Journal of Systems Engineering and Electronics ›› 2019, Vol. 30 ›› Issue (6): 1160-1181.doi: 10.21629/JSEE.2019.06.11

• Systems Engineering • Previous Articles     Next Articles

A consistency improving method in the analytic hierarchy process based on directed circuit analysis

Shihui WU*(), Xiaodong LIU(), Zhengxin LI(), Yu ZHOU()   

  • Received:2018-08-20 Online:2019-12-20 Published:2019-12-25
  • Contact: Shihui WU E-mail:wu_s_h82@sina.com;liuxiaodong@163.com;lizhengxin_2005@163.com;zhouyu_gfkd@126.com
  • About author:WU Shihui was born in 1982. He received his M.S. and Ph.D. degrees in management science and engineering from Air Force Engineering University, Xi'an, China, in 2007 and 2010, respectively. He is currently a lecturer in Air Force Engineering University. His research interests focus on decision theory, simulation optimization and so on. E-mail: wu_s_h82@sina.com|LIU Xiaodong was born in 1966. He is currently a professor and Ph.D. student supervisor in Air Force Engineering University. His research interests focus on management of weapon equipment, weapon equipment economics and so on. E-mail: liuxiaodong@163.com|LI Zhengxin was born in 1982. He is currently a Ph.D. candidate and a lecturer in Air Force Engineering University. His research interests focus on data mining, machine learning, time series analysis and so on. E-mail: lizhengxin_2005@163.com|ZHOU Yu was born in 1983. He is currently a Ph.D. candidate and a lecturer in Air Force Engineering University. His research interests focus on test and evaluation for military equipment and so on. E-mail: zhouyu_gfkd@126.com
  • Supported by:
    the National Natural Science Foundation of China(61601501);the National Natural Science Foundation of China(61502521);This work was supported by the National Natural Science Foundation of China (61601501; 61502521)

Abstract:

Test of consistency is critical for the analytic hierarchy process (AHP) methodology. When a pairwise comparison matrix (PCM) fails the consistency test, the decision maker (DM) needs to make revisions. The state of the art focuses on changing a single entry or creating a new matrix based on the original inconsistent matrix so that the modified matrix can satisfy the consistency requirement. However, we have noticed that the reason that causes inconsistency is not only numerical inconsistency, but also logical inconsistency, which may play a more important role in the whole inconsistency. Therefore, to realize satisfactory consistency, first of all, we should change some entries that form a directed circuit to make the matrix logically consistent, and then adjust other entries within acceptable deviations to make the matrix numerically consistent while preserving most of the original comparison information. In this paper, we firstly present some definitions and theories, based on which two effective methods are provided to identify directed circuits. Four optimization models are proposed to adjust the original inconsistent matrix. Finally, illustrative examples and comparison studies show the effectiveness and feasibility of our method.

Key words: analytic hierarchy process (AHP), pairwise comparison matrix (PCM), logical inconsistency, numerical inconsistency, directed circuit