Interval weight vector of judgment matrix and ranking of the alternatives

When a judgment matrix is inconsistent in the analytic hierarchy process, the weight vector educed from it by traditional methods such as eigenvalue method can only reflect an approximate sort result. Sometimes the result may be even error. Aimed at this problem, an interval weight vector is obtained from the judgment matrix through a linear programming model. As a result, the solution becomes more flexible. In the following an order relation between interval numbers is proposed which reflects the decision maker's satisfaction with the order. Based on this a full ranking is made on all the alternatives. Finally an example is given.