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In ambiguous decision domain, interval numbers are employed to evaluate the overall value of alternatives (e.g., the faculty candidates) due to the inherent problems related to the uncertainty of the multiple attribute decision making (MADM). However, it is uneasy to compare interval numbers of different alternatives with multiple attributes. In current approaches, to rank and select the faculty candidates, some superiority possibility information will lose in the process of transforming interval numbers to crisp values. In order to overcome the shortcomings of Bryson and Mobolurinpsila approach, a new approach is proposed, in which the weights of attributes are determined by maximizing the weighted distance among the alternatives, hereafter the maximum intervals for the overall values of every alternative are calculated, and the superiority possibility among them are also calculated for assessing the faculty candidates (alternatives).