Improvement Of The Analytic Hierarchy Process Method

The Analytic Hierarchy Process (AHP) due to Thomas L. Saaty ~[1] is a very useful method for multi-criteria decision.It is applied to many practical multi-criteria decision problem in many fields, such as the economic analysis, environment, maintenance strategy, management, etc~ [2,3,4] Complex problem is decomposed into criteria, sub-criteria and alternatives from which the choice is made ~[5] . Then people express their preference by setting a matrix A of pairwise comparisons for the set of criteria or alternatives with respect to a single criterion. For n alternatives we have a square matrix of order n on the scale of 1 - 9,1/9 - 1 which is called a comparison matrix or judgement matrix, whose element a_ij estimates the dominance(weight)of alternative / over j. Obviously the matrix A is a positive reciprocal matrix.Many authors proposed various methods to study the consistency of the matrix A. Almost all known methods require the use of consistency test and modular consistency test ~[6,7,8] which is hard and complicated to deal with, and doesn't necessarily give the best judgment of consistency [7,9] During the decision process by AHP, if the decision-maker is not consistent, then pairwise comparison judgments of the relative importance of the elements have to be done again, at each level of the hierarchy . Under this situation, since AHP is applied popularly in multi-criteria decision problems, the decision-maker will spend a lot of time and money. Moreover, the decision-maker perhaps add some subjective factors to the pair-wise comparison judgments to make the matrix consistent enough. Obviously, the decision is no more optimal. If the decision-maker suddenly becomes incapacitated or even pass away before making his judgement, this will disrupt the whole process since others may not be able to continue from where he stopped.How will they deduce the optimal decision from the decision-maker's previous judgments? We know that the relative judgment scale is restricted, in AHP ,from 1/9, 1/8,1, 2,... 9. Not in every situation can it produce a perfectly consistent comparison matrix.In this thesis,supposing that the decision-maker is rational, we offer a new , valid and reasonable decision method to deal with the situation where the decision-maker is not consistent enough, and we do not change his mind. The method, doesn't require the consistency test ,includes all the judgement preferences of the decision- maker, is easier to deal with and the decision process can be carried out successfully in any case.This thesis is organized as follows: First, the AHP is described in sufficient details so that the reader can understand the motivation of this technique, second we present our method, third we give an example to show the use of this method and finally we give a conclusion.