Computing Relative weights in AHP and Ranked Units in the Presence of Large Dimensionality of data set based on Orthogonal Gram Schmidt Technique

Background: The purpose of this paper is to determine the local weights in Analytical Hierarchy Process (AHP) by using the maximum variance method based on Gram Schmidt technique in the presence of large dimensionality of data set. This method was utilized for reducing the dimension in data with large dimensionality. In order to gain significant efficiency, the condition should be satisfied (n is the number of Decision Making Units, m is the number of inputs and s is the number of outputs). Since in most presented models in AHP using Data Envelopment Analysis (DEA) experimental principle is not satisfied and have long computing problems, in this paper a new method will be proposed which makes the condition true and reduced the data as well as reducing the dimensions. Also, by reducing the set of performance indicators we will be able to rank decision making units.