¹School of Computer Science and Engineering, Jiangsu University of Science and Technology, Zhenjiang, China
²Institute of Computing Technology, Chinese Academy of Sciences,Beijing, China

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Abstract—It is well known that the Analytic Hierarchy Process (AHP) of Saaty is one of the most powerful approach for decision aid in solving of a multi criteria decision making (MCDM) problem. Several computing weights methods in AHP are analyzed. Based on least square method, three methods for calculating weights using the least the sum of squares of error criterion, the least the sum of error absolute value criterion and the least the error absolute value criterion are proposed. New least squares method is translated into linear system and Minimax method and absolute deviation method are translated into linear programming. New proposed methods can apply to the ranking estimation in incomplete AHP, which is very important to estimate incomplete comparisons data to have alternative’s weights. The computation methods and results are given through numerical examples. The new methods have fast convergence and smaller computational complexity.

Index Terms—analytic hierarchy process (AHP) , weights, error, linear programming, incomplete matrices.

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Cite: Shang Gao, Zaiyue Zhang, Cungen Cao, "Calculating Weights Methods in Complete Matrices and Incomplete Matrices," Journal of Software vol. 5, no. 3, pp. 304-311, 2010.