Detecting and adjusting ordinal and cardinal inconsistencies through a graphical and optimal approach in analytic hierarchy process 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 suggested 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.