The Grey Analytic Hierarshy Process-ahp

The traditional AHP processing data is the so-called "point" data or "rigidity" data. However, the real social economic system is a flexible system, the studying issue is also a flexible issue, so describing this kind of issue by the traditional mathematics' method may not be effective. Therefore, the mentioned AHP is a decision-making judgment under this circumstance. As an expert, the judgment he gave out should include the coincident information he wanted to express. That is to say, when the required information is clear enough, the expert's more confirming and coincident decision-making is a numerical value in the field of his judgments. So the introduction of the concept of gray-element in gray-system will benefit the further discussion of the coincident information.By the studying of coincident information in the gray judgment matrix, and by using some graph's essential theories, this issue brings forward the concepts of estimating coincidence, coincidence, equivalence gray judgment matrix, gray-weight vector, ect. It also gives out and proves several sufficiency and necessary conditions of the gray judgment matrix existing estimating coincidence or coincidence, and gives out a calculation of judging the gray judgment matrix having estimating coincidence or not, furthermore, we can get the equivalence coincidence gray judgment matrix in its field through this calculation.For the coincidence gray judgment matrix, this issue presents some conditions in judging whether two cases exist rank-quantities, and gives a method to calculate the gray weight-vector under a single rule. When the sort of some schemes cannot be given according to these judgments and conditions, we advance a whitened-method, which can entirely reflect the experts' affection, and this will have a whitened result of gray sort, which can feed back to experts and help them to make a decision.In respect that insufficiencies those judgment matrix decision-makers filled and excessive making cases (the first called insufficient judgment and second called the mass decision.) Therefore, the issue also makes studying on the grey insufficient judgment matrix, pointing out acceptable concepts and presenting management of them; when comes to the grey mass decision, it tells the sort calculation methods and provides compound sort programs for the multi-level configuration.In the end, the issue discusses the order-keeping conditions of reducing elements and introductions of new elements under the maintenance of the original schemes.