On the analytic hierarchy process with normalized interval weight vector
Junpeng Guo · Systems engineering and electronics · 2004
When a judgment matrix in the analytic hierarchy process (AHP) is inconsistent, the weight vector deduced from it by traditional methods can only reflect an approximate sorting result. Sometimes the result may be even wrong. Aimed at this problem, the original AHP is extended by obtaining normalized interval weights which are more flexible than the old ones. Firstly a linear programming model is set up by which an interval weight vector of a judgment matrix can be achieved. Then on the basis of analyzing the possible errors in computing combined weights simply by interval operation, another linear programming model is built. By this model, from bottom to top the combined interval weight of the alternative relative to each criterion is gained. As a result, the solution is more rational. Finally an example is given.