Geometric mean and super-transitive approximate method of AHP group decision

The judgment matrix combination problem of analytic hierarchy process(AHP) group decision making is studied. Firstly,it is proved that geometric mean matrix of m judgment matrices is a judgment matrix,and the weighted geometric mean matrix of m judgment matrices is a judgment matrix too.After that,a simplified over super-transitive approximate method in AHP decision making and a geometric mean over super-transitive approximate method in AHP group decision making are proposed.The method does not require a consistency check,while maintaining the original opinion of the experts. Finally,an example illustrates the effectiveness and feasibility of the proposed method.