A new approach for deriving fuzzy global priorities in fuzzy analytic network process

This paper proposes a new approach for deriving fuzzy global priorities in fuzzy analytic network process. Due to the convergence problem in taking the limit of the fuzzy supermatrix, it is relatively difficult to generate fuzzy global priorities from fuzzy analytic network process. The presented methodology solves the convergence problem by producing a normalized fuzzy supermatrix and raising it to the limiting power based on a linear goal programming model. Consequently, the fuzzy global priorities can be extracted from the fuzzy limiting supermatrix, whose fuzzy column vectors are normalized and identical. The approach is applicable for triangular, interval and trapezoidal fuzzy cases. Finally, two examples are given. One illustrates the effectiveness of the proposed approach and the other demonstrates the use of the obtained fuzzy global priorities in reflecting the uncertainty of the order caused by fuzzy judgments of the expert.