Discussion And Application Of Rank Reversal Phenomenon In Analytic Hierarchy Process And Grey Relational Analysis

At present, the Analytic Hierarchy Process and Gray Relational Analysis methodis widely used in many areas of corporate, economic, technological, management andgovernment decision-making, educational planning, resource allocation, and it hassolved many practical problems. Application of these two methods, decision-makersthrough a number of levels and a number of indicators will simplify complex issues,the Analytic Hierarchy Process can be drawn to the weight of the different options, theGray Relational Analysis method can calculate the correlation of the program with thereference sequence, to provide evidence for the selection of the best solutions.Although the Analytic Hierarchy Process and Gray Relational Analysis method toanalyze and solve problems both simply and practically, but they still have someproblems in the evaluation. Using AHP evaluation process, policy makers often need tomake pair wise comparison of decision-making programs and to structure judgmentmatrix, while in practical problems, the decision-making program may increase ordecrease, which changes the weight value of each program on the decision-makinggoals which may change the order of weight value producing the reverse problem. Inthe evaluation process using GRA, when making data dimensionless with extremummethod, as traditional Gray Relational Analysis to select the maximum and minimumvalues from the comparison of series, when removing a program, this program maycontain the previous selected the maximum or minimum value, the dimensionlessvalue of the size of the order will lead to the data changes, it is possible to make thecorrelation coefficient of the various indicators of the original program change, therelevance of the program will change the sort of the affected program, generate reversephenomenon. the article described primarily as follows:(1) Make further research into isotonic issues of the analytic hierarchy process onthe basis of previous, proposed a new approach to a treatment of program weight,make sort of programs by the introduction of the dissatisfaction of the program to solvethe reverse problem of the analytic hierarchy process in the evaluation, and eliminate the reverse phenomenon.(2) Apply the improved extreme value method and introduce the minimum andmaximum limits to the data dimensionless for the reverse problem emerged in theevaluation of the gray relational analysis, to avoid the order change of datadimensionless value caused by the remove of the previously selected maximum or theminimum included in the program, so the reverse problem is solved, the reversephenomenon is eliminated, and the decision analysis is more reasonable.