Detecting and adjusting ordinal and cardinal inconsistencies through a graphical and optimal approach in AHP models

An AHP model suffering from significant cardinal or/and ordinal inconsistencies in its preference matrix is difficult to rank rationally the alternatives. This study proposes an iterative method to assist a decision maker to detect/adjust inconsistencies and to represent his/her judgments properly. A Gower plot is first used to detect ordinal and cardinal inconsistencies. Two optimization models are then constructed to provide suggeted adjustments upon the request of the decision maker. By examining the Gower plots and numerical suggestions, the decision maker may revise iteratively the preference ratios to improve inconsistencies until all alternatives are ranked.

[1]  Luis G. Vargas,et al.  Comparison of eigenvalue, logarithmic least squares and least squares methods in estimating ratios , 1984 .

[2]  Thomas L. Saaty,et al.  Decision making with dependence and feedback : the analytic network process : the organization and prioritization of complexity , 1996 .

[3]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[4]  Zeshui Xu,et al.  A consistency improving method in the analytic hierarchy process , 1999, Eur. J. Oper. Res..

[5]  Thomas L. Saaty,et al.  Decision-making with the AHP: Why is the principal eigenvector necessary , 2003, Eur. J. Oper. Res..

[6]  C. Eckart,et al.  The approximation of one matrix by another of lower rank , 1936 .

[7]  T. L. Saaty.  A Scaling Method for Priorities in Hierarchical Structures , 1977 .

[8]  Peter P. Wakker,et al.  On solving intransitivities in repeated pairwise choices , 1995 .

[9]  X. Zeshui,et al.  A consistency improving method in the analytic hierarchy process , 1999, Eur. J. Oper. Res..

[10]  R E Jensen.  Aggregation (Composition) Schema For Eigenvector Scaling Of Criteria Priorities In Hierarchical Structures. , 1983, Multivariate behavioral research.

[11]  Christian Genest,et al.  A graphical analysis of ratio-scaled paired comparison data , 1996 .

[12]  T. Saaty,et al.  The Analytic Hierarchy Process , 1985 .

[13]  C. Genest,et al.  A statistical look at Saaty's method of estimating pairwise preferences expressed on a ratio scale , 1994 .

[14]  D. DeTurck.  THE APPROACH TO CONSISTENCY IN THE ANALYTIC HIERARCHY PROCESS , 1987 .

[15]  Oleg I. Larichev,et al.  ZAPROS-LM — A method and system for ordering multiattribute alternatives , 1995 .

[16]  Stan Lipovetsky,et al.  Robust estimation of priorities in the AHP , 2002, Eur. J. Oper. Res..

[17]  R. E. Jensen.  An alternative scaling method for priorities in hierarchical structures , 1984 .

[18]  J. Barra,et al.  Recent Developments in Statistics , 1978 .