On a Revised analytic Network process(ANP) for Avoiding Irrational rank Reversal - A Revised Normalization Procedure and Calculation Method -
Kouichi Taji, Yousuke Sagayama, Hiroyuki Tamura · ISAHP proceedings · 1999
In this paper we propose a revised ANP by using the aspiration level of decision maker.In the ordinary ANP, the irrational rank reversal of alternatives may arise when we add another alternative or extract an alternative.Such irrational rank reversal is caused by the ordinary normalization procedure in which the weights of alternatives sum to 1.To avoid this, we introduce the revised normalization procedure in which the aspiration level determined by the decision maker for each criterion equals to 1.But since, by using this normalization, the resulting supermatrix may not be a stochastic matrix, the weight vector doesn't converge to a constant vector when the power method is used.So, we also propose the calculation method for relative importance based on the Perron-Frobenius theorem.A simple example shows that the irrational rank reversal is avoided in the proposed AN?.