CONSISTENCY IMPROVING MODELS AND ALGORITHMS IN THE ANALYTICAL HIERARCHY PROCESS

摘要

The modification to the inconsistent comparison matrix (ICM) in the Analytical Hierarchy Process (AHP) is concerned. Two modification optimization models and algorithms are put forward according to two preservation criteria, which can decrease the consistency ratio (CR), can offer more possible suggestions for a decision maker (DM), importantly can preserve most information that the original matrix contains. The idea of the first model is the departure should be limited between the improved matrix and the original matrix. To one entry, let it extend some distance towards right and left directions respectively, then, the original matrix will be converted into the interval number comparison matrix after all entries are extended. The matrix with the minimum CR inside the interval number comparison matrix can be taken as the improved matrix. Based on the above-mentioned idea, a computation model is put forward. The model is a nonlinear program and the genetic algorithm is designed. The second model focuses on the matrix contains the Unusual and False Observations (UFO) entry. In this case, the key problem is to find the UFO entry. To solve this problem, the relationship between the CR and one given entry is analyzed. Next, a modification algorithm is developed.