 143(1) ( 2002) 171] and Zhu [EUR. J. Operat. Res. 154( 2004) 150] propose a buyer -seller game model that evaluate the efficiency of alternative bids with respect to the ideal target set by the buyer. We prove some theorem in the current paper about this model. The bids cannot be easily evaluated and selected, while inputs and outputs each vary in interval. In this paper, presenting a new idea for evaluating the bids with interval data, an interval will be defined for the efficiency score of each bid. And finally, a method for selecting bids by the obtained efficiency interval is presented. And, the new technique will be applied to a set of real data.