An Approach To Simplify The Super-multiindex Analytic Hiberarchy And Its Decision Application Study

According to the principle of traditional Analytic Hierarchy Process (abbreviate as AHP), the most important step of the method is to construct reasonable hierarchy. Along with the more and more research about the complicated system of people, AHP presents its shortcoming. For the difficulty of finding out random consistency index to carry out a consistency examination on the matrix when the rank of the judgment matrix is more than 9 and the difficulty of getting exact information for the expert when there are so many indexs on lower layer, the AHP hiberarchy requests that the number of the the indexs on every lower layer can't be more than 9 .However, for the complicated system problems always have a lot of influential factors, the hiberarchy can't satisfy the request about the indexs' number of 9 while set up the problem's hiberarchy.At this time, AHP usually set up the hiberarchy through deleting some factors subjectively to satisfy the request about indexs' number of 9.Obviously, this kind of hiberarchy can't guarantee it's accuracy of reflecting the objective regulation of the complicated system problem and it always result in an imprecise even false conclusion.From the research result of existing we can see that some experts have done research about how to select factors to set up a hiberarchy for the complicated system problem,but we think that these researches still didn't resolve the question about setting up a reasonable structure by the root.From the characteristics of the complicated system problem we define concept of super-multiindex hiberarchy and investigate a method to simplify the super-multiindex hiberarchy of the complicated system problem .The purpose of simplifying is to delete the important indexs which don't influence on the ranking of priority vectors on the lower layers and promote AHP's further using. The super-multiindex hiberarchy means that the number of indexs on the lower layer is more than 9. According to the concept, the decision maker no longer needs to delete some factors subjectively to satisfy the request about indexs' number of 9 but identify all possible indexs while build up the complicated system problem's hiberarchy. It can make that the hiberarchy reflect the objective regulation of problem well.Undeniably, the numerous indexs in the super-multiindex hiberarchy may confuse the decision maker's judgment and result in inaccurate informationbe. As this, we put out the method of simplifying the super-multiindex hiberarchy of the complicated system problem. It means deleting the unimportant indexs reasonablly through using the method of simplifying the super-multiindex hiberarchy .The method includes two steps——the first one is to simplify the lower index layer and the second one is to to simplify the layers above the index layer. Then we can carry out to simplify the super-multiindex hiberarchy.On the basis of setting up the hiberarchy we can find out the criteria whose indexs below are more than 9 .These indexs below are simplified objecets of the method. The author think that the most important thing of the method is find out a method to evaluate the indexs. As this, we put out a new method called pair- programs compared. Pair-programs is the combination of any two programs on the program layer of the hiberarchy .And comparison of the pair-programs means evaluating the indexs' importance based on every pair-programs. There is value changes occure to every index based on every pair-programs.The expert give every index a different preference when considered all indexs at the same time.And we define these different preferences as the different importance of the indexs between each other. We defined the ratio of preference of any two indexs below the same upper elements as the relative different importance of the indexs between each other. The author makes use of general formula forms to carry on expression to these two definitions in the text.Pair-programs is the combination of any two Through the judgement about the the different importance of the indexs ,the experts can set up matrix whose order is more than 9 about relative different importance of the indexs. If we calculate the matrix directly, it is difficult to find out random consistency index to carry out a consistency examination on the matrix what is precisely worried by AHP. As this, we put out an idea of translating the score information as basic probability assignment by introducing evidence theory. And then we can get the ranking of the different importance of every index through continuously synthesizing about these basic probability assignments.In order to translate the score information of experts as basic probability assignment reasonably, we build the basic probability assignment fuction basic on compared judgement by experts. Let the expert's judgment information as variable of the function and put in the discount of the judgement of expert as another variable.We give the seven steps of the method of simplifying the lower index layer first.Then in order to validate if the method is scientific,we use the numerical simulation analysis tool.First of all, the experts give their judge information based on simulating the original data.Then we can get the ranking of the different importance of the indexs by using the method of simplifying the lower index layer. At last,we can get the conclusion that the method is reasonably by comparing the ranking to the original data.On the basis of simplifying the lower index layer, we do some research about the upper layers' simplifying based on the upper layers' characteristic. We discuss the simplying of the upper layers in three situations.The first one is deleting some elements on the upper layer through the discussing of simplying of the lower indexs layer.In the second situation,the upper layers needn't to be simplyed because the number of the indexs on these layers always less than 9. And in the last situation,we can't do any simplying about the upper layers because all of the elements on the upper layers are very important for the structure.In order to validate the practical value of the method to simplify the super-multiindex hiberarchy of the complicated system problem,the method is applied to resolve the site optimization problems of building up new campus for××University. The result of application in the case shows that the method of simplifying the super-multiindex hiberarchy has practicability and applicability.