Using Gower Plots and Decision Balls to rank alternatives involving inconsistent preferences

Ranking alternatives involving inconsistent preferences is one of the most important topics in decision-making. Determining how to assist decision makers in understanding the decision context and adjusting inconsistencies in judgment are two important issues in ranking alternatives. This study proposes a visualization approach which will assist decision makers in ranking alternatives involving inconsistent preferences. Gower Plots are adopted to detect alternatives involving inconsistencies. An adjusting model is developed to provide suggestions for simultaneously improving ordinal and cardinal inconsistencies. A Decision Ball model is applied to visualize the decision context. By a graphical and interactive interface, decision makers can iteratively detect inconsistencies, choose the preferred way to adjust inconsistencies, observe relationships among alternatives, and then rank alternatives.