An assessment of the prominence and total engagement metrics for ranking interdependent attributes in DEMATEL and WINGS

• Assess the prominence and total engagement metrics in DEMATEL and WINGS. • Consider various interdependency scenarios among the attributes. • Show the insensitivity of the total engagement/prominence metrics to the level and direction of influence among attributes. • Demonstrate the inability of the total engagement metric to distinguish between most and least influential attributes. • Exhibit the sensitivity of the total impact metric to the level and direction of influence among attributes. A weight vector is assigned to the attributes in multiple-attribute decision-making to show their relative importance. The interdependencies among the attributes often influence this weight vector. The decision-making trial and evaluation laboratory (DEMATEL) and weighted influence non-linear gauge system (WINGS) are among those methods that consider these interdependencies. These methods require matrix manipulation with several metrics to evaluate interdependencies. This study investigates the potential irregularities within the metrics employed by these two methods for weighing criteria. It examines these metrics and analyzes their sensitivity to the direction and the level of influence among attributes. We provide several numerical examples and mathematical analyses to evaluate their consistency by comparing the expected outcomes with the outcomes of the metrics. Although the metrics are expected to assign higher importance to the more influencing criteria, the total engagement/prominence metric is not sensitive to the direction and level of influence among attributes. We conclude these metrics are inconsistent and can not be used reliably as a composite indicator. In contrast, we show that the total impact factor reflects both the direction and the level of influence and is a reliable choice for this purpose.