Optimization Model Of Uncertain Hierarchy Analysis

In our daily life, we often have to face numerous multi-objective selection prob-lems. For example, to select a cloth, we need to consider it’s price, character,com-fortability, and so on; to determine a hydropower site, government should consider economic factors, environmental factors and so on. These are optimization problems. This thesis mainly investigates how to select the best project from some candidate selections. Based on uncertainty theory, this paper proposes two methods on account of empirical data of experts:one is uncertain optimization based on expected value, the other is uncertain optimization based on optimistic value.The system is divided into two levels in both of two methods. In the first level, we can get the experts’uncertainty distributions through experts’empirical data, and then obtain expected values (optimistic values or pessimistic values) for every factor. According to expected values (optimistic values or pessimistic values), we will get an imaginary excellent project for the first level. We obtain the difference between each project and the imaginary excellent project through calculating expected value distances (optimistic value distance), and then select the project with the minimum difference as the excellent project for the first level.In the second level, we make a matrix as the system’s distance matrix, whose elements are the distances of each project with the excellent project in each subsystem. We make a system-distance vector whose elements are the minimum distances of each project with the excellent project in each subsystem. Comparing all project’s distance with the system-distance vector, we will select project with the minimum difference project as the optimal project. Finally, examples are proposed as applications of our methods.