Research On Some Problems Of The Analytic Hierarchy Process And Its Application

With the development of society, the decision problems are becoming more and more complicated. One side, the decision makers need to make decisions rapidly. The other side, they need to analyze the decision-making difficulty owing to the uncertainty of the decision-making problems. As one important constitutive part of the decision-making problem, the multi attribute decision-making problem exists widely in our life. The analytic hierarchy process (AHP) is widely used in many fields as a classical multi attribute decision-making approach. However, many theories problem haven't solved and some approaches have many shortcomings. Therefore, new approaches should be put forward. The following four sides about the AHP theories and approaches are concerned.(1) Comparison matrix consistency research. Comparison matrix consistency is the core problem in the AHP. To the consistency test of the comparison matrix, it is not enough to check its consistency ratio to test whether the comparison matrix is consistent or not. Otherwise, it should check both the basic consistency and the rank consistency of the comparison matrix. Firstly, the 1~9 scale comparison matrix is transferred into the 0~1 comparison matrix. And then, the test algorithm is put forward based on the chart theory. Secondly, two modification rules are developed to modify the rank inconsistent matrix.The existing modification approaches to modify the inconsistent comparison matrix have not considered keeping the original decision-making information. To solve this problem, two new modification models based on keeping the most information that the original comparison matrix contains are put forward.In addition, the sensitivity and consistency integration analysis approach is put forward based on the consistency analysis result of the comparison matrix.Then, the integration decision-making region which can preserve the original preference and can satisfy the consistency requirement is obtained via the suggested approach.(2) AHP theory research under the uncertainty decision-making condition.The interval numbers AHP is widely used when solving the complicated decision-making problems. However, the consistency and weights analysis are not perfectly.The notions of the local consistency and the consistency extent are introduced to measure the consistency of the interval numbers comparison matrix based on the idea of the stochastic crisp comparison matrix. Then a new model is developed to estimate the weights. Furthermore, the weights of the interval numbers complementary comparison matrix are studied. The aim of this paper is to perfect the weights theory frame of the AHP under the uncertainty decision-making condition.When solving the complicated decision-making problems, the decision maker can often obtain the incomplete pairwise comparison matrix (IPCM). The consistency and weights analysis of the incomplete pairwise comparison matrix are studied in this paper. According to the definition of stochastic crisp comparison matrix, the local consistency and local satisfactory consistency for the incomplete pairwise comparison matrix are defined. Then, a mathematical notion model is developed to test whether the IPCM is consistent or not. In addition, to solve the problem of Harker's weights method that it cannot estimate the uncertainty that the incomplete pairwise comparison matrix contains, a new weight model solved by particle swarm optimization is put forward to estimate the weight upper range and low range.The decision makers may not express their preferences correctly via the original approaches or its extensions in AHP under some uncertainty decision-making environments. In addition, information losing is inevitable when integrating multiple experts' preferences under the group. decision-making environments. To solve these problems, the comparison matrix which entries are subject to the discrete distribution is studied and the unascertained number is introduced for a pairwise comparison matrix. Moreover, the consistency concept of the unascertained numbers comparison matrix is analyzed, and two consistency indexes, the local consistency and the consistency extent are developed. According to the property of the unascertained numbers comparison matrix, two weight approaches are put forward, one is based on the rule of unascertained numbers, and the other is via the Monte Carlo simulation.(3) Combination weights based on the AHP. When solving the multi attribute decision-making problems, most approaches are involved in the attribute weights calculation. It can be divided into the subjective weights and the objective weights approaches. To make the decision-making results more...