Establishing a multiple structures AHP evaluation by extending Hierarchies Consistency Analysis Y-Y Guh 1 , H-M Wee 2 and R-W Po 3 1 Graduate School of Business Administration Chung Yuan Christian University, Chung li 320, Taiwan, R.O.C. 2 Department of Industrial Engineering, Chung Yuan Christian University Chung li 320, Taiwan, R.O.C. 3 Graduate School of Technology Management, Chung Hua University Hsinchu 300, Taiwan, R.O.C Abstract The purpose of this paper is to extend the theory of Hierarchies Consistency Analysis (HCA) to establish a multiple structures evaluation model for the AHP. Traditionally, the AHP process is based on a single evaluation hierarchy, according to statistics and group decision theories, a more objective evaluation will be obtained if we can compromise several estimates. We will construct several different structure schemata for a problem to be analyzed by the AHP, and determine the weight of criteria for all levels of each structure. Finally, we use the weight consistent property and compromise process of the HCA to integrate these AHP models to obtain more objective evaluation result that is as free as possible from structure bias. The multiple structures of AHP model can be regarded as a generalized AHP model; hence the AHP model based on only one hierarchy structure is a special instance of the proposed method. Keywords : AHP 、 Hierarchical Weighting 、 Group Decision、Evaluation、Multiple Attribute 1. Introduction AHP is a multiple-criterion decision making methodology that was developed by Saaty in 1971[1, 2, 3]. For years, the practical nature of the method, suitable for solving complicated and elusive evaluation problems, has been applied in highly diverse fields such as resource allocation, performance measurement, alternative selection, project evaluation and public policy analysis. The AHP process begins with setting up an evaluation hierarchy structure for the problem based upon interrelated criteria drawn from the problem itself. Next, a matrix of pair-wise comparisons of the interrelated criteria for each clusters of the hierarchy is made by the Decision Maker (DM). Finally, the relative weight of criteria is obtained by utilizing the eigenvalue method. With the acquisition of the largest eigenvalue from the comparison matrix, a consistency index is constructed to measure the degree of rationality of the DM in making pair-wise comparisons. The HCA method, developed by Guh in 1996 [4, 5, 6], considers the analysis of an evaluation problem. The DM must, therefore, create various evaluation hierarchy structures based on different viewpoints. According to the consistent weight property, the HCA methodology integrates these different hierarchy structures to obtain compromised weight for all levels and for all hierarchy structures. Taking the evaluation of faculty performance as an example will show the problem more succinctly. If the evaluation criteria of lowest level is divided into the quality of teaching(x 11 ), quantity of teaching(x 12 ), quality of research(x 21 ), quantity of research(x 22 ), quality of service(x 31 ) and quantity of service(x 32 ), then each of the four instances may be appropriate as an evaluation structure. (See Figure 1). Performance Quantity X 11 X 12 Performance Teaching Service Research Non-teachin g X 11 Quality X 12 X 21 X 22 X 31 X 32 X 21 X 22 X 31 X 32 Performance Non-service Service X 11 Performance Teaching Service Research X 11 X 12 X 21 X 22 X 31 X 32 X 12 X 21 X 22 X 31 X 32 Figure 1 Multiple structures model of HCA