A new approach of revising unstable data in the analytic network process by Bayes theorem

A new approach of revising unstable data in the analytic network process by Bayes theorem

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Article ID: iaor20053248
Country: Japan
Volume: 48
Issue: 1
Start Page Number: 24
End Page Number: 40
Publication Date: Mar 2005
Journal: Journal of the Operations Research Society of Japan
Authors: ,
Keywords: decision: studies, programming: fractional, analytic hierarchy process
Abstract:

In the typical type of ANP with a matrix U evaluating alternatives by criteria and a matrix W evaluating criteria by alternatives in the so-called supermatrix S, W is often said to be unstable. Here, we propose a method to revise W into a stable Ŵ and to calculate the weights of criteria and alternatives at the same time under the revised supermatrix Ŝ. Our method is formulated as an optimization problem based on Bayes theorem which T.L. Saaty claimed to be included in ANP scheme. Concurrent Convergence method developed by Kinoshita and Nakanishi also intends to be correct W, but this method includes some contradictions. We prove that our method has no such contradiction. We introduce some eigenvalue problems, which give a lower bound of our optimal value and their special cases coincide with our problem. Furthermore, we clear what perturbations of W preserve weights of criteria and alternatives to be invariant under the concept of inactive alternatives.

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