A MATRIX METHOD FOR THE FUZZY ANALYTIC NETWORK PROCESS

In this paper, the fuzzy analytic network process (FANP) is proposed. For achieving this purpose, two problems are highlighted and overcome in this paper. First, the postulate of the reciprocal matrix should be released, because this property is not satisfied in the fuzzy comparison matrix. Second, the convergent problem for raising the fuzzy supermatrix to limiting power should be appropriately handled. In this paper, we directly fuzzify Cogger and Yu's method for obtaining the fuzzy local vectors, because their method releases the postulate of the reciprocal matrix in the analytic hierarchy process (AHP). Then, we derive the particular matrix problem for obtaining the fuzzy global weight vector so that the convergent problem in a fuzzy limiting supermatrix can be overcome.